diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s3/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l2-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s3/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..56ad4bec395334d8a748614f9e4c117a2f45b7b4
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s3/environment/instance.json
@@ -0,0 +1 @@
+{"N": 106, "t": 30, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s3/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l2-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f9848cb6502c7576b66a66141097812e4f679002
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [360, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 36, 36, 36, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 41, 41, 42, 43, 43, 46, 46, 46, 46, 47, 47, 49, 49, 49, 49, 49, 49, 49, 49, 53, 53, 58, 58, 58, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/check.py
@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..56ad4bec395334d8a748614f9e4c117a2f45b7b4
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/instance.json
@@ -0,0 +1 @@
+{"N": 106, "t": 30, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s4/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l2-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s4/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a35a8bd1e2e18e095df773a460f65fe60770edeb
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s4/environment/instance.json
@@ -0,0 +1 @@
+{"N": 110, "t": 31, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s4/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l2-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f4cb7c92036cca2d95283e49f1daa944fdba430b
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [186, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 43, 43, 46, 46, 46, 46, 47, 47, 53, 53, 58, 58, 58, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/check.py
@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a35a8bd1e2e18e095df773a460f65fe60770edeb
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/instance.json
@@ -0,0 +1 @@
+{"N": 110, "t": 31, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p38-factorial-factors-l5-s7/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l5-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l5-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p38-factorial-factors-l5-s7/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l5-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d15c3c523d7a19a4cf3ff0305318dc17a706a43
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l5-s7/environment/instance.json
@@ -0,0 +1 @@
+{"N": 3059, "t": 980, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l5-s7/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l5-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3fa9dbe3c182a0085173685b771e0a7122b1f079
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l5-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [9800, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 982, 982, 982, 982, 982, 982, 983, 983, 983, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 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1741, 1747, 1753, 1754, 1754, 1754, 1759, 1762, 1762, 1762, 1766, 1766, 1766, 1774, 1774, 1774, 1777, 1783, 1787, 1789, 1801, 1811, 1814, 1814, 1814, 1822, 1822, 1822, 1823, 1831, 1838, 1838, 1838, 1847, 1858, 1858, 1858, 1861, 1867, 1871, 1873, 1874, 1874, 1874, 1877, 1879, 1882, 1882, 1882, 1889, 1894, 1894, 1894, 1901, 1906, 1906, 1906, 1907, 1913, 1931, 1933, 1934, 1934, 1934, 1942, 1942, 1942, 1949, 1951, 1954, 1954, 1954, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/check.py
@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}
diff --git a/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d15c3c523d7a19a4cf3ff0305318dc17a706a43
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/instance.json
@@ -0,0 +1 @@
+{"N": 3059, "t": 980, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l5-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s2/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s2/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..70925007a9c97800c3eeae6cdcf577fd54f2c569
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"N": 6230, "t": 2021, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s2/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2c8c76c0463f1551596c55c3837508caaf360db6
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [94987, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 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2841, 2841, 2841, 2841, 2841, 2843, 2843, 2846, 2846, 2846, 2846, 2851, 2851, 2854, 2854, 2854, 2854, 2857, 2857, 2858, 2858, 2858, 2858, 2859, 2859, 2859, 2859, 2859, 2859, 2861, 2861, 2866, 2866, 2866, 2866, 2878, 2878, 2878, 2878, 2879, 2879, 2887, 2887, 2894, 2894, 2894, 2894, 2897, 2897, 2901, 2901, 2901, 2901, 2901, 2901, 2902, 2902, 2902, 2902, 2903, 2903, 2906, 2906, 2906, 2906, 2909, 2909, 2913, 2913, 2913, 2913, 2913, 2913, 2917, 2917, 2918, 2918, 2918, 2918, 2927, 2927, 2931, 2931, 2931, 2931, 2931, 2931, 2939, 2939, 2942, 2942, 2942, 2942, 2949, 2949, 2949, 2949, 2949, 2949, 2953, 2953, 2957, 2957, 2962, 2962, 2962, 2962, 2963, 2963, 2966, 2966, 2966, 2966, 2969, 2969, 2971, 2971, 2973, 2973, 2973, 2973, 2973, 2973, 2974, 2974, 2974, 2974, 2978, 2978, 2978, 2978, 2986, 2986, 2986, 2986, 2991, 2991, 2991, 2991, 2991, 2991, 2998, 2998, 2998, 2998, 2999, 2999, 3001, 3001, 3011, 3011, 3019, 3019, 3022, 3022, 3022, 3022, 3023, 3023, 3027, 3027, 3027, 3027, 3027, 3027, 3037, 3037, 3041, 3041, 3046, 3046, 3046, 3046, 3049, 3049, 3061, 3061, 3062, 3062, 3062, 3062, 3067, 3067, 3079, 3079, 3083, 3083, 3086, 3086, 3086, 3086, 3089, 3089, 3098, 3098, 3098, 3098, 3106, 3106, 3106, 3106, 3109, 3109, 3118, 3118, 3118, 3119, 3121, 3134, 3134, 3134, 3137, 3142, 3142, 3142, 3158, 3158, 3158, 3163, 3166, 3166, 3166, 3167, 3169, 3181, 3187, 3191, 3194, 3194, 3194, 3202, 3202, 3202, 3203, 3209, 3214, 3214, 3214, 3217, 3218, 3218, 3218, 3221, 3226, 3226, 3226, 3229, 3238, 3238, 3238, 3242, 3242, 3242, 3251, 3253, 3254, 3254, 3254, 3257, 3259, 3271, 3274, 3274, 3274, 3299, 3301, 3307, 3313, 3314, 3314, 3314, 3319, 3323, 3326, 3326, 3326, 3329, 3331, 3334, 3334, 3334, 3338, 3338, 3338, 3343, 3347, 3359, 3361, 3371, 3373, 3386, 3386, 3386, 3389, 3391, 3394, 3394, 3394, 3398, 3398, 3398, 3407, 3413, 3418, 3418, 3418, 3433, 3442, 3442, 3442, 3446, 3446, 3446, 3449, 3457, 3461, 3463, 3466, 3466, 3466, 3467, 3469, 3482, 3482, 3482, 3491, 3494, 3494, 3494, 3499, 3506, 3506, 3506, 3511, 3517, 3518, 3518, 3518, 3527, 3529, 3533, 3539, 3541, 3547, 3554, 3554, 3554, 3557, 3559, 3566, 3566, 3566, 3571, 3574, 3574, 3574, 3578, 3578, 3578, 3581, 3583, 3593, 3602, 3602, 3602, 3607, 3613, 3617, 3622, 3622, 3622, 3623, 3631, 3637, 3643, 3646, 3646, 3646, 3659, 3662, 3662, 3662, 3671, 3673, 3677, 3691, 3694, 3694, 3694, 3697, 3701, 3709, 3719, 3722, 3722, 3722, 3727, 3733, 3734, 3734, 3734, 3739, 3742, 3742, 3742, 3746, 3746, 3746, 3754, 3754, 3754, 3758, 3758, 3758, 3761, 3767, 3769, 3778, 3778, 3778, 3779, 3793, 3797, 3802, 3802, 3802, 3803, 3814, 3814, 3814, 3821, 3823, 3826, 3826, 3826, 3833, 3847, 3851, 3853, 3862, 3862, 3862, 3863, 3866, 3866, 3866, 3877, 3881, 3889, 3898, 3898, 3898, 3902, 3902, 3902, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3946, 3946, 3946, 3947, 3958, 3958, 3958, 3967, 3974, 3974, 3974, 3986, 3986, 3986, 3989, 3994, 3994, 3994, 3998, 3998, 3998, 4001, 4003, 4006, 4006, 4006, 4007, 4013, 4019, 4021, 4022, 4022, 4022, 4027, 4034, 4034, 4034, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/check.py
@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..70925007a9c97800c3eeae6cdcf577fd54f2c569
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"N": 6230, "t": 2021, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/Dockerfile b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..960a74d3d868c28944cc23f1a355e8ef54063fb1
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"N": 54, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l1-s4/solution/solve.sh b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..64edc60b2777c8ab206ef2453c453061679e49f0
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/check.py b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..87e15b242f211059193ba122baecdee9add99130
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/check.py
@@ -0,0 +1,38 @@
+"""Erdos squarefree problem (AlphaEvolve problem 52): A in [1, N], |A| >= t, ab+1 NOT squarefree for all a, b in A
+(a = b included). The repo's problem page says "square-free"; the notebook and the Erdos problem ask for
+"never squarefree", which is what we check. Exact: for every pair we find a prime p with p^2 | ab+1."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _primes(n):
+    s = np.ones(n + 1, dtype=bool)
+    s[:2] = False
+    for i in range(2, int(n ** .5) + 1):
+        if s[i]:
+            s[i * i::i] = False
+    return np.nonzero(s)[0]
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    a = ans.get("A")
+    if not isinstance(a, list) or not (t <= len(a) <= 2 * t + 20):
+        raise Invalid(f"A must be a list of {t}..{2 * t + 20} integers")
+    int_list(a, None, 1, n, "A")
+    if len(set(a)) != len(a):
+        raise Invalid("A must consist of distinct integers")
+    x = np.array(sorted(a), dtype=np.int64)
+    iu, ju = np.triu_indices(len(x))
+    va, vb = x[iu], x[ju]
+    left = np.ones(len(iu), dtype=bool)  # pairs without a square divisor found yet
+    for p in _primes(int((n * n + 1) ** .5) + 1):
+        q = int(p) * int(p)
+        idx = np.nonzero(left)[0]
+        hit = ((va[idx] % q) * (vb[idx] % q) + 1) % q == 0
+        left[idx[hit]] = False
+        if not left.any():
+            return None, {"size": len(a)}
+    k = int(np.nonzero(left)[0][0])
+    raise Invalid(f"{int(va[k])}*{int(vb[k])}+1 = {int(va[k]) * int(vb[k]) + 1} is squarefree")
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..960a74d3d868c28944cc23f1a355e8ef54063fb1
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"N": 54, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/run.py b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/test.sh b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/Dockerfile b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..00760d94b202f144604565e7dc4930ce89f11187
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"N": 124, "t": 5, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s1/solution/solve.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b6c050b7f1a69fce328d246ba66a8611e0c1111e
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32, 57, 82, 107]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/check.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..87e15b242f211059193ba122baecdee9add99130
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/check.py
@@ -0,0 +1,38 @@
+"""Erdos squarefree problem (AlphaEvolve problem 52): A in [1, N], |A| >= t, ab+1 NOT squarefree for all a, b in A
+(a = b included). The repo's problem page says "square-free"; the notebook and the Erdos problem ask for
+"never squarefree", which is what we check. Exact: for every pair we find a prime p with p^2 | ab+1."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _primes(n):
+    s = np.ones(n + 1, dtype=bool)
+    s[:2] = False
+    for i in range(2, int(n ** .5) + 1):
+        if s[i]:
+            s[i * i::i] = False
+    return np.nonzero(s)[0]
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    a = ans.get("A")
+    if not isinstance(a, list) or not (t <= len(a) <= 2 * t + 20):
+        raise Invalid(f"A must be a list of {t}..{2 * t + 20} integers")
+    int_list(a, None, 1, n, "A")
+    if len(set(a)) != len(a):
+        raise Invalid("A must consist of distinct integers")
+    x = np.array(sorted(a), dtype=np.int64)
+    iu, ju = np.triu_indices(len(x))
+    va, vb = x[iu], x[ju]
+    left = np.ones(len(iu), dtype=bool)  # pairs without a square divisor found yet
+    for p in _primes(int((n * n + 1) ** .5) + 1):
+        q = int(p) * int(p)
+        idx = np.nonzero(left)[0]
+        hit = ((va[idx] % q) * (vb[idx] % q) + 1) % q == 0
+        left[idx[hit]] = False
+        if not left.any():
+            return None, {"size": len(a)}
+    k = int(np.nonzero(left)[0][0])
+    raise Invalid(f"{int(va[k])}*{int(vb[k])}+1 = {int(va[k]) * int(vb[k]) + 1} is squarefree")
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..00760d94b202f144604565e7dc4930ce89f11187
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"N": 124, "t": 5, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/run.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/test.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/Dockerfile b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..84d0415137ece4c4f44758ea7a688fe697ca106d
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"N": 207, "t": 9, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s8/solution/solve.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..33f0b9274cfe2a3c82f15e9f907733e9551af897
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32, 57, 82, 107, 132, 157, 182, 207]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/check.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..87e15b242f211059193ba122baecdee9add99130
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/check.py
@@ -0,0 +1,38 @@
+"""Erdos squarefree problem (AlphaEvolve problem 52): A in [1, N], |A| >= t, ab+1 NOT squarefree for all a, b in A
+(a = b included). The repo's problem page says "square-free"; the notebook and the Erdos problem ask for
+"never squarefree", which is what we check. Exact: for every pair we find a prime p with p^2 | ab+1."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _primes(n):
+    s = np.ones(n + 1, dtype=bool)
+    s[:2] = False
+    for i in range(2, int(n ** .5) + 1):
+        if s[i]:
+            s[i * i::i] = False
+    return np.nonzero(s)[0]
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    a = ans.get("A")
+    if not isinstance(a, list) or not (t <= len(a) <= 2 * t + 20):
+        raise Invalid(f"A must be a list of {t}..{2 * t + 20} integers")
+    int_list(a, None, 1, n, "A")
+    if len(set(a)) != len(a):
+        raise Invalid("A must consist of distinct integers")
+    x = np.array(sorted(a), dtype=np.int64)
+    iu, ju = np.triu_indices(len(x))
+    va, vb = x[iu], x[ju]
+    left = np.ones(len(iu), dtype=bool)  # pairs without a square divisor found yet
+    for p in _primes(int((n * n + 1) ** .5) + 1):
+        q = int(p) * int(p)
+        idx = np.nonzero(left)[0]
+        hit = ((va[idx] % q) * (vb[idx] % q) + 1) % q == 0
+        left[idx[hit]] = False
+        if not left.any():
+            return None, {"size": len(a)}
+    k = int(np.nonzero(left)[0][0])
+    raise Invalid(f"{int(va[k])}*{int(vb[k])}+1 = {int(va[k]) * int(vb[k]) + 1} is squarefree")
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..84d0415137ece4c4f44758ea7a688fe697ca106d
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"N": 207, "t": 9, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/run.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/test.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/environment/Dockerfile b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/environment/instance.json b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..42f09e9808ccb7e224be04f87b669a6fe11767d3
--- /dev/null
+++ b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 9, "max_tiles": 12, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/solution/solve.sh b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fb58bceba7e9a3bb727c133976204fb519d203ea
--- /dev/null
+++ b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"tiles": [[0, 0, 3, 2], [0, 3, 1, 6], [1, 2, 3, 3], [1, 6, 1, 3], [2, 5, 3, 3], [3, 0, 3, 1], [3, 8, 6, 1], [4, 1, 3, 3], [5, 4, 3, 3], [6, 7, 3, 1], [7, 0, 2, 3], [8, 3, 1, 3]]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/check.py b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..401de49cfa895e6f1c47b996fa5e8bdc8fc609e4
--- /dev/null
+++ b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/check.py
@@ -0,0 +1,24 @@
+"""IMO 2025 Problem 6 variant (AlphaEvolve problem 65): at most T rectangular tiles on an n x n grid, no overlaps,
+every row and every column has exactly one uncovered unit square."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, cap = inst["n"], inst["max_tiles"]
+    tiles = ans.get("tiles")
+    if not isinstance(tiles, list) or not (1 <= len(tiles) <= cap):
+        raise Invalid(f"tiles must be a list of 1..{cap} [row, col, height, width] entries")
+    cover = np.zeros((n, n), dtype=np.int32)
+    for t in tiles:
+        r, c, h, w = int_list(t, 4, 0, n, "tile")
+        if h < 1 or w < 1 or r + h > n or c + w > n:
+            raise Invalid(f"tile {t} is empty or leaves the grid")
+        cover[r:r + h, c:c + w] += 1
+    if cover.max() > 1:
+        raise Invalid("tiles overlap")
+    free = cover == 0
+    if not (free.sum(axis=1) == 1).all() or not (free.sum(axis=0) == 1).all():
+        raise Invalid("some row or column does not have exactly one uncovered square")
+    return None, {"tiles": len(tiles)}
diff --git a/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/instance.json b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..42f09e9808ccb7e224be04f87b669a6fe11767d3
--- /dev/null
+++ b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 9, "max_tiles": 12, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/run.py b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/test.sh b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-all-interval-l1-s1/environment/Dockerfile b/tasks/construct-mc-all-interval-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l1-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-all-interval-l1-s1/environment/instance.json b/tasks/construct-mc-all-interval-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f9a1095199b5b913d326c0c19329b93273d37211
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 4, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l1-s1/solution/solve.sh b/tasks/construct-mc-all-interval-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b90d403c3ad5b2848eb0e461b9dbec719ebb3b57
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l1-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 3, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-all-interval-l1-s1/tests/check.py b/tasks/construct-mc-all-interval-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e39eec264b6422a47e35921b8cdbe1fa1748307
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l1-s1/tests/check.py
@@ -0,0 +1,17 @@
+"""All-interval series of size n (MathConstraint all_interval, CC-BY-4.0). Accepts any valid series."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    d = [abs(x[i + 1] - x[i]) for i in range(n - 1)]
+    if sorted(d) != list(range(1, n)):
+        raise Invalid("consecutive differences are not a permutation of 1..n-1")
+    seqs = {"x": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-all-interval-l1-s1/tests/instance.json b/tasks/construct-mc-all-interval-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f9a1095199b5b913d326c0c19329b93273d37211
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 4, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l1-s1/tests/run.py b/tasks/construct-mc-all-interval-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l1-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-all-interval-l1-s1/tests/test.sh b/tasks/construct-mc-all-interval-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l1-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-all-interval-l2-s3/environment/Dockerfile b/tasks/construct-mc-all-interval-l2-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-all-interval-l2-s3/environment/instance.json b/tasks/construct-mc-all-interval-l2-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1e500b61bb9b4f4f1595d13f8eefd245694b7b67
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 9, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l2-s3/solution/solve.sh b/tasks/construct-mc-all-interval-l2-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..da0770f82c348ae7ebc37ae6f8e0007241e109bf
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 8, 1, 7, 2, 6, 3, 5, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-all-interval-l2-s3/tests/check.py b/tasks/construct-mc-all-interval-l2-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e39eec264b6422a47e35921b8cdbe1fa1748307
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s3/tests/check.py
@@ -0,0 +1,17 @@
+"""All-interval series of size n (MathConstraint all_interval, CC-BY-4.0). Accepts any valid series."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    d = [abs(x[i + 1] - x[i]) for i in range(n - 1)]
+    if sorted(d) != list(range(1, n)):
+        raise Invalid("consecutive differences are not a permutation of 1..n-1")
+    seqs = {"x": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-all-interval-l2-s3/tests/instance.json b/tasks/construct-mc-all-interval-l2-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1e500b61bb9b4f4f1595d13f8eefd245694b7b67
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 9, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l2-s3/tests/run.py b/tasks/construct-mc-all-interval-l2-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-all-interval-l2-s3/tests/test.sh b/tasks/construct-mc-all-interval-l2-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-all-interval-l6-s2/environment/Dockerfile b/tasks/construct-mc-all-interval-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-all-interval-l6-s2/environment/instance.json b/tasks/construct-mc-all-interval-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa32179a5922bf74253a5c317c3ef42e407210d7
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 104, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l6-s2/solution/solve.sh b/tasks/construct-mc-all-interval-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..31b7545a9be91acba9c0f0fec9e88f7b1d229e8f
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 103, 1, 102, 2, 101, 3, 100, 4, 99, 5, 98, 6, 97, 7, 96, 8, 95, 9, 94, 10, 93, 11, 92, 12, 91, 13, 90, 14, 89, 15, 88, 16, 87, 17, 86, 18, 85, 19, 84, 20, 83, 21, 82, 22, 81, 23, 80, 24, 79, 25, 78, 26, 77, 27, 76, 28, 75, 29, 74, 30, 73, 31, 72, 32, 71, 33, 70, 34, 69, 35, 68, 36, 67, 37, 66, 38, 65, 39, 64, 40, 63, 41, 62, 42, 61, 43, 60, 44, 59, 45, 58, 46, 57, 47, 56, 48, 55, 49, 54, 50, 53, 51, 52]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-all-interval-l6-s2/tests/check.py b/tasks/construct-mc-all-interval-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e39eec264b6422a47e35921b8cdbe1fa1748307
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s2/tests/check.py
@@ -0,0 +1,17 @@
+"""All-interval series of size n (MathConstraint all_interval, CC-BY-4.0). Accepts any valid series."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    d = [abs(x[i + 1] - x[i]) for i in range(n - 1)]
+    if sorted(d) != list(range(1, n)):
+        raise Invalid("consecutive differences are not a permutation of 1..n-1")
+    seqs = {"x": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-all-interval-l6-s2/tests/instance.json b/tasks/construct-mc-all-interval-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa32179a5922bf74253a5c317c3ef42e407210d7
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 104, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l6-s2/tests/run.py b/tasks/construct-mc-all-interval-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-all-interval-l6-s2/tests/test.sh b/tasks/construct-mc-all-interval-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-all-interval-l6-s5/environment/Dockerfile b/tasks/construct-mc-all-interval-l6-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-all-interval-l6-s5/environment/instance.json b/tasks/construct-mc-all-interval-l6-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d35ffa759e80b8d4804f11973285b1e352aa27bd
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 128, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l6-s5/solution/solve.sh b/tasks/construct-mc-all-interval-l6-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5d02e363f467eed9ec0b6ff94aa0bdc7540a3444
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 127, 1, 126, 2, 125, 3, 124, 4, 123, 5, 122, 6, 121, 7, 120, 8, 119, 9, 118, 10, 117, 11, 116, 12, 115, 13, 114, 14, 113, 15, 112, 16, 111, 17, 110, 18, 109, 19, 108, 20, 107, 21, 106, 22, 105, 23, 104, 24, 103, 25, 102, 26, 101, 27, 100, 28, 99, 29, 98, 30, 97, 31, 96, 32, 95, 33, 94, 34, 93, 35, 92, 36, 91, 37, 90, 38, 89, 39, 88, 40, 87, 41, 86, 42, 85, 43, 84, 44, 83, 45, 82, 46, 81, 47, 80, 48, 79, 49, 78, 50, 77, 51, 76, 52, 75, 53, 74, 54, 73, 55, 72, 56, 71, 57, 70, 58, 69, 59, 68, 60, 67, 61, 66, 62, 65, 63, 64]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-all-interval-l6-s5/tests/check.py b/tasks/construct-mc-all-interval-l6-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e39eec264b6422a47e35921b8cdbe1fa1748307
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s5/tests/check.py
@@ -0,0 +1,17 @@
+"""All-interval series of size n (MathConstraint all_interval, CC-BY-4.0). Accepts any valid series."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    d = [abs(x[i + 1] - x[i]) for i in range(n - 1)]
+    if sorted(d) != list(range(1, n)):
+        raise Invalid("consecutive differences are not a permutation of 1..n-1")
+    seqs = {"x": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-all-interval-l6-s5/tests/instance.json b/tasks/construct-mc-all-interval-l6-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d35ffa759e80b8d4804f11973285b1e352aa27bd
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 128, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l6-s5/tests/run.py b/tasks/construct-mc-all-interval-l6-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-all-interval-l6-s5/tests/test.sh b/tasks/construct-mc-all-interval-l6-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l6-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-antimagic-square-l6-s0/environment/Dockerfile b/tasks/construct-mc-antimagic-square-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-antimagic-square-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-antimagic-square-l6-s0/environment/instance.json b/tasks/construct-mc-antimagic-square-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..926331bce1dc5fee862953f8a6c60c43620b222c
--- /dev/null
+++ b/tasks/construct-mc-antimagic-square-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 9, "family": "mc_antimagic_square", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-antimagic-square-l6-s0/solution/solve.sh b/tasks/construct-mc-antimagic-square-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d1b84c638f178ceaf0a73286b784f945ef82ea65
--- /dev/null
+++ b/tasks/construct-mc-antimagic-square-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"grid": [[14, 45, 64, 49, 48, 41, 19, 67, 25], [58, 17, 69, 23, 73, 18, 77, 8, 34], [78, 24, 74, 3, 16, 52, 21, 68, 32], [50, 75, 5, 56, 65, 43, 6, 39, 27], [10, 71, 9, 61, 7, 79, 53, 29, 46], [31, 37, 1, 80, 51, 26, 76, 28, 44], [35, 30, 81, 36, 22, 11, 70, 15, 60], [59, 62, 4, 38, 63, 20, 2, 55, 66], [40, 12, 57, 13, 33, 72, 47, 54, 42]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-antimagic-square-l6-s0/tests/check.py b/tasks/construct-mc-antimagic-square-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c86a40bef203632c61a8ba237cae03eb53251a6
--- /dev/null
+++ b/tasks/construct-mc-antimagic-square-l6-s0/tests/check.py
@@ -0,0 +1,20 @@
+"""Antimagic square of order n (MathConstraint antimagic_square, CC-BY-4.0): the numbers 1..n^2 in an
+n x n grid whose 2n+2 line sums (rows, columns, both main diagonals) are 2n+2 consecutive integers."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    g = ans.get("grid")
+    if not isinstance(g, list) or len(g) != n:
+        raise Invalid(f"grid must be a list of {n} rows")
+    g = [int_list(r, n, 1, n * n, "grid row") for r in g]
+    flat = [v for r in g for v in r]
+    if sorted(flat) != list(range(1, n * n + 1)):
+        raise Invalid(f"grid must contain each of 1..{n * n} exactly once")
+    sums = [sum(r) for r in g] + [sum(g[i][j] for i in range(n)) for j in range(n)]
+    sums += [sum(g[i][i] for i in range(n)), sum(g[i][n - 1 - i] for i in range(n))]
+    s = sorted(sums)
+    if any(s[i + 1] != s[i] + 1 for i in range(len(s) - 1)):
+        raise Invalid(f"line sums {sums} are not {2 * n + 2} consecutive integers")
+    return None, {}
diff --git a/tasks/construct-mc-antimagic-square-l6-s0/tests/instance.json b/tasks/construct-mc-antimagic-square-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..926331bce1dc5fee862953f8a6c60c43620b222c
--- /dev/null
+++ b/tasks/construct-mc-antimagic-square-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 9, "family": "mc_antimagic_square", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-antimagic-square-l6-s0/tests/run.py b/tasks/construct-mc-antimagic-square-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-antimagic-square-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-antimagic-square-l6-s0/tests/test.sh b/tasks/construct-mc-antimagic-square-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-antimagic-square-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-debruijn-l1-s1/environment/Dockerfile b/tasks/construct-mc-debruijn-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l1-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-debruijn-l1-s1/environment/instance.json b/tasks/construct-mc-debruijn-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..17d042371d2aaafa2e5687cddf602e536b6ce3f8
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"b": 2, "n": 3, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l1-s1/solution/solve.sh b/tasks/construct-mc-debruijn-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f3718b2c16cf206f136e65f01f998d9942aa33ac
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l1-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"seq": [0, 0, 0, 1, 0, 1, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-debruijn-l1-s1/tests/check.py b/tasks/construct-mc-debruijn-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c9d6f0177d2b3bde8306d74939ee9704c1501a23
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l1-s1/tests/check.py
@@ -0,0 +1,15 @@
+"""De Bruijn sequence B(b, n) (MathConstraint debruijn, CC-BY-4.0). Accepts any valid cyclic sequence."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    b, n = inst["b"], inst["n"]
+    m = b ** n
+    x = int_list(ans.get("seq"), m, 0, b - 1, "seq")
+    seen = set()
+    for i in range(m):
+        w = tuple(x[(i + k) % m] for k in range(n))
+        if w in seen:
+            raise Invalid(f"window {w} occurs twice")
+        seen.add(w)
+    return None, {}
diff --git a/tasks/construct-mc-debruijn-l1-s1/tests/instance.json b/tasks/construct-mc-debruijn-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..17d042371d2aaafa2e5687cddf602e536b6ce3f8
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"b": 2, "n": 3, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l1-s1/tests/run.py b/tasks/construct-mc-debruijn-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l1-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-debruijn-l1-s1/tests/test.sh b/tasks/construct-mc-debruijn-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l1-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-debruijn-l5-s0/environment/Dockerfile b/tasks/construct-mc-debruijn-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-debruijn-l5-s0/environment/instance.json b/tasks/construct-mc-debruijn-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..035119a84eec08c46402fb232e56bba6b1e44480
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"b": 3, "n": 6, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l5-s0/solution/solve.sh b/tasks/construct-mc-debruijn-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d1c8b266d88b0dcaf18248312b04e6db45268e9f
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"seq": [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 2, 0, 0, 1, 2, 0, 1, 0, 0, 1, 2, 0, 2, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 1, 2, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 1, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 0, 1, 0, 0, 2, 1, 0, 2, 0, 0, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 2, 1, 0, 0, 2, 1, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 1, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 2, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 2, 1, 0, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 2, 1, 0, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 2, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 2, 0, 1, 2, 2, 0, 2, 0, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 2, 0, 1, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 2, 1, 0, 2, 2, 0, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 2, 1, 0, 2, 1, 1, 2, 2, 0, 2, 1, 2, 1, 1, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 2, 0, 2, 2, 1, 2, 1, 0, 2, 2, 1, 2, 2, 0, 2, 2, 2, 1, 1, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-debruijn-l5-s0/tests/check.py b/tasks/construct-mc-debruijn-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c9d6f0177d2b3bde8306d74939ee9704c1501a23
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s0/tests/check.py
@@ -0,0 +1,15 @@
+"""De Bruijn sequence B(b, n) (MathConstraint debruijn, CC-BY-4.0). Accepts any valid cyclic sequence."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    b, n = inst["b"], inst["n"]
+    m = b ** n
+    x = int_list(ans.get("seq"), m, 0, b - 1, "seq")
+    seen = set()
+    for i in range(m):
+        w = tuple(x[(i + k) % m] for k in range(n))
+        if w in seen:
+            raise Invalid(f"window {w} occurs twice")
+        seen.add(w)
+    return None, {}
diff --git a/tasks/construct-mc-debruijn-l5-s0/tests/instance.json b/tasks/construct-mc-debruijn-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..035119a84eec08c46402fb232e56bba6b1e44480
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"b": 3, "n": 6, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l5-s0/tests/run.py b/tasks/construct-mc-debruijn-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-debruijn-l5-s0/tests/test.sh b/tasks/construct-mc-debruijn-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-debruijn-l6-s2/environment/Dockerfile b/tasks/construct-mc-debruijn-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-debruijn-l6-s2/environment/instance.json b/tasks/construct-mc-debruijn-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a1a06bc6f681fdc8b8e87b3479ecf8bb459c6056
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"b": 3, "n": 7, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l6-s2/solution/solve.sh b/tasks/construct-mc-debruijn-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3d67da4928ac520dc91bd2bd83b0df1ce9f4b95a
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"seq": [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 2, 1, 1, 2, 0, 0, 0, 2, 1, 2, 1, 0, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 0, 2, 1, 1, 0, 0, 1, 0, 2, 1, 2, 0, 0, 1, 0, 2, 2, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 0, 2, 2, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 2, 1, 0, 0, 1, 1, 1, 2, 2, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 2, 1, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 1, 2, 2, 1, 0, 0, 1, 1, 2, 2, 2, 0, 0, 1, 2, 0, 0, 2, 0, 0, 1, 2, 0, 1, 1, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 1, 0, 0, 1, 2, 0, 2, 2, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 2, 1, 1, 2, 0, 0, 1, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 2, 2, 0, 1, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 2, 1, 2, 0, 0, 1, 2, 2, 2, 1, 0, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 1, 1, 1, 0, 0, 2, 0, 1, 1, 2, 0, 0, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 1, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 0, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 1, 0, 2, 0, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 2, 0, 0, 2, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 0, 2, 1, 2, 0, 1, 0, 0, 2, 1, 2, 0, 2, 0, 0, 2, 1, 2, 1, 1, 0, 0, 2, 1, 2, 1, 2, 0, 0, 2, 1, 2, 2, 1, 0, 0, 2, 1, 2, 2, 2, 0, 0, 2, 2, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 1, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 1, 1, 1, 0, 0, 2, 2, 1, 1, 2, 0, 0, 2, 2, 1, 2, 1, 0, 0, 2, 2, 1, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 0, 2, 1, 0, 1, 0, 1, 0, 2, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 0, 1, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 2, 2, 0, 1, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 2, 1, 0, 1, 0, 1, 2, 2, 2, 0, 1, 0, 2, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 0, 2, 1, 1, 1, 0, 1, 0, 2, 1, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 2, 1, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 1, 1, 0, 1, 0, 2, 2, 1, 2, 0, 1, 0, 2, 2, 2, 1, 0, 1, 0, 2, 2, 2, 2, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 1, 0, 2, 0, 2, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 0, 2, 1, 2, 0, 1, 1, 0, 2, 2, 1, 0, 1, 1, 0, 2, 2, 2, 0, 1, 1, 1, 0, 1, 2, 0, 1, 1, 1, 0, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 2, 2, 0, 1, 1, 1, 2, 0, 2, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 2, 2, 1, 0, 1, 1, 1, 2, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 1, 1, 2, 0, 2, 1, 0, 1, 1, 2, 0, 2, 2, 0, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 1, 1, 1, 0, 1, 1, 2, 1, 1, 2, 0, 1, 1, 2, 1, 2, 1, 0, 1, 1, 2, 1, 2, 2, 0, 1, 1, 2, 2, 0, 2, 0, 1, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 0, 1, 1, 2, 2, 2, 1, 0, 1, 1, 2, 2, 2, 2, 0, 1, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 1, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1, 2, 0, 2, 2, 1, 0, 1, 2, 0, 2, 2, 2, 0, 1, 2, 1, 0, 2, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 2, 1, 1, 0, 2, 0, 1, 2, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 2, 0, 2, 0, 1, 2, 1, 2, 1, 1, 0, 1, 2, 1, 2, 1, 2, 0, 1, 2, 1, 2, 2, 1, 0, 1, 2, 1, 2, 2, 2, 0, 1, 2, 2, 0, 2, 1, 0, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 1, 0, 2, 0, 1, 2, 2, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 0, 1, 2, 2, 1, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 1, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2, 1, 1, 0, 1, 2, 2, 2, 1, 2, 0, 1, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 2, 0, 2, 1, 2, 1, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 1, 1, 0, 2, 0, 2, 2, 1, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 2, 0, 2, 1, 1, 0, 2, 2, 0, 2, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 1, 0, 2, 1, 1, 1, 2, 2, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 1, 2, 1, 2, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 2, 1, 2, 1, 1, 1, 0, 2, 1, 2, 1, 1, 2, 0, 2, 1, 2, 1, 2, 1, 0, 2, 1, 2, 1, 2, 2, 0, 2, 1, 2, 2, 1, 1, 0, 2, 1, 2, 2, 1, 2, 0, 2, 1, 2, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 2, 0, 2, 2, 1, 1, 2, 1, 0, 2, 2, 1, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 2, 1, 2, 1, 2, 0, 2, 2, 1, 2, 2, 1, 0, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 1, 1, 1, 0, 2, 2, 2, 1, 1, 2, 0, 2, 2, 2, 1, 2, 1, 0, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 1, 1, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-debruijn-l6-s2/tests/check.py b/tasks/construct-mc-debruijn-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c9d6f0177d2b3bde8306d74939ee9704c1501a23
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l6-s2/tests/check.py
@@ -0,0 +1,15 @@
+"""De Bruijn sequence B(b, n) (MathConstraint debruijn, CC-BY-4.0). Accepts any valid cyclic sequence."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    b, n = inst["b"], inst["n"]
+    m = b ** n
+    x = int_list(ans.get("seq"), m, 0, b - 1, "seq")
+    seen = set()
+    for i in range(m):
+        w = tuple(x[(i + k) % m] for k in range(n))
+        if w in seen:
+            raise Invalid(f"window {w} occurs twice")
+        seen.add(w)
+    return None, {}
diff --git a/tasks/construct-mc-debruijn-l6-s2/tests/instance.json b/tasks/construct-mc-debruijn-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a1a06bc6f681fdc8b8e87b3479ecf8bb459c6056
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"b": 3, "n": 7, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l6-s2/tests/run.py b/tasks/construct-mc-debruijn-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-debruijn-l6-s2/tests/test.sh b/tasks/construct-mc-debruijn-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-golomb-l3-s0/environment/Dockerfile b/tasks/construct-mc-golomb-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-golomb-l3-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-golomb-l3-s0/environment/instance.json b/tasks/construct-mc-golomb-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..877dc8558f26ac80e8db1185330b059e95778db6
--- /dev/null
+++ b/tasks/construct-mc-golomb-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 10, "max_length": 55, "fixed": [], "family": "mc_golomb", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-golomb-l3-s0/solution/solve.sh b/tasks/construct-mc-golomb-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4b55de176852ecf089f8e938bce39ef10f68eb1b
--- /dev/null
+++ b/tasks/construct-mc-golomb-l3-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"marks": [0, 2, 14, 21, 29, 32, 45, 49, 54, 55]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-golomb-l3-s0/tests/check.py b/tasks/construct-mc-golomb-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..84aedd6e33fee7271543bfa49ab05128e23c31ee
--- /dev/null
+++ b/tasks/construct-mc-golomb-l3-s0/tests/check.py
@@ -0,0 +1,27 @@
+"""Golomb ruler with n marks and length <= L (MathConstraint golomb, CC-BY-4.0, reframed as a decision
+problem with the target length stated). Accepts any valid ruler.
+Upstream note: the upstream prompt states no length bound and its verifier re-solves the optimisation
+model with the marks fixed, which returns OPTIMUM for any Golomb ruler, so any ruler (e.g. 0,1,3,7,15,..)
+was accepted. Here the length bound is part of the instance and enforced."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, L = inst["n"], inst["max_length"]
+    a = int_list(ans.get("marks"), n, 0, L, "marks")
+    if a[0] != 0:
+        raise Invalid("first mark must be 0")
+    if any(a[i] >= a[i + 1] for i in range(n - 1)):
+        raise Invalid("marks must be strictly increasing")
+    for name, i, v in inst.get("fixed", []):
+        if a[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    seen = set()
+    for i, j in itertools.combinations(range(n), 2):
+        d = a[j] - a[i]
+        if d in seen:
+            raise Invalid(f"difference {d} occurs twice")
+        seen.add(d)
+    return None, {"length": a[-1]}
diff --git a/tasks/construct-mc-golomb-l3-s0/tests/instance.json b/tasks/construct-mc-golomb-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..877dc8558f26ac80e8db1185330b059e95778db6
--- /dev/null
+++ b/tasks/construct-mc-golomb-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 10, "max_length": 55, "fixed": [], "family": "mc_golomb", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-golomb-l3-s0/tests/run.py b/tasks/construct-mc-golomb-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-golomb-l3-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-golomb-l3-s0/tests/test.sh b/tasks/construct-mc-golomb-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-golomb-l3-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-graceful-graph-l2-s0/environment/Dockerfile b/tasks/construct-mc-graceful-graph-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l2-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-graceful-graph-l2-s0/environment/instance.json b/tasks/construct-mc-graceful-graph-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5842d804be61f8663d04595d4c863e9e33985cea
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"k": 3, "p": 3, "num_vertices": 9, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l2-s0/solution/solve.sh b/tasks/construct-mc-graceful-graph-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a576b264cc5c3a4a792342523d74a7611f36d07b
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l2-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"labels": [2, 12, 0, 1, 6, 15, 14, 3, 7]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-graceful-graph-l2-s0/tests/check.py b/tasks/construct-mc-graceful-graph-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..f4d33af1d63c0495c3b32d34db6ae10f0fb45923
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l2-s0/tests/check.py
@@ -0,0 +1,19 @@
+"""Graceful labelling of K_k x P_p (MathConstraint graceful_graph, CC-BY-4.0): distinct vertex labels in
+0..m (m = number of edges) whose edge differences |l(u) - l(v)| are all distinct."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    nv, edges = inst["num_vertices"], inst["edges"]
+    m = len(edges)
+    x = int_list(ans.get("labels"), nv, 0, m, "labels")
+    if len(set(x)) != nv:
+        raise Invalid("vertex labels must be distinct")
+    d = [abs(x[u] - x[v]) for u, v in edges]
+    if len(set(d)) != m:
+        raise Invalid("edge labels are not distinct")
+    seqs = {"labels": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-graceful-graph-l2-s0/tests/instance.json b/tasks/construct-mc-graceful-graph-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5842d804be61f8663d04595d4c863e9e33985cea
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"k": 3, "p": 3, "num_vertices": 9, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l2-s0/tests/run.py b/tasks/construct-mc-graceful-graph-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l2-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-graceful-graph-l2-s0/tests/test.sh b/tasks/construct-mc-graceful-graph-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l2-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-graceful-graph-l5-s3/environment/Dockerfile b/tasks/construct-mc-graceful-graph-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l5-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-graceful-graph-l5-s3/environment/instance.json b/tasks/construct-mc-graceful-graph-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7d1868c27681593f9a5ff097a808974680d51f9
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"k": 3, "p": 10, "num_vertices": 30, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [21, 22], [21, 23], [22, 23], [24, 25], [24, 26], [25, 26], [27, 28], [27, 29], [28, 29], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], [10, 13], [11, 14], [12, 15], [13, 16], [14, 17], [15, 18], [16, 19], [17, 20], [18, 21], [19, 22], [20, 23], [21, 24], [22, 25], [23, 26], [24, 27], [25, 28], [26, 29]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l5-s3/solution/solve.sh b/tasks/construct-mc-graceful-graph-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..61a34252ca6a09abfb751f6e41c64e62026ea5eb
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l5-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"labels": [39, 51, 20, 10, 35, 53, 45, 9, 30, 23, 50, 6, 37, 3, 57, 5, 55, 0, 16, 7, 56, 24, 52, 14, 54, 15, 8, 1, 2, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-graceful-graph-l5-s3/tests/check.py b/tasks/construct-mc-graceful-graph-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..f4d33af1d63c0495c3b32d34db6ae10f0fb45923
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l5-s3/tests/check.py
@@ -0,0 +1,19 @@
+"""Graceful labelling of K_k x P_p (MathConstraint graceful_graph, CC-BY-4.0): distinct vertex labels in
+0..m (m = number of edges) whose edge differences |l(u) - l(v)| are all distinct."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    nv, edges = inst["num_vertices"], inst["edges"]
+    m = len(edges)
+    x = int_list(ans.get("labels"), nv, 0, m, "labels")
+    if len(set(x)) != nv:
+        raise Invalid("vertex labels must be distinct")
+    d = [abs(x[u] - x[v]) for u, v in edges]
+    if len(set(d)) != m:
+        raise Invalid("edge labels are not distinct")
+    seqs = {"labels": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-graceful-graph-l5-s3/tests/instance.json b/tasks/construct-mc-graceful-graph-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7d1868c27681593f9a5ff097a808974680d51f9
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"k": 3, "p": 10, "num_vertices": 30, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [21, 22], [21, 23], [22, 23], [24, 25], [24, 26], [25, 26], [27, 28], [27, 29], [28, 29], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], [10, 13], [11, 14], [12, 15], [13, 16], [14, 17], [15, 18], [16, 19], [17, 20], [18, 21], [19, 22], [20, 23], [21, 24], [22, 25], [23, 26], [24, 27], [25, 28], [26, 29]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l5-s3/tests/run.py b/tasks/construct-mc-graceful-graph-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l5-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-graceful-graph-l5-s3/tests/test.sh b/tasks/construct-mc-graceful-graph-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l5-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-graph-k-coloring-l1-s4/environment/Dockerfile b/tasks/construct-mc-graph-k-coloring-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-graph-k-coloring-l1-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-graph-k-coloring-l1-s4/environment/instance.json b/tasks/construct-mc-graph-k-coloring-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..717d8fc484d2c1d07a3da5272fe4a494e2375e8f
--- /dev/null
+++ b/tasks/construct-mc-graph-k-coloring-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 3, "edges": [[0, 5], [0, 7], [0, 9], [0, 12], [0, 15], [1, 9], [2, 4], [2, 12], [2, 15], [2, 17], [2, 19], [3, 6], [3, 9], [3, 15], [3, 16], [4, 10], [4, 13], [5, 9], [5, 10], [6, 8], [6, 16], [6, 17], [7, 11], [8, 9], [8, 14], [8, 18], [9, 17], [10, 19], [12, 15], [12, 17]], "family": "mc_graph_k_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graph-k-coloring-l1-s4/solution/solve.sh b/tasks/construct-mc-graph-k-coloring-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d9376e8e6cfa6abd861003f05f7beda69fb6ee07
--- /dev/null
+++ b/tasks/construct-mc-graph-k-coloring-l1-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"coloring": [1, 1, 1, 1, 0, 0, 2, 0, 0, 2, 1, 1, 2, 2, 2, 0, 0, 0, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-graph-k-coloring-l1-s4/tests/check.py b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2b5f38cd0c22ac1b4ba37c0d3ff0a34635f08854
--- /dev/null
+++ b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/check.py
@@ -0,0 +1,11 @@
+"""Proper k-colouring of a given graph (MathConstraint graph_k_coloring, CC-BY-4.0). Any valid colouring."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"edge ({u},{v}) is monochromatic")
+    return None, {}
diff --git a/tasks/construct-mc-graph-k-coloring-l1-s4/tests/instance.json b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..717d8fc484d2c1d07a3da5272fe4a494e2375e8f
--- /dev/null
+++ b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 3, "edges": [[0, 5], [0, 7], [0, 9], [0, 12], [0, 15], [1, 9], [2, 4], [2, 12], [2, 15], [2, 17], [2, 19], [3, 6], [3, 9], [3, 15], [3, 16], [4, 10], [4, 13], [5, 9], [5, 10], [6, 8], [6, 16], [6, 17], [7, 11], [8, 9], [8, 14], [8, 18], [9, 17], [10, 19], [12, 15], [12, 17]], "family": "mc_graph_k_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graph-k-coloring-l1-s4/tests/run.py b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-graph-k-coloring-l1-s4/tests/test.sh b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-graph-k-coloring-l1-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-hadamard-l2-s0/environment/Dockerfile b/tasks/construct-mc-hadamard-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l2-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-hadamard-l2-s0/environment/instance.json b/tasks/construct-mc-hadamard-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b17b04b8cb213a9dc51b97eb67f0bda2c4f2b07
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 13, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l2-s0/solution/solve.sh b/tasks/construct-mc-hadamard-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..57f6d453966acccf7c18b4451e46d99703ce3051
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l2-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1], "y": [1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-hadamard-l2-s0/tests/check.py b/tasks/construct-mc-hadamard-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc4b93160fd7473dd14935db9d712e52abdd00c2
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l2-s0/tests/check.py
@@ -0,0 +1,18 @@
+"""Legendre pair of odd length n (MathConstraint hadamard, CC-BY-4.0): x, y in {-1,+1}^n with
+sum(x) = sum(y) = 1 and PAF_x(k) + PAF_y(k) = -2 for k = 1..(n-1)/2 (periodic autocorrelation)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, -1, 1, "x")
+    y = int_list(ans.get("y"), n, -1, 1, "y")
+    if 0 in x or 0 in y:
+        raise Invalid("entries must be -1 or +1")
+    if sum(x) != 1 or sum(y) != 1:
+        raise Invalid("sum(x) and sum(y) must both equal 1")
+    for k in range(1, (n - 1) // 2 + 1):
+        p = sum(x[i] * x[(i + k) % n] for i in range(n)) + sum(y[i] * y[(i + k) % n] for i in range(n))
+        if p != -2:
+            raise Invalid(f"PAF_x({k}) + PAF_y({k}) = {p}, need -2")
+    return None, {}
diff --git a/tasks/construct-mc-hadamard-l2-s0/tests/instance.json b/tasks/construct-mc-hadamard-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b17b04b8cb213a9dc51b97eb67f0bda2c4f2b07
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 13, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l2-s0/tests/run.py b/tasks/construct-mc-hadamard-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l2-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-hadamard-l2-s0/tests/test.sh b/tasks/construct-mc-hadamard-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l2-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-hadamard-l5-s3/environment/Dockerfile b/tasks/construct-mc-hadamard-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-hadamard-l5-s3/environment/instance.json b/tasks/construct-mc-hadamard-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a70809c35e4f86bbdb90674ca9edd4d68fb28202
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 43, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l5-s3/solution/solve.sh b/tasks/construct-mc-hadamard-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8fe131da472d2944a1f5519c8850569877a427d2
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1], "y": [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-hadamard-l5-s3/tests/check.py b/tasks/construct-mc-hadamard-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc4b93160fd7473dd14935db9d712e52abdd00c2
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s3/tests/check.py
@@ -0,0 +1,18 @@
+"""Legendre pair of odd length n (MathConstraint hadamard, CC-BY-4.0): x, y in {-1,+1}^n with
+sum(x) = sum(y) = 1 and PAF_x(k) + PAF_y(k) = -2 for k = 1..(n-1)/2 (periodic autocorrelation)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, -1, 1, "x")
+    y = int_list(ans.get("y"), n, -1, 1, "y")
+    if 0 in x or 0 in y:
+        raise Invalid("entries must be -1 or +1")
+    if sum(x) != 1 or sum(y) != 1:
+        raise Invalid("sum(x) and sum(y) must both equal 1")
+    for k in range(1, (n - 1) // 2 + 1):
+        p = sum(x[i] * x[(i + k) % n] for i in range(n)) + sum(y[i] * y[(i + k) % n] for i in range(n))
+        if p != -2:
+            raise Invalid(f"PAF_x({k}) + PAF_y({k}) = {p}, need -2")
+    return None, {}
diff --git a/tasks/construct-mc-hadamard-l5-s3/tests/instance.json b/tasks/construct-mc-hadamard-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a70809c35e4f86bbdb90674ca9edd4d68fb28202
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 43, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l5-s3/tests/run.py b/tasks/construct-mc-hadamard-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-hadamard-l5-s3/tests/test.sh b/tasks/construct-mc-hadamard-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-hadamard-l5-s4/environment/Dockerfile b/tasks/construct-mc-hadamard-l5-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-hadamard-l5-s4/environment/instance.json b/tasks/construct-mc-hadamard-l5-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6648da5f846a5a74b93f4a9c1b2d9be0ec1a53d0
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 47, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l5-s4/solution/solve.sh b/tasks/construct-mc-hadamard-l5-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1c22372c0132eb7d176a560c0848444eb5ce60a7
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1], "y": [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-hadamard-l5-s4/tests/check.py b/tasks/construct-mc-hadamard-l5-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc4b93160fd7473dd14935db9d712e52abdd00c2
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s4/tests/check.py
@@ -0,0 +1,18 @@
+"""Legendre pair of odd length n (MathConstraint hadamard, CC-BY-4.0): x, y in {-1,+1}^n with
+sum(x) = sum(y) = 1 and PAF_x(k) + PAF_y(k) = -2 for k = 1..(n-1)/2 (periodic autocorrelation)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, -1, 1, "x")
+    y = int_list(ans.get("y"), n, -1, 1, "y")
+    if 0 in x or 0 in y:
+        raise Invalid("entries must be -1 or +1")
+    if sum(x) != 1 or sum(y) != 1:
+        raise Invalid("sum(x) and sum(y) must both equal 1")
+    for k in range(1, (n - 1) // 2 + 1):
+        p = sum(x[i] * x[(i + k) % n] for i in range(n)) + sum(y[i] * y[(i + k) % n] for i in range(n))
+        if p != -2:
+            raise Invalid(f"PAF_x({k}) + PAF_y({k}) = {p}, need -2")
+    return None, {}
diff --git a/tasks/construct-mc-hadamard-l5-s4/tests/instance.json b/tasks/construct-mc-hadamard-l5-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6648da5f846a5a74b93f4a9c1b2d9be0ec1a53d0
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s4/tests/instance.json
@@ -0,0 +1 @@
+{"n": 47, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l5-s4/tests/run.py b/tasks/construct-mc-hadamard-l5-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-hadamard-l5-s4/tests/test.sh b/tasks/construct-mc-hadamard-l5-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l5-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-hadamard-l6-s8/environment/Dockerfile b/tasks/construct-mc-hadamard-l6-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l6-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-hadamard-l6-s8/environment/instance.json b/tasks/construct-mc-hadamard-l6-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6e5eeed072ef1d9de81a5f6e03d15af1d40cd573
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l6-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 59, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l6-s8/solution/solve.sh b/tasks/construct-mc-hadamard-l6-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4b39ce5ff433fc2c63af228c8e6b9293dd101d05
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l6-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1], "y": [1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-hadamard-l6-s8/tests/check.py b/tasks/construct-mc-hadamard-l6-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc4b93160fd7473dd14935db9d712e52abdd00c2
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l6-s8/tests/check.py
@@ -0,0 +1,18 @@
+"""Legendre pair of odd length n (MathConstraint hadamard, CC-BY-4.0): x, y in {-1,+1}^n with
+sum(x) = sum(y) = 1 and PAF_x(k) + PAF_y(k) = -2 for k = 1..(n-1)/2 (periodic autocorrelation)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, -1, 1, "x")
+    y = int_list(ans.get("y"), n, -1, 1, "y")
+    if 0 in x or 0 in y:
+        raise Invalid("entries must be -1 or +1")
+    if sum(x) != 1 or sum(y) != 1:
+        raise Invalid("sum(x) and sum(y) must both equal 1")
+    for k in range(1, (n - 1) // 2 + 1):
+        p = sum(x[i] * x[(i + k) % n] for i in range(n)) + sum(y[i] * y[(i + k) % n] for i in range(n))
+        if p != -2:
+            raise Invalid(f"PAF_x({k}) + PAF_y({k}) = {p}, need -2")
+    return None, {}
diff --git a/tasks/construct-mc-hadamard-l6-s8/tests/instance.json b/tasks/construct-mc-hadamard-l6-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6e5eeed072ef1d9de81a5f6e03d15af1d40cd573
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l6-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 59, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l6-s8/tests/run.py b/tasks/construct-mc-hadamard-l6-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l6-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-hadamard-l6-s8/tests/test.sh b/tasks/construct-mc-hadamard-l6-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l6-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-langford-l5-s2/environment/Dockerfile b/tasks/construct-mc-langford-l5-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-langford-l5-s2/environment/instance.json b/tasks/construct-mc-langford-l5-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..014cfdd327d939f1af508eb1d67ea1f07cae0041
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 36, "fixed": [], "family": "mc_langford", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-langford-l5-s2/solution/solve.sh b/tasks/construct-mc-langford-l5-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e76aaed75a4781be7e26c001537750cff47d438c
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"seq": [11, 13, 29, 35, 31, 34, 36, 17, 33, 18, 5, 2, 11, 6, 2, 13, 5, 19, 30, 32, 6, 28, 23, 24, 9, 17, 14, 16, 18, 21, 22, 25, 29, 26, 9, 27, 31, 19, 20, 35, 34, 14, 33, 36, 16, 1, 23, 1, 24, 30, 28, 21, 32, 22, 15, 10, 8, 25, 12, 20, 26, 7, 4, 27, 3, 8, 10, 4, 3, 7, 15, 12]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-langford-l5-s2/tests/check.py b/tasks/construct-mc-langford-l5-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4672d7eacf321991933cb280d6c940f1c4a67935
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s2/tests/check.py
@@ -0,0 +1,17 @@
+"""Langford sequence L(2, n) (MathConstraint langford, CC-BY-4.0). Accepts any valid sequence."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    seq = int_list(ans.get("seq"), 2 * n, 1, n, "seq")
+    for v in range(1, n + 1):
+        pos = [i for i, s in enumerate(seq) if s == v]
+        if len(pos) != 2:
+            raise Invalid(f"value {v} occurs {len(pos)} times (need exactly 2)")
+        if pos[1] - pos[0] != v + 1:
+            raise Invalid(f"the two copies of {v} are {pos[1] - pos[0]} positions apart (need {v + 1})")
+    for name, i, v in inst.get("fixed", []):
+        if seq[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-langford-l5-s2/tests/instance.json b/tasks/construct-mc-langford-l5-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..014cfdd327d939f1af508eb1d67ea1f07cae0041
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 36, "fixed": [], "family": "mc_langford", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-langford-l5-s2/tests/run.py b/tasks/construct-mc-langford-l5-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-langford-l5-s2/tests/test.sh b/tasks/construct-mc-langford-l5-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-low-autocorrelation-l3-s1/environment/Dockerfile b/tasks/construct-mc-low-autocorrelation-l3-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l3-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-low-autocorrelation-l3-s1/environment/instance.json b/tasks/construct-mc-low-autocorrelation-l3-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..913b787324c033014bcae2db7ff5d05479e620a3
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l3-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 19, "bound": 46, "fixed": [["seq", 4, -1], ["seq", 12, 1], ["seq", 13, -1], ["c", 1, -1], ["c", 2, 0], ["c", 7, -3]], "family": "mc_low_autocorrelation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-low-autocorrelation-l3-s1/solution/solve.sh b/tasks/construct-mc-low-autocorrelation-l3-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d0b20d2d723271fdd07ca36ce126f3ec3f25324b
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l3-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"seq": [1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-low-autocorrelation-l3-s1/tests/check.py b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..8456f7b1c0ff0c9fb4bc9ae5a49074c8afa7d1aa
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/check.py
@@ -0,0 +1,20 @@
+"""+-1 sequence of length n with aperiodic autocorrelation energy sum_k C_k^2 <= bound
+(MathConstraint low_autocorrelation, CC-BY-4.0). Exact integer arithmetic."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, bound = inst["n"], inst["bound"]
+    s = int_list(ans.get("seq"), n, -1, 1, "seq")
+    if any(v == 0 for v in s):
+        raise Invalid("entries must be -1 or +1")
+    c = [sum(s[i] * s[i + k] for i in range(n - k)) for k in range(1, n)]
+    e = sum(v * v for v in c)
+    # fixed values: seq[i] or c[k] (c[k] is the autocorrelation at shift k+1, as upstream)
+    seqs = {"seq": s, "c": c}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    if e > bound:
+        raise Invalid(f"energy {e} exceeds the bound {bound}")
+    return None, {"energy": e}
diff --git a/tasks/construct-mc-low-autocorrelation-l3-s1/tests/instance.json b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..913b787324c033014bcae2db7ff5d05479e620a3
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 19, "bound": 46, "fixed": [["seq", 4, -1], ["seq", 12, 1], ["seq", 13, -1], ["c", 1, -1], ["c", 2, 0], ["c", 7, -3]], "family": "mc_low_autocorrelation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-low-autocorrelation-l3-s1/tests/run.py b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-low-autocorrelation-l3-s1/tests/test.sh b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l3-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-clique-l3-s1/environment/Dockerfile b/tasks/construct-mc-max-clique-l3-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-clique-l3-s1/environment/instance.json b/tasks/construct-mc-max-clique-l3-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3c89d6ca8d673932e5a600f9388c1066e28a4503
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 52, "k": 5, "edges": [[0, 5], [0, 8], [0, 16], [0, 22], [0, 26], [0, 27], [0, 28], [0, 30], [0, 31], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 41], [0, 43], [0, 48], [0, 49], [0, 50], [0, 51], [1, 2], [1, 3], [1, 5], [1, 7], [1, 10], [1, 13], [1, 14], [1, 16], [1, 20], [1, 22], [1, 25], [1, 27], [1, 28], [1, 31], [1, 32], [1, 35], [1, 37], [1, 41], [1, 42], [1, 43], [1, 48], [1, 49], [1, 51], [2, 3], [2, 8], [2, 9], [2, 12], [2, 15], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 23], [2, 25], [2, 26], [2, 28], [2, 32], [2, 38], [2, 39], [2, 45], [2, 47], [2, 49], [2, 50], [3, 7], [3, 9], [3, 11], [3, 13], [3, 15], [3, 17], [3, 18], [3, 20], [3, 21], [3, 22], [3, 23], [3, 25], [3, 26], [3, 30], [3, 34], [3, 40], [3, 41], [3, 44], [3, 47], [3, 48], [3, 49], [3, 51], [4, 5], [4, 8], [4, 12], [4, 14], [4, 15], [4, 16], [4, 17], [4, 22], [4, 23], [4, 24], [4, 25], [4, 27], [4, 31], [4, 42], [4, 43], [4, 44], [4, 46], [4, 47], [4, 48], [4, 50], [4, 51], [5, 6], [5, 7], [5, 8], [5, 10], [5, 14], [5, 16], [5, 23], [5, 26], [5, 28], [5, 29], [5, 30], [5, 31], [5, 32], [5, 33], [5, 34], [5, 35], [5, 40], [5, 41], [5, 44], [5, 45], [5, 46], [5, 49], [5, 50], [6, 7], [6, 9], [6, 10], [6, 11], [6, 13], [6, 18], [6, 21], [6, 23], [6, 24], [6, 27], [6, 28], [6, 30], [6, 31], [6, 36], [6, 45], [6, 48], [6, 49], [6, 51], [7, 8], [7, 9], [7, 10], [7, 14], [7, 15], [7, 16], [7, 17], [7, 22], [7, 23], [7, 25], [7, 26], [7, 27], [7, 30], [7, 37], [7, 43], [7, 44], [7, 46], [7, 48], [7, 49], [8, 9], [8, 12], [8, 14], [8, 18], [8, 20], [8, 22], [8, 24], [8, 29], [8, 31], [8, 37], [8, 40], [8, 41], [8, 43], [8, 46], [8, 48], [9, 14], [9, 15], [9, 20], [9, 23], [9, 24], [9, 25], [9, 26], [9, 27], [9, 28], [9, 30], [9, 34], [9, 37], [9, 39], [9, 40], [9, 41], [9, 43], [9, 44], [9, 51], [10, 11], [10, 13], [10, 20], [10, 22], [10, 23], [10, 24], [10, 25], [10, 29], [10, 36], [10, 39], [10, 40], [10, 41], [10, 42], [10, 43], [10, 48], [10, 49], [10, 51], [11, 13], [11, 16], [11, 19], [11, 20], [11, 21], [11, 23], [11, 24], [11, 26], [11, 27], [11, 29], [11, 31], [11, 32], [11, 34], [11, 35], [11, 38], [11, 42], [11, 46], [11, 48], [11, 49], [11, 51], [12, 13], [12, 15], [12, 17], [12, 19], [12, 21], [12, 24], [12, 25], [12, 32], [12, 35], [12, 36], [12, 37], [12, 39], [12, 40], [12, 41], [12, 43], [12, 46], [12, 47], [12, 48], [12, 49], [13, 18], [13, 19], [13, 23], [13, 25], [13, 26], [13, 29], [13, 30], [13, 32], [13, 34], [13, 36], [13, 38], [13, 41], [13, 42], [13, 45], [14, 16], [14, 18], [14, 19], [14, 21], [14, 24], [14, 29], [14, 30], [14, 33], [14, 34], [14, 35], [14, 37], [14, 39], [14, 40], [14, 44], [14, 45], [14, 48], [15, 16], [15, 17], [15, 19], [15, 20], [15, 23], [15, 28], [15, 30], [15, 32], [15, 36], [15, 37], [15, 38], [15, 39], [15, 46], [15, 47], [15, 48], [16, 18], [16, 20], [16, 23], [16, 24], [16, 26], [16, 28], [16, 29], [16, 35], [16, 36], [16, 43], [16, 44], [16, 50], [16, 51], [17, 18], [17, 19], [17, 20], [17, 21], [17, 22], [17, 23], [17, 25], [17, 27], [17, 30], [17, 38], [17, 42], [17, 50], [17, 51], [18, 19], [18, 20], [18, 21], [18, 27], [18, 28], [18, 29], [18, 30], [18, 35], [18, 41], [18, 42], [18, 43], [18, 47], [18, 49], [18, 50], [18, 51], [19, 20], [19, 26], [19, 36], [19, 37], [19, 39], [19, 43], [19, 44], [19, 47], [19, 49], [20, 22], [20, 27], [20, 35], [20, 38], [20, 39], [20, 40], [20, 41], [20, 44], [20, 45], [20, 50], [21, 23], [21, 24], [21, 26], [21, 27], [21, 28], [21, 29], [21, 33], [21, 37], [21, 42], [21, 43], [21, 44], [21, 46], [21, 47], [21, 50], [22, 23], [22, 26], [22, 31], [22, 33], [22, 35], [22, 44], [22, 45], [22, 47], [23, 24], [23, 25], [23, 29], [23, 35], [23, 37], [23, 39], [23, 42], [23, 44], [23, 45], [23, 51], [24, 26], [24, 31], [24, 34], [24, 35], [24, 40], [24, 42], [24, 43], [24, 44], [24, 45], [25, 31], [25, 32], [25, 36], [25, 38], [25, 42], [25, 44], [25, 45], [25, 49], [25, 51], [26, 27], [26, 32], [26, 34], [26, 38], [26, 40], [26, 42], [26, 43], [26, 47], [27, 32], [27, 34], [27, 37], [27, 38], [27, 39], [27, 41], [27, 42], [27, 43], [28, 29], [28, 30], [28, 32], [28, 36], [28, 46], [28, 49], [29, 30], [29, 31], [29, 32], [29, 34], [29, 35], [29, 36], [29, 38], [29, 42], [29, 44], [29, 45], [29, 48], [30, 36], [30, 38], [30, 42], [30, 43], [30, 44], [30, 45], [30, 46], [30, 48], [30, 51], [31, 32], [31, 33], [31, 37], [31, 38], [31, 42], [31, 44], [31, 45], [31, 48], [31, 49], [31, 50], [31, 51], [32, 33], [32, 34], [32, 35], [32, 36], [32, 37], [32, 38], [32, 42], [32, 43], [32, 44], [32, 49], [32, 50], [33, 34], [33, 35], [33, 41], [33, 43], [33, 50], [33, 51], [34, 35], [34, 36], [34, 39], [34, 40], [34, 47], [34, 49], [35, 38], [35, 47], [35, 48], [35, 49], [36, 41], [36, 45], [36, 46], [36, 47], [36, 48], [37, 40], [37, 41], [37, 43], [37, 44], [37, 45], [37, 49], [37, 50], [37, 51], [38, 43], [38, 47], [38, 48], [38, 51], [39, 40], [39, 44], [39, 45], [39, 49], [39, 51], [40, 42], [40, 44], [40, 45], [40, 46], [40, 47], [40, 48], [41, 44], [41, 45], [41, 46], [41, 47], [41, 49], [42, 43], [42, 44], [42, 45], [43, 45], [43, 46], [43, 47], [44, 49], [44, 50], [44, 51], [45, 47], [45, 50], [45, 51], [46, 48], [46, 49], [46, 51], [47, 51], [49, 50]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l3-s1/solution/solve.sh b/tasks/construct-mc-max-clique-l3-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e2cf35ba7eee25db099d95fed1032909f845dc61
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [8, 12, 40, 46, 48]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-clique-l3-s1/tests/check.py b/tasks/construct-mc-max-clique-l3-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3f70dbd5b155a3514c2102aa4ad460201495210
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s1/tests/check.py
@@ -0,0 +1,18 @@
+"""Clique of size >= k in a given graph (MathConstraint max_clique decision version, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"clique has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) not in E:
+            raise Invalid(f"vertices {u} and {v} are not adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-clique-l3-s1/tests/instance.json b/tasks/construct-mc-max-clique-l3-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3c89d6ca8d673932e5a600f9388c1066e28a4503
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 52, "k": 5, "edges": [[0, 5], [0, 8], [0, 16], [0, 22], [0, 26], [0, 27], [0, 28], [0, 30], [0, 31], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 41], [0, 43], [0, 48], [0, 49], [0, 50], [0, 51], [1, 2], [1, 3], [1, 5], [1, 7], [1, 10], [1, 13], [1, 14], [1, 16], [1, 20], [1, 22], [1, 25], [1, 27], [1, 28], [1, 31], [1, 32], [1, 35], [1, 37], [1, 41], [1, 42], [1, 43], [1, 48], [1, 49], [1, 51], [2, 3], [2, 8], [2, 9], [2, 12], [2, 15], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 23], [2, 25], [2, 26], [2, 28], [2, 32], [2, 38], [2, 39], [2, 45], [2, 47], [2, 49], [2, 50], [3, 7], [3, 9], [3, 11], [3, 13], [3, 15], [3, 17], [3, 18], [3, 20], [3, 21], [3, 22], [3, 23], [3, 25], [3, 26], [3, 30], [3, 34], [3, 40], [3, 41], [3, 44], [3, 47], [3, 48], [3, 49], [3, 51], [4, 5], [4, 8], [4, 12], [4, 14], [4, 15], [4, 16], [4, 17], [4, 22], [4, 23], [4, 24], [4, 25], [4, 27], [4, 31], [4, 42], [4, 43], [4, 44], [4, 46], [4, 47], [4, 48], [4, 50], [4, 51], [5, 6], [5, 7], [5, 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[27, 32], [27, 34], [27, 37], [27, 38], [27, 39], [27, 41], [27, 42], [27, 43], [28, 29], [28, 30], [28, 32], [28, 36], [28, 46], [28, 49], [29, 30], [29, 31], [29, 32], [29, 34], [29, 35], [29, 36], [29, 38], [29, 42], [29, 44], [29, 45], [29, 48], [30, 36], [30, 38], [30, 42], [30, 43], [30, 44], [30, 45], [30, 46], [30, 48], [30, 51], [31, 32], [31, 33], [31, 37], [31, 38], [31, 42], [31, 44], [31, 45], [31, 48], [31, 49], [31, 50], [31, 51], [32, 33], [32, 34], [32, 35], [32, 36], [32, 37], [32, 38], [32, 42], [32, 43], [32, 44], [32, 49], [32, 50], [33, 34], [33, 35], [33, 41], [33, 43], [33, 50], [33, 51], [34, 35], [34, 36], [34, 39], [34, 40], [34, 47], [34, 49], [35, 38], [35, 47], [35, 48], [35, 49], [36, 41], [36, 45], [36, 46], [36, 47], [36, 48], [37, 40], [37, 41], [37, 43], [37, 44], [37, 45], [37, 49], [37, 50], [37, 51], [38, 43], [38, 47], [38, 48], [38, 51], [39, 40], [39, 44], [39, 45], [39, 49], [39, 51], [40, 42], [40, 44], [40, 45], [40, 46], [40, 47], [40, 48], [41, 44], [41, 45], [41, 46], [41, 47], [41, 49], [42, 43], [42, 44], [42, 45], [43, 45], [43, 46], [43, 47], [44, 49], [44, 50], [44, 51], [45, 47], [45, 50], [45, 51], [46, 48], [46, 49], [46, 51], [47, 51], [49, 50]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l3-s1/tests/run.py b/tasks/construct-mc-max-clique-l3-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-clique-l3-s1/tests/test.sh b/tasks/construct-mc-max-clique-l3-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-clique-l3-s6/environment/Dockerfile b/tasks/construct-mc-max-clique-l3-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-clique-l3-s6/environment/instance.json b/tasks/construct-mc-max-clique-l3-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..29baed4614a1cb290ec7547d7e7f3920db3ef3b7
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 46, "k": 7, "edges": [[0, 6], [0, 7], [0, 9], [0, 10], [0, 12], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 30], [0, 32], [0, 33], [0, 36], [0, 37], [0, 39], [0, 41], [0, 42], [0, 43], [0, 44], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [1, 14], [1, 15], [1, 18], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 34], [1, 35], [1, 36], [1, 37], [1, 38], [1, 41], [1, 42], [1, 43], [1, 44], [1, 45], [2, 3], [2, 4], [2, 7], [2, 8], [2, 9], [2, 13], [2, 14], [2, 15], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [2, 34], [2, 36], [2, 39], [2, 40], [2, 41], [3, 5], [3, 7], [3, 8], [3, 10], [3, 12], [3, 13], [3, 14], [3, 16], [3, 18], [3, 19], [3, 21], [3, 22], [3, 24], [3, 27], [3, 28], [3, 29], [3, 32], [3, 33], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [3, 40], [3, 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39], [8, 40], [8, 41], [8, 43], [8, 45], [9, 11], [9, 12], [9, 14], [9, 15], [9, 16], [9, 18], [9, 19], [9, 20], [9, 24], [9, 27], [9, 28], [9, 29], [9, 31], [9, 32], [9, 34], [9, 36], [9, 37], [9, 38], [9, 39], [9, 40], [9, 41], [9, 42], [9, 43], [9, 44], [10, 12], [10, 14], [10, 15], [10, 17], [10, 20], [10, 21], [10, 22], [10, 28], [10, 32], [10, 33], [10, 35], [10, 37], [10, 38], [10, 40], [10, 43], [11, 12], [11, 13], [11, 14], [11, 19], [11, 20], [11, 21], [11, 25], [11, 26], [11, 27], [11, 28], [11, 30], [11, 31], [11, 32], [11, 33], [11, 36], [11, 37], [11, 39], [11, 41], [11, 42], [11, 43], [11, 45], [12, 14], [12, 15], [12, 16], [12, 18], [12, 19], [12, 20], [12, 22], [12, 23], [12, 24], [12, 25], [12, 26], [12, 27], [12, 28], [12, 31], [12, 32], [12, 33], [12, 34], [12, 35], [12, 38], [12, 40], [12, 41], [12, 42], [12, 43], [12, 44], [12, 45], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [13, 22], [13, 24], [13, 27], [13, 28], [13, 29], [13, 30], [13, 31], [13, 32], [13, 35], [13, 36], [13, 37], [13, 38], [13, 39], [13, 40], [13, 41], [13, 42], [13, 43], [13, 45], [14, 15], [14, 16], [14, 17], [14, 19], [14, 21], [14, 23], [14, 25], [14, 26], [14, 29], [14, 32], [14, 33], [14, 36], [14, 37], [14, 44], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 25], [15, 26], [15, 28], [15, 29], [15, 30], [15, 32], [15, 34], [15, 35], [15, 36], [15, 37], [15, 39], [15, 40], [15, 41], [15, 43], [15, 44], [15, 45], [16, 18], [16, 21], [16, 22], [16, 23], [16, 25], [16, 26], [16, 29], [16, 31], [16, 32], [16, 34], [16, 35], [16, 36], [16, 38], [16, 39], [16, 41], [16, 43], [16, 44], [16, 45], [17, 18], [17, 19], [17, 24], [17, 25], [17, 27], [17, 28], [17, 29], [17, 30], [17, 31], [17, 32], [17, 33], [17, 36], [17, 37], [17, 39], [17, 40], [17, 41], [17, 42], [17, 43], [17, 44], [17, 45], [18, 19], [18, 22], [18, 23], [18, 25], [18, 28], [18, 29], [18, 30], [18, 32], [18, 33], [18, 34], [18, 35], [18, 37], [18, 38], [18, 42], [18, 43], [18, 45], [19, 21], [19, 23], [19, 24], [19, 26], [19, 27], [19, 28], [19, 29], [19, 30], [19, 31], [19, 32], [19, 33], [19, 34], [19, 35], [19, 38], [19, 39], [19, 41], [19, 42], [20, 23], [20, 25], [20, 26], [20, 27], [20, 28], [20, 31], [20, 33], [20, 35], [20, 36], [20, 39], [20, 40], [20, 41], [20, 43], [20, 44], [20, 45], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 29], [21, 31], [21, 33], [21, 34], [21, 35], [21, 40], [21, 41], [21, 42], [21, 43], [21, 44], [21, 45], [22, 26], [22, 28], [22, 31], [22, 32], [22, 33], [22, 35], [22, 36], [22, 38], [22, 41], [22, 42], [22, 43], [22, 44], [22, 45], [23, 24], [23, 28], [23, 29], [23, 30], [23, 31], [23, 32], [23, 33], [23, 34], [23, 36], [23, 37], [23, 40], [23, 42], [24, 25], [24, 26], [24, 28], [24, 31], [24, 32], [24, 33], [24, 34], [24, 35], [24, 36], [24, 37], [24, 38], [24, 39], [24, 42], [24, 43], [24, 44], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 33], [25, 34], [25, 36], [25, 41], [25, 42], [25, 45], [26, 27], [26, 28], [26, 29], [26, 31], [26, 32], [26, 33], [26, 34], [26, 37], [26, 40], [26, 41], [26, 43], [26, 45], [27, 29], [27, 31], [27, 32], [27, 33], [27, 34], [27, 38], [27, 39], [27, 40], [27, 41], [27, 43], [27, 45], [28, 29], [28, 30], [28, 31], [28, 32], [28, 35], [28, 37], [28, 39], [28, 40], [28, 42], [28, 43], [28, 44], [28, 45], [29, 30], [29, 33], [29, 35], [29, 36], [29, 37], [29, 38], [29, 41], [29, 44], [29, 45], [30, 31], [30, 32], [30, 34], [30, 37], [30, 38], [30, 42], [30, 44], [31, 32], [31, 33], [31, 34], [31, 35], [31, 36], [31, 38], [31, 39], [31, 40], [31, 41], [31, 42], [32, 33], [32, 34], [32, 35], [32, 37], [32, 38], [32, 40], [32, 41], [32, 43], [32, 44], [32, 45], [33, 34], [33, 35], [33, 37], [33, 38], [33, 39], [33, 40], [33, 41], [33, 43], [33, 44], [33, 45], [34, 35], [34, 38], [34, 39], [34, 41], [34, 44], [35, 36], [35, 37], [35, 38], [35, 39], [35, 40], [35, 41], [35, 42], [35, 44], [36, 39], [36, 40], [36, 41], [36, 42], [36, 43], [36, 45], [37, 40], [37, 41], [37, 43], [37, 45], [38, 39], [38, 41], [38, 43], [38, 44], [38, 45], [39, 40], [39, 41], [39, 42], [39, 43], [39, 44], [39, 45], [40, 41], [40, 42], [40, 43], [40, 44], [41, 42], [41, 44], [41, 45], [42, 43], [42, 44], [43, 44]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l3-s6/solution/solve.sh b/tasks/construct-mc-max-clique-l3-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5d35de93d864bdfd28b02b998460183aea12927d
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [33, 34, 35, 38, 39, 41, 44]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-clique-l3-s6/tests/check.py b/tasks/construct-mc-max-clique-l3-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3f70dbd5b155a3514c2102aa4ad460201495210
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s6/tests/check.py
@@ -0,0 +1,18 @@
+"""Clique of size >= k in a given graph (MathConstraint max_clique decision version, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"clique has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) not in E:
+            raise Invalid(f"vertices {u} and {v} are not adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-clique-l3-s6/tests/instance.json b/tasks/construct-mc-max-clique-l3-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..29baed4614a1cb290ec7547d7e7f3920db3ef3b7
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 46, "k": 7, "edges": [[0, 6], [0, 7], [0, 9], [0, 10], [0, 12], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 30], [0, 32], [0, 33], [0, 36], [0, 37], [0, 39], [0, 41], [0, 42], [0, 43], [0, 44], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [1, 14], [1, 15], [1, 18], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 34], [1, 35], [1, 36], [1, 37], [1, 38], [1, 41], [1, 42], [1, 43], [1, 44], [1, 45], [2, 3], [2, 4], [2, 7], [2, 8], [2, 9], [2, 13], [2, 14], [2, 15], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [2, 34], [2, 36], [2, 39], [2, 40], [2, 41], [3, 5], [3, 7], [3, 8], [3, 10], [3, 12], [3, 13], [3, 14], [3, 16], [3, 18], [3, 19], [3, 21], [3, 22], [3, 24], [3, 27], [3, 28], [3, 29], [3, 32], [3, 33], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [3, 40], [3, 42], [3, 43], [3, 44], [4, 7], [4, 11], [4, 12], [4, 13], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [4, 23], [4, 24], [4, 25], [4, 26], [4, 30], [4, 31], [4, 32], [4, 33], [4, 34], [4, 35], [4, 36], [4, 37], [4, 38], [4, 39], [4, 40], [4, 41], [4, 44], [4, 45], [5, 6], [5, 8], [5, 9], [5, 10], [5, 18], [5, 20], [5, 21], [5, 22], [5, 23], [5, 25], [5, 26], [5, 27], [5, 28], [5, 29], [5, 30], [5, 33], [5, 36], [5, 38], [5, 39], [5, 40], [5, 41], [5, 42], [5, 43], [5, 44], [5, 45], [6, 7], [6, 10], [6, 11], [6, 12], [6, 14], [6, 16], [6, 18], [6, 19], [6, 20], [6, 23], [6, 25], [6, 27], [6, 28], [6, 31], [6, 33], [6, 34], [6, 36], [6, 37], [6, 40], [6, 42], [6, 43], [6, 45], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 14], [7, 15], [7, 16], [7, 18], [7, 23], [7, 29], [7, 31], [7, 32], [7, 33], [7, 34], [7, 35], [7, 39], [7, 40], [7, 43], [7, 44], [8, 12], [8, 13], [8, 14], [8, 18], [8, 20], [8, 23], [8, 24], [8, 25], [8, 27], [8, 28], [8, 29], [8, 32], [8, 34], [8, 37], [8, 38], [8, 39], [8, 40], [8, 41], [8, 43], [8, 45], [9, 11], [9, 12], [9, 14], [9, 15], [9, 16], [9, 18], [9, 19], [9, 20], [9, 24], [9, 27], [9, 28], [9, 29], [9, 31], [9, 32], [9, 34], [9, 36], [9, 37], [9, 38], [9, 39], [9, 40], [9, 41], [9, 42], [9, 43], [9, 44], [10, 12], [10, 14], [10, 15], [10, 17], [10, 20], [10, 21], [10, 22], [10, 28], [10, 32], [10, 33], [10, 35], [10, 37], [10, 38], [10, 40], [10, 43], [11, 12], [11, 13], [11, 14], [11, 19], [11, 20], [11, 21], [11, 25], [11, 26], [11, 27], [11, 28], [11, 30], [11, 31], [11, 32], [11, 33], [11, 36], [11, 37], [11, 39], [11, 41], [11, 42], [11, 43], [11, 45], [12, 14], [12, 15], [12, 16], [12, 18], [12, 19], [12, 20], [12, 22], [12, 23], [12, 24], [12, 25], [12, 26], [12, 27], [12, 28], [12, 31], [12, 32], [12, 33], [12, 34], [12, 35], [12, 38], [12, 40], [12, 41], [12, 42], [12, 43], [12, 44], [12, 45], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [13, 22], [13, 24], [13, 27], [13, 28], [13, 29], [13, 30], [13, 31], [13, 32], [13, 35], [13, 36], [13, 37], [13, 38], [13, 39], [13, 40], [13, 41], [13, 42], [13, 43], [13, 45], [14, 15], [14, 16], [14, 17], [14, 19], [14, 21], [14, 23], [14, 25], [14, 26], [14, 29], [14, 32], [14, 33], [14, 36], [14, 37], [14, 44], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 25], [15, 26], [15, 28], [15, 29], [15, 30], [15, 32], [15, 34], [15, 35], [15, 36], [15, 37], [15, 39], [15, 40], [15, 41], [15, 43], [15, 44], [15, 45], [16, 18], [16, 21], [16, 22], [16, 23], [16, 25], [16, 26], [16, 29], [16, 31], [16, 32], [16, 34], [16, 35], [16, 36], [16, 38], [16, 39], [16, 41], [16, 43], [16, 44], [16, 45], [17, 18], [17, 19], [17, 24], [17, 25], [17, 27], [17, 28], [17, 29], [17, 30], [17, 31], [17, 32], [17, 33], [17, 36], [17, 37], [17, 39], [17, 40], [17, 41], [17, 42], [17, 43], [17, 44], [17, 45], [18, 19], [18, 22], [18, 23], [18, 25], [18, 28], [18, 29], [18, 30], [18, 32], [18, 33], [18, 34], [18, 35], [18, 37], [18, 38], [18, 42], [18, 43], [18, 45], [19, 21], [19, 23], [19, 24], [19, 26], [19, 27], [19, 28], [19, 29], [19, 30], [19, 31], [19, 32], [19, 33], [19, 34], [19, 35], [19, 38], [19, 39], [19, 41], [19, 42], [20, 23], [20, 25], [20, 26], [20, 27], [20, 28], [20, 31], [20, 33], [20, 35], [20, 36], [20, 39], [20, 40], [20, 41], [20, 43], [20, 44], [20, 45], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 29], [21, 31], [21, 33], [21, 34], [21, 35], [21, 40], [21, 41], [21, 42], [21, 43], [21, 44], [21, 45], [22, 26], [22, 28], [22, 31], [22, 32], [22, 33], [22, 35], [22, 36], [22, 38], [22, 41], [22, 42], [22, 43], [22, 44], [22, 45], [23, 24], [23, 28], [23, 29], [23, 30], [23, 31], [23, 32], [23, 33], [23, 34], [23, 36], [23, 37], [23, 40], [23, 42], [24, 25], [24, 26], [24, 28], [24, 31], [24, 32], [24, 33], [24, 34], [24, 35], [24, 36], [24, 37], [24, 38], [24, 39], [24, 42], [24, 43], [24, 44], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 33], [25, 34], [25, 36], [25, 41], [25, 42], [25, 45], [26, 27], [26, 28], [26, 29], [26, 31], [26, 32], [26, 33], [26, 34], [26, 37], [26, 40], [26, 41], [26, 43], [26, 45], [27, 29], [27, 31], [27, 32], [27, 33], [27, 34], [27, 38], [27, 39], [27, 40], [27, 41], [27, 43], [27, 45], [28, 29], [28, 30], [28, 31], [28, 32], [28, 35], [28, 37], [28, 39], [28, 40], [28, 42], [28, 43], [28, 44], [28, 45], [29, 30], [29, 33], [29, 35], [29, 36], [29, 37], [29, 38], [29, 41], [29, 44], [29, 45], [30, 31], [30, 32], [30, 34], [30, 37], [30, 38], [30, 42], [30, 44], [31, 32], [31, 33], [31, 34], [31, 35], [31, 36], [31, 38], [31, 39], [31, 40], [31, 41], [31, 42], [32, 33], [32, 34], [32, 35], [32, 37], [32, 38], [32, 40], [32, 41], [32, 43], [32, 44], [32, 45], [33, 34], [33, 35], [33, 37], [33, 38], [33, 39], [33, 40], [33, 41], [33, 43], [33, 44], [33, 45], [34, 35], [34, 38], [34, 39], [34, 41], [34, 44], [35, 36], [35, 37], [35, 38], [35, 39], [35, 40], [35, 41], [35, 42], [35, 44], [36, 39], [36, 40], [36, 41], [36, 42], [36, 43], [36, 45], [37, 40], [37, 41], [37, 43], [37, 45], [38, 39], [38, 41], [38, 43], [38, 44], [38, 45], [39, 40], [39, 41], [39, 42], [39, 43], [39, 44], [39, 45], [40, 41], [40, 42], [40, 43], [40, 44], [41, 42], [41, 44], [41, 45], [42, 43], [42, 44], [43, 44]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l3-s6/tests/run.py b/tasks/construct-mc-max-clique-l3-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-clique-l3-s6/tests/test.sh b/tasks/construct-mc-max-clique-l3-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l3-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l3-s1/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l3-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l3-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l3-s1/environment/instance.json b/tasks/construct-mc-max-independent-set-l3-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..87deca068a1fee58be7ee0f2769d248426362312
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l3-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 45, "k": 11, "edges": [[0, 11], [0, 16], [0, 17], [0, 19], [0, 22], [0, 25], [0, 26], [0, 27], [0, 31], [0, 32], [0, 34], [0, 36], [0, 37], [0, 40], [0, 44], [1, 2], [1, 4], [1, 10], [1, 11], [1, 14], [1, 18], [1, 19], [1, 20], [1, 21], [1, 28], [1, 30], [1, 37], [1, 39], [1, 40], [1, 42], [2, 3], [2, 7], [2, 13], [2, 14], [2, 18], [2, 22], [2, 33], [2, 37], [2, 41], [2, 43], [3, 4], [3, 14], [3, 16], [3, 19], [3, 22], [3, 25], [3, 32], [3, 34], [3, 37], [3, 39], [3, 42], [3, 43], [4, 7], [4, 9], [4, 12], [4, 22], [4, 24], [4, 29], [4, 30], [4, 39], [4, 43], [5, 6], [5, 7], [5, 12], [5, 14], [5, 27], [5, 28], [5, 30], [5, 35], [5, 37], [5, 39], [6, 8], [6, 9], [6, 15], [6, 18], [6, 19], [6, 27], [6, 36], [6, 40], [6, 41], [6, 44], [7, 8], [7, 9], [7, 11], [7, 14], [7, 16], [7, 17], [7, 20], [7, 25], [7, 28], [7, 29], [7, 31], [7, 39], [8, 21], [8, 28], [8, 30], [8, 31], [8, 35], [8, 36], [8, 38], [8, 39], [8, 42], [8, 43], [9, 12], [9, 14], [9, 16], [9, 20], [9, 21], [9, 31], [9, 37], [9, 38], [10, 13], [10, 18], [10, 23], [10, 38], [10, 42], [11, 13], [11, 15], [11, 16], [11, 19], [11, 23], [11, 24], [11, 25], [11, 31], [11, 35], [11, 38], [11, 43], [12, 13], [12, 19], [12, 20], [12, 23], [12, 24], [12, 28], [12, 30], [12, 32], [12, 33], [12, 38], [12, 39], [12, 40], [12, 41], [12, 44], [13, 21], [13, 32], [14, 17], [14, 18], [14, 30], [14, 32], [14, 33], [14, 35], [14, 37], [14, 42], [14, 44], [15, 18], [15, 19], [15, 30], [15, 31], [15, 32], [15, 35], [15, 37], [16, 22], [16, 24], [16, 26], [16, 30], [16, 35], [16, 37], [16, 41], [17, 22], [17, 23], [17, 26], [17, 38], [17, 41], [18, 20], [18, 24], [18, 29], [18, 31], [18, 33], [18, 37], [19, 20], [19, 21], [19, 24], [19, 32], [19, 40], [19, 41], [19, 42], [20, 29], [20, 30], [20, 31], [20, 43], [21, 23], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 33], [21, 41], [21, 42], [22, 28], [22, 29], [22, 31], [22, 39], [22, 44], [23, 28], [23, 29], [23, 31], [23, 34], [23, 36], [23, 38], [23, 41], [23, 42], [23, 43], [24, 25], [24, 27], [24, 30], [24, 32], [24, 40], [24, 43], [25, 27], [25, 33], [25, 34], [25, 39], [25, 43], [26, 30], [26, 31], [26, 36], [26, 39], [26, 42], [26, 44], [27, 32], [27, 34], [27, 38], [28, 32], [28, 33], [28, 34], [28, 38], [28, 44], [29, 33], [29, 36], [29, 38], [29, 40], [29, 41], [29, 42], [30, 34], [30, 36], [30, 41], [31, 32], [31, 33], [31, 36], [31, 41], [31, 42], [32, 34], [32, 39], [32, 43], [33, 38], [33, 39], [33, 42], [34, 37], [34, 38], [34, 41], [35, 36], [35, 38], [36, 37], [36, 41], [37, 38], [37, 41], [38, 39], [38, 42], [40, 43], [42, 43], [42, 44]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l3-s1/solution/solve.sh b/tasks/construct-mc-max-independent-set-l3-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..80bc74b54c7869aa28158ff5199b3b11d40ccca6
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l3-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [2, 4, 5, 10, 11, 17, 20, 34, 36, 40, 44]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l3-s1/tests/check.py b/tasks/construct-mc-max-independent-set-l3-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l3-s1/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l3-s1/tests/instance.json b/tasks/construct-mc-max-independent-set-l3-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..87deca068a1fee58be7ee0f2769d248426362312
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l3-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 45, "k": 11, "edges": [[0, 11], [0, 16], [0, 17], [0, 19], [0, 22], [0, 25], [0, 26], [0, 27], [0, 31], [0, 32], [0, 34], [0, 36], [0, 37], [0, 40], [0, 44], [1, 2], [1, 4], [1, 10], [1, 11], [1, 14], [1, 18], [1, 19], [1, 20], [1, 21], [1, 28], [1, 30], [1, 37], [1, 39], [1, 40], [1, 42], [2, 3], [2, 7], [2, 13], [2, 14], [2, 18], [2, 22], [2, 33], [2, 37], [2, 41], [2, 43], [3, 4], [3, 14], [3, 16], [3, 19], [3, 22], [3, 25], [3, 32], [3, 34], [3, 37], [3, 39], [3, 42], [3, 43], [4, 7], [4, 9], [4, 12], [4, 22], [4, 24], [4, 29], [4, 30], [4, 39], [4, 43], [5, 6], [5, 7], [5, 12], [5, 14], [5, 27], [5, 28], [5, 30], [5, 35], [5, 37], [5, 39], [6, 8], [6, 9], [6, 15], [6, 18], [6, 19], [6, 27], [6, 36], [6, 40], [6, 41], [6, 44], [7, 8], [7, 9], [7, 11], [7, 14], [7, 16], [7, 17], [7, 20], [7, 25], [7, 28], [7, 29], [7, 31], [7, 39], [8, 21], [8, 28], [8, 30], [8, 31], [8, 35], [8, 36], [8, 38], [8, 39], [8, 42], [8, 43], [9, 12], [9, 14], [9, 16], [9, 20], [9, 21], [9, 31], [9, 37], [9, 38], [10, 13], [10, 18], [10, 23], [10, 38], [10, 42], [11, 13], [11, 15], [11, 16], [11, 19], [11, 23], [11, 24], [11, 25], [11, 31], [11, 35], [11, 38], [11, 43], [12, 13], [12, 19], [12, 20], [12, 23], [12, 24], [12, 28], [12, 30], [12, 32], [12, 33], [12, 38], [12, 39], [12, 40], [12, 41], [12, 44], [13, 21], [13, 32], [14, 17], [14, 18], [14, 30], [14, 32], [14, 33], [14, 35], [14, 37], [14, 42], [14, 44], [15, 18], [15, 19], [15, 30], [15, 31], [15, 32], [15, 35], [15, 37], [16, 22], [16, 24], [16, 26], [16, 30], [16, 35], [16, 37], [16, 41], [17, 22], [17, 23], [17, 26], [17, 38], [17, 41], [18, 20], [18, 24], [18, 29], [18, 31], [18, 33], [18, 37], [19, 20], [19, 21], [19, 24], [19, 32], [19, 40], [19, 41], [19, 42], [20, 29], [20, 30], [20, 31], [20, 43], [21, 23], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 33], [21, 41], [21, 42], [22, 28], [22, 29], [22, 31], [22, 39], [22, 44], [23, 28], [23, 29], [23, 31], [23, 34], [23, 36], [23, 38], [23, 41], [23, 42], [23, 43], [24, 25], [24, 27], [24, 30], [24, 32], [24, 40], [24, 43], [25, 27], [25, 33], [25, 34], [25, 39], [25, 43], [26, 30], [26, 31], [26, 36], [26, 39], [26, 42], [26, 44], [27, 32], [27, 34], [27, 38], [28, 32], [28, 33], [28, 34], [28, 38], [28, 44], [29, 33], [29, 36], [29, 38], [29, 40], [29, 41], [29, 42], [30, 34], [30, 36], [30, 41], [31, 32], [31, 33], [31, 36], [31, 41], [31, 42], [32, 34], [32, 39], [32, 43], [33, 38], [33, 39], [33, 42], [34, 37], [34, 38], [34, 41], [35, 36], [35, 38], [36, 37], [36, 41], [37, 38], [37, 41], [38, 39], [38, 42], [40, 43], [42, 43], [42, 44]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l3-s1/tests/run.py b/tasks/construct-mc-max-independent-set-l3-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l3-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-independent-set-l3-s1/tests/test.sh b/tasks/construct-mc-max-independent-set-l3-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l3-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l4-s2/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l4-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l4-s2/environment/instance.json b/tasks/construct-mc-max-independent-set-l4-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..752c2e51e798d878d09176d562844a5105de8e14
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 14, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 13], [0, 14], [0, 16], [0, 19], [0, 21], [0, 24], [0, 26], [0, 32], [0, 40], [0, 42], [0, 43], [0, 45], [0, 59], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 20], [1, 22], [1, 28], [1, 31], [1, 46], [1, 52], [1, 54], [1, 57], [2, 3], [2, 4], [2, 11], [2, 14], [2, 19], [2, 26], [2, 27], [2, 28], [2, 30], [2, 46], [2, 47], [2, 48], [2, 49], [2, 51], [2, 56], [2, 58], [3, 4], [3, 7], [3, 12], [3, 15], [3, 17], [3, 18], [3, 21], [3, 22], [3, 31], [3, 35], [3, 36], [3, 37], [3, 45], [3, 51], [3, 53], [3, 54], [3, 56], [3, 58], [4, 5], [4, 14], [4, 17], [4, 19], [4, 22], [4, 23], [4, 29], [4, 30], [4, 31], [4, 32], [4, 36], [4, 40], [4, 43], [4, 48], [4, 49], [4, 54], [4, 55], [4, 57], [5, 9], [5, 10], [5, 17], [5, 18], [5, 19], [5, 20], [5, 23], [5, 30], [5, 31], [5, 33], [5, 35], [5, 36], [5, 37], [5, 38], [5, 39], [5, 43], [5, 48], [5, 56], [5, 58], [6, 7], [6, 9], [6, 16], [6, 18], [6, 20], [6, 23], [6, 26], [6, 31], [6, 41], [6, 46], [6, 47], [6, 54], [6, 59], [7, 12], [7, 16], [7, 18], [7, 24], [7, 27], [7, 30], [7, 31], [7, 36], [7, 38], [7, 44], [7, 45], [7, 49], [7, 50], [7, 53], [7, 55], [7, 57], [8, 12], [8, 23], [8, 24], [8, 27], [8, 32], [8, 34], [8, 36], [8, 41], [8, 43], [8, 44], [8, 47], [8, 50], [8, 51], [8, 55], [8, 56], [8, 58], [8, 59], [9, 13], [9, 15], [9, 21], [9, 26], [9, 28], [9, 30], [9, 45], [9, 47], [9, 50], [10, 19], [10, 21], [10, 25], [10, 38], [10, 58], [11, 24], [11, 34], [11, 38], [11, 41], [11, 45], [11, 49], [11, 53], [11, 59], [12, 16], [12, 25], [12, 26], [12, 29], [12, 42], [12, 48], [12, 55], [12, 57], [12, 59], [13, 17], [13, 30], [13, 35], [13, 36], [13, 40], [13, 44], [13, 46], [13, 47], [13, 53], [13, 55], [14, 15], [14, 17], [14, 18], [14, 20], [14, 23], [14, 24], [14, 25], [14, 26], [14, 29], [14, 33], [14, 36], [14, 37], [14, 39], [14, 41], [14, 43], [14, 47], [14, 53], [14, 58], [15, 17], [15, 19], [15, 26], [15, 27], [15, 28], [15, 38], [15, 40], [15, 47], [15, 49], [15, 50], [15, 51], [15, 55], [15, 57], [16, 24], [16, 26], [16, 33], [16, 34], [16, 37], [16, 38], [16, 39], [16, 40], [16, 46], [16, 47], [16, 51], [16, 52], [16, 55], [16, 57], [17, 18], [17, 20], [17, 25], [17, 28], [17, 33], [17, 35], [17, 39], [17, 40], [17, 43], [17, 47], [17, 53], [17, 54], [17, 59], [18, 20], [18, 21], [18, 23], [18, 24], [18, 27], [18, 28], [18, 31], [18, 43], [18, 58], [19, 25], [19, 31], [19, 32], [19, 36], [19, 45], [19, 47], [19, 51], [19, 53], [19, 54], [19, 56], [19, 57], [19, 58], [19, 59], [20, 23], [20, 40], [20, 43], [20, 45], [20, 46], [20, 47], [20, 49], [21, 22], [21, 26], [21, 32], [21, 38], [21, 39], [21, 45], [21, 51], [21, 54], [21, 59], [22, 24], [22, 30], [22, 36], [22, 37], [22, 38], [22, 43], [22, 48], [22, 50], [22, 56], [22, 57], [22, 58], [23, 25], [23, 27], [23, 28], [23, 30], [23, 34], [23, 35], [23, 36], [23, 40], [23, 49], [23, 50], [23, 53], [23, 55], [23, 56], [24, 29], [24, 38], [24, 39], [24, 47], [24, 51], [24, 54], [24, 55], [24, 58], [24, 59], [25, 26], [25, 29], [25, 31], [25, 32], [25, 39], [25, 44], [25, 45], [25, 47], [25, 52], [25, 55], [25, 57], [26, 27], [26, 28], [26, 31], [26, 39], [26, 41], [26, 46], [26, 47], [26, 48], [26, 50], [26, 51], [26, 58], [27, 37], [27, 38], [27, 41], [27, 43], [27, 44], [27, 46], [27, 49], [27, 57], [28, 29], [28, 34], [28, 35], [28, 40], [28, 42], [28, 46], [28, 51], [28, 54], [28, 56], [28, 58], [29, 33], [29, 43], [29, 44], [29, 46], [29, 51], [29, 52], [29, 53], [29, 57], [30, 31], [30, 32], [30, 35], [30, 36], [30, 37], [30, 42], [30, 43], [30, 47], [30, 51], [31, 32], [31, 37], [31, 38], [31, 41], [31, 44], [31, 46], [31, 50], [31, 57], [32, 33], [32, 36], [32, 43], [32, 47], [32, 55], [32, 58], [33, 47], [33, 49], [33, 53], [33, 59], [34, 37], [34, 39], [34, 42], [34, 49], [34, 51], [34, 52], [34, 57], [35, 38], [35, 39], [35, 41], [35, 43], [35, 45], [35, 49], [35, 50], [35, 57], [35, 58], [36, 38], [36, 42], [36, 44], [36, 51], [36, 52], [36, 53], [36, 54], [36, 56], [37, 40], [37, 41], [37, 42], [37, 46], [37, 48], [37, 55], [37, 56], [37, 58], [38, 42], [38, 44], [38, 45], [38, 47], [38, 52], [38, 54], [38, 55], [39, 40], [39, 50], [39, 52], [39, 53], [39, 54], [39, 56], [40, 41], [40, 48], [40, 56], [40, 59], [41, 46], [41, 49], [41, 51], [41, 56], [42, 48], [42, 53], [43, 50], [43, 54], [43, 57], [43, 59], [44, 54], [44, 55], [45, 49], [45, 52], [45, 57], [46, 53], [46, 56], [47, 49], [47, 51], [47, 53], [47, 54], [48, 50], [48, 54], [48, 59], [49, 50], [49, 51], [49, 53], [49, 58], [50, 58], [51, 52], [51, 53], [51, 54], [51, 57], [52, 56], [52, 57], [53, 54], [53, 55], [54, 57], [55, 56], [55, 58], [56, 58]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l4-s2/solution/solve.sh b/tasks/construct-mc-max-independent-set-l4-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c593d687676732799ff1cf484b1a41e204af8e51
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [2, 10, 13, 15, 16, 18, 22, 29, 32, 41, 42, 45, 54, 59]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l4-s2/tests/check.py b/tasks/construct-mc-max-independent-set-l4-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s2/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l4-s2/tests/instance.json b/tasks/construct-mc-max-independent-set-l4-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..752c2e51e798d878d09176d562844a5105de8e14
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 14, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 13], [0, 14], [0, 16], [0, 19], [0, 21], [0, 24], [0, 26], [0, 32], [0, 40], [0, 42], [0, 43], [0, 45], [0, 59], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 20], [1, 22], [1, 28], [1, 31], [1, 46], [1, 52], [1, 54], [1, 57], [2, 3], [2, 4], [2, 11], [2, 14], [2, 19], [2, 26], [2, 27], [2, 28], [2, 30], [2, 46], [2, 47], [2, 48], [2, 49], [2, 51], [2, 56], [2, 58], [3, 4], [3, 7], [3, 12], [3, 15], [3, 17], [3, 18], [3, 21], [3, 22], [3, 31], [3, 35], [3, 36], [3, 37], [3, 45], [3, 51], [3, 53], [3, 54], [3, 56], [3, 58], [4, 5], [4, 14], [4, 17], [4, 19], [4, 22], [4, 23], [4, 29], [4, 30], [4, 31], [4, 32], [4, 36], [4, 40], [4, 43], [4, 48], [4, 49], [4, 54], [4, 55], [4, 57], [5, 9], [5, 10], [5, 17], [5, 18], [5, 19], [5, 20], [5, 23], [5, 30], [5, 31], [5, 33], [5, 35], [5, 36], [5, 37], [5, 38], [5, 39], [5, 43], [5, 48], [5, 56], [5, 58], [6, 7], [6, 9], [6, 16], [6, 18], [6, 20], [6, 23], [6, 26], [6, 31], [6, 41], [6, 46], [6, 47], [6, 54], [6, 59], [7, 12], [7, 16], [7, 18], [7, 24], [7, 27], [7, 30], [7, 31], [7, 36], [7, 38], [7, 44], [7, 45], [7, 49], [7, 50], [7, 53], [7, 55], [7, 57], [8, 12], [8, 23], [8, 24], [8, 27], [8, 32], [8, 34], [8, 36], [8, 41], [8, 43], [8, 44], [8, 47], [8, 50], [8, 51], [8, 55], [8, 56], [8, 58], [8, 59], [9, 13], [9, 15], [9, 21], [9, 26], [9, 28], [9, 30], [9, 45], [9, 47], [9, 50], [10, 19], [10, 21], [10, 25], [10, 38], [10, 58], [11, 24], [11, 34], [11, 38], [11, 41], [11, 45], [11, 49], [11, 53], [11, 59], [12, 16], [12, 25], [12, 26], [12, 29], [12, 42], [12, 48], [12, 55], [12, 57], [12, 59], [13, 17], [13, 30], [13, 35], [13, 36], [13, 40], [13, 44], [13, 46], [13, 47], [13, 53], [13, 55], [14, 15], [14, 17], [14, 18], [14, 20], [14, 23], [14, 24], [14, 25], [14, 26], [14, 29], [14, 33], [14, 36], [14, 37], [14, 39], [14, 41], [14, 43], [14, 47], [14, 53], [14, 58], [15, 17], [15, 19], [15, 26], [15, 27], [15, 28], [15, 38], [15, 40], [15, 47], [15, 49], [15, 50], [15, 51], [15, 55], [15, 57], [16, 24], [16, 26], [16, 33], [16, 34], [16, 37], [16, 38], [16, 39], [16, 40], [16, 46], [16, 47], [16, 51], [16, 52], [16, 55], [16, 57], [17, 18], [17, 20], [17, 25], [17, 28], [17, 33], [17, 35], [17, 39], [17, 40], [17, 43], [17, 47], [17, 53], [17, 54], [17, 59], [18, 20], [18, 21], [18, 23], [18, 24], [18, 27], [18, 28], [18, 31], [18, 43], [18, 58], [19, 25], [19, 31], [19, 32], [19, 36], [19, 45], [19, 47], [19, 51], [19, 53], [19, 54], [19, 56], [19, 57], [19, 58], [19, 59], [20, 23], [20, 40], [20, 43], [20, 45], [20, 46], [20, 47], [20, 49], [21, 22], [21, 26], [21, 32], [21, 38], [21, 39], [21, 45], [21, 51], [21, 54], [21, 59], [22, 24], [22, 30], [22, 36], [22, 37], [22, 38], [22, 43], [22, 48], [22, 50], [22, 56], [22, 57], [22, 58], [23, 25], [23, 27], [23, 28], [23, 30], [23, 34], [23, 35], [23, 36], [23, 40], [23, 49], [23, 50], [23, 53], [23, 55], [23, 56], [24, 29], [24, 38], [24, 39], [24, 47], [24, 51], [24, 54], [24, 55], [24, 58], [24, 59], [25, 26], [25, 29], [25, 31], [25, 32], [25, 39], [25, 44], [25, 45], [25, 47], [25, 52], [25, 55], [25, 57], [26, 27], [26, 28], [26, 31], [26, 39], [26, 41], [26, 46], [26, 47], [26, 48], [26, 50], [26, 51], [26, 58], [27, 37], [27, 38], [27, 41], [27, 43], [27, 44], [27, 46], [27, 49], [27, 57], [28, 29], [28, 34], [28, 35], [28, 40], [28, 42], [28, 46], [28, 51], [28, 54], [28, 56], [28, 58], [29, 33], [29, 43], [29, 44], [29, 46], [29, 51], [29, 52], [29, 53], [29, 57], [30, 31], [30, 32], [30, 35], [30, 36], [30, 37], [30, 42], [30, 43], [30, 47], [30, 51], [31, 32], [31, 37], [31, 38], [31, 41], [31, 44], [31, 46], [31, 50], [31, 57], [32, 33], [32, 36], [32, 43], [32, 47], [32, 55], [32, 58], [33, 47], [33, 49], [33, 53], [33, 59], [34, 37], [34, 39], [34, 42], [34, 49], [34, 51], [34, 52], [34, 57], [35, 38], [35, 39], [35, 41], [35, 43], [35, 45], [35, 49], [35, 50], [35, 57], [35, 58], [36, 38], [36, 42], [36, 44], [36, 51], [36, 52], [36, 53], [36, 54], [36, 56], [37, 40], [37, 41], [37, 42], [37, 46], [37, 48], [37, 55], [37, 56], [37, 58], [38, 42], [38, 44], [38, 45], [38, 47], [38, 52], [38, 54], [38, 55], [39, 40], [39, 50], [39, 52], [39, 53], [39, 54], [39, 56], [40, 41], [40, 48], [40, 56], [40, 59], [41, 46], [41, 49], [41, 51], [41, 56], [42, 48], [42, 53], [43, 50], [43, 54], [43, 57], [43, 59], [44, 54], [44, 55], [45, 49], [45, 52], [45, 57], [46, 53], [46, 56], [47, 49], [47, 51], [47, 53], [47, 54], [48, 50], [48, 54], [48, 59], [49, 50], [49, 51], [49, 53], [49, 58], [50, 58], [51, 52], [51, 53], [51, 54], [51, 57], [52, 56], [52, 57], [53, 54], [53, 55], [54, 57], [55, 56], [55, 58], [56, 58]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l4-s2/tests/run.py b/tasks/construct-mc-max-independent-set-l4-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-independent-set-l4-s2/tests/test.sh b/tasks/construct-mc-max-independent-set-l4-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l4-s5/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l4-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l4-s5/environment/instance.json b/tasks/construct-mc-max-independent-set-l4-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ac83e2eb7301dc2c2410b3141d671e2a5cca66d7
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 14, "edges": [[0, 1], [0, 5], [0, 10], [0, 16], [0, 18], [0, 21], [0, 22], [0, 25], [0, 31], [0, 33], [0, 34], [0, 40], [0, 54], [0, 57], [0, 59], [1, 7], [1, 10], [1, 11], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 27], [1, 28], [1, 31], [1, 33], [1, 39], [1, 41], [1, 43], [1, 47], [1, 48], [1, 54], [2, 4], [2, 8], [2, 12], [2, 13], [2, 15], [2, 17], [2, 23], [2, 24], [2, 27], [2, 31], [2, 33], [2, 34], [2, 38], [2, 41], [2, 42], [2, 43], [2, 47], [2, 49], [2, 51], [2, 54], [2, 57], [2, 59], [3, 4], [3, 21], [3, 28], [3, 30], [3, 33], [3, 35], [3, 37], [3, 42], [3, 44], [3, 47], [3, 48], [3, 49], [3, 50], [3, 51], [3, 54], [3, 55], [3, 56], [3, 57], [4, 6], [4, 7], [4, 12], [4, 25], [4, 30], [4, 34], [4, 40], [4, 44], [4, 45], [4, 46], [4, 47], [5, 17], [5, 20], [5, 21], [5, 22], [5, 24], [5, 25], [5, 26], [5, 30], [5, 31], [5, 36], [5, 37], [5, 39], [5, 51], [5, 52], [5, 55], [5, 56], [6, 7], [6, 9], [6, 15], [6, 16], [6, 18], [6, 20], [6, 21], [6, 23], [6, 27], [6, 33], [6, 36], [6, 37], [6, 38], [6, 42], [6, 44], [6, 45], [6, 47], [6, 52], [6, 53], [6, 59], [7, 11], [7, 12], [7, 15], [7, 16], [7, 20], [7, 21], [7, 25], [7, 26], [7, 32], [7, 33], [7, 40], [7, 42], [7, 47], [7, 49], [7, 55], [7, 56], [7, 59], [8, 9], [8, 10], [8, 11], [8, 13], [8, 14], [8, 18], [8, 22], [8, 26], [8, 35], [8, 40], [8, 42], [8, 44], [8, 53], [9, 11], [9, 12], [9, 14], [9, 15], [9, 18], [9, 22], [9, 25], [9, 32], [9, 34], [9, 38], [9, 42], [9, 46], [9, 49], [9, 55], [10, 11], [10, 17], [10, 18], [10, 21], [10, 24], [10, 25], [10, 26], [10, 34], [10, 35], [10, 38], [10, 39], [10, 41], [10, 48], [10, 49], [10, 54], [10, 56], [11, 15], [11, 21], [11, 26], [11, 27], [11, 29], [11, 31], [11, 34], [11, 36], [11, 37], [11, 43], [11, 48], [11, 55], [11, 57], [11, 58], [12, 14], [12, 15], [12, 17], [12, 20], [12, 30], [12, 32], [12, 35], [12, 36], [12, 40], [12, 43], [12, 47], [12, 49], [12, 51], [12, 54], [12, 55], [12, 59], [13, 14], [13, 16], [13, 18], [13, 19], [13, 23], [13, 29], [13, 31], [13, 34], [13, 39], [13, 42], [13, 46], [13, 47], [13, 51], [13, 53], [13, 55], [13, 56], [14, 18], [14, 29], [14, 31], [14, 38], [14, 44], [14, 49], [14, 53], [15, 16], [15, 18], [15, 24], [15, 27], [15, 31], [15, 32], [15, 35], [15, 48], [15, 50], [15, 52], [15, 55], [16, 18], [16, 25], [16, 33], [16, 39], [16, 52], [16, 53], [16, 56], [17, 18], [17, 20], [17, 22], [17, 24], [17, 27], [17, 35], [17, 45], [17, 48], [18, 20], [18, 22], [18, 23], [18, 24], [18, 36], [18, 47], [18, 57], [19, 25], [19, 27], [19, 28], [19, 32], [19, 35], [19, 39], [19, 40], [19, 48], [20, 25], [20, 27], [20, 28], [20, 39], [20, 41], [20, 43], [20, 44], [20, 46], [20, 48], [20, 51], [20, 53], [20, 59], [21, 22], [21, 30], [21, 31], [21, 39], [21, 45], [21, 47], [21, 52], [21, 57], [22, 44], [22, 47], [22, 48], [22, 55], [22, 56], [23, 30], [23, 33], [23, 35], [23, 36], [23, 37], [23, 39], [23, 40], [23, 41], [23, 42], [23, 47], [23, 49], [23, 52], [23, 56], [23, 57], [24, 30], [24, 33], [24, 34], [24, 35], [24, 37], [24, 42], [24, 43], [24, 47], [24, 48], [24, 59], [25, 32], [25, 36], [25, 38], [25, 40], [25, 42], [25, 44], [25, 45], [25, 48], [25, 49], [25, 50], [25, 55], [25, 57], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 34], [26, 39], [26, 41], [26, 43], [26, 55], [26, 56], [27, 31], [27, 36], [27, 39], [27, 41], [27, 47], [27, 48], [27, 53], [27, 54], [27, 57], [28, 29], [28, 34], [28, 48], [28, 54], [28, 56], [29, 36], [29, 37], [29, 41], [29, 42], [29, 50], [29, 56], [30, 34], [30, 40], [30, 42], [30, 43], [30, 46], [30, 47], [30, 49], [30, 55], [31, 34], [31, 36], [31, 38], [31, 44], [31, 47], [31, 49], [31, 51], [31, 54], [31, 55], [31, 57], [32, 35], [32, 45], [32, 52], [32, 55], [32, 56], [33, 39], [33, 41], [33, 44], [33, 46], [33, 51], [33, 54], [33, 57], [34, 35], [34, 39], [34, 42], [34, 46], [34, 47], [34, 51], [34, 53], [35, 37], [35, 38], [35, 39], [35, 41], [35, 45], [35, 49], [35, 54], [35, 58], [36, 39], [36, 41], [36, 44], [36, 48], [36, 57], [37, 42], [37, 47], [37, 52], [37, 56], [38, 44], [38, 50], [38, 52], [38, 59], [39, 41], [39, 42], [39, 47], [39, 51], [39, 55], [39, 56], [40, 41], [40, 47], [40, 48], [40, 49], [40, 55], [41, 42], [41, 43], [41, 45], [41, 46], [41, 47], [41, 51], [41, 53], [41, 55], [41, 58], [41, 59], [42, 46], [42, 54], [42, 55], [42, 59], [43, 44], [43, 48], [43, 53], [43, 54], [43, 55], [44, 46], [44, 47], [44, 51], [44, 55], [44, 56], [45, 48], [45, 51], [45, 55], [45, 58], [46, 47], [46, 48], [46, 51], [46, 52], [46, 53], [46, 58], [47, 50], [47, 58], [48, 49], [48, 50], [48, 52], [48, 57], [48, 59], [49, 52], [49, 53], [49, 54], [49, 57], [50, 53], [51, 56], [51, 57], [52, 53], [52, 55], [52, 57], [53, 58], [54, 55], [54, 59], [55, 57], [56, 58], [57, 58]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l4-s5/solution/solve.sh b/tasks/construct-mc-max-independent-set-l4-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..84bab6f20c74cce14545e552dbbbddb27f293f43
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [4, 8, 16, 17, 19, 21, 36, 37, 49, 50, 51, 55, 58, 59]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l4-s5/tests/check.py b/tasks/construct-mc-max-independent-set-l4-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s5/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l4-s5/tests/instance.json b/tasks/construct-mc-max-independent-set-l4-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ac83e2eb7301dc2c2410b3141d671e2a5cca66d7
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 14, "edges": [[0, 1], [0, 5], [0, 10], [0, 16], [0, 18], [0, 21], [0, 22], [0, 25], [0, 31], [0, 33], [0, 34], [0, 40], [0, 54], [0, 57], [0, 59], [1, 7], [1, 10], [1, 11], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 27], [1, 28], [1, 31], [1, 33], [1, 39], [1, 41], [1, 43], [1, 47], [1, 48], [1, 54], [2, 4], [2, 8], [2, 12], [2, 13], [2, 15], [2, 17], [2, 23], [2, 24], [2, 27], [2, 31], [2, 33], [2, 34], [2, 38], [2, 41], [2, 42], [2, 43], [2, 47], [2, 49], [2, 51], [2, 54], [2, 57], [2, 59], [3, 4], [3, 21], [3, 28], [3, 30], [3, 33], [3, 35], [3, 37], [3, 42], [3, 44], [3, 47], [3, 48], [3, 49], [3, 50], [3, 51], [3, 54], [3, 55], [3, 56], [3, 57], [4, 6], [4, 7], [4, 12], [4, 25], [4, 30], [4, 34], [4, 40], [4, 44], [4, 45], [4, 46], [4, 47], [5, 17], [5, 20], [5, 21], [5, 22], [5, 24], [5, 25], [5, 26], [5, 30], [5, 31], [5, 36], [5, 37], [5, 39], [5, 51], [5, 52], [5, 55], [5, 56], [6, 7], [6, 9], [6, 15], [6, 16], [6, 18], [6, 20], [6, 21], [6, 23], [6, 27], [6, 33], [6, 36], [6, 37], [6, 38], [6, 42], [6, 44], [6, 45], [6, 47], [6, 52], [6, 53], [6, 59], [7, 11], [7, 12], [7, 15], [7, 16], [7, 20], [7, 21], [7, 25], [7, 26], [7, 32], [7, 33], [7, 40], [7, 42], [7, 47], [7, 49], [7, 55], [7, 56], [7, 59], [8, 9], [8, 10], [8, 11], [8, 13], [8, 14], [8, 18], [8, 22], [8, 26], [8, 35], [8, 40], [8, 42], [8, 44], [8, 53], [9, 11], [9, 12], [9, 14], [9, 15], [9, 18], [9, 22], [9, 25], [9, 32], [9, 34], [9, 38], [9, 42], [9, 46], [9, 49], [9, 55], [10, 11], [10, 17], [10, 18], [10, 21], [10, 24], [10, 25], [10, 26], [10, 34], [10, 35], [10, 38], [10, 39], [10, 41], [10, 48], [10, 49], [10, 54], [10, 56], [11, 15], [11, 21], [11, 26], [11, 27], [11, 29], [11, 31], [11, 34], [11, 36], [11, 37], [11, 43], [11, 48], [11, 55], [11, 57], [11, 58], [12, 14], [12, 15], [12, 17], [12, 20], [12, 30], [12, 32], [12, 35], [12, 36], [12, 40], [12, 43], [12, 47], [12, 49], [12, 51], [12, 54], [12, 55], [12, 59], [13, 14], [13, 16], [13, 18], [13, 19], [13, 23], [13, 29], [13, 31], [13, 34], [13, 39], [13, 42], [13, 46], [13, 47], [13, 51], [13, 53], [13, 55], [13, 56], [14, 18], [14, 29], [14, 31], [14, 38], [14, 44], [14, 49], [14, 53], [15, 16], [15, 18], [15, 24], [15, 27], [15, 31], [15, 32], [15, 35], [15, 48], [15, 50], [15, 52], [15, 55], [16, 18], [16, 25], [16, 33], [16, 39], [16, 52], [16, 53], [16, 56], [17, 18], [17, 20], [17, 22], [17, 24], [17, 27], [17, 35], [17, 45], [17, 48], [18, 20], [18, 22], [18, 23], [18, 24], [18, 36], [18, 47], [18, 57], [19, 25], [19, 27], [19, 28], [19, 32], [19, 35], [19, 39], [19, 40], [19, 48], [20, 25], [20, 27], [20, 28], [20, 39], [20, 41], [20, 43], [20, 44], [20, 46], [20, 48], [20, 51], [20, 53], [20, 59], [21, 22], [21, 30], [21, 31], [21, 39], [21, 45], [21, 47], [21, 52], [21, 57], [22, 44], [22, 47], [22, 48], [22, 55], [22, 56], [23, 30], [23, 33], [23, 35], [23, 36], [23, 37], [23, 39], [23, 40], [23, 41], [23, 42], [23, 47], [23, 49], [23, 52], [23, 56], [23, 57], [24, 30], [24, 33], [24, 34], [24, 35], [24, 37], [24, 42], [24, 43], [24, 47], [24, 48], [24, 59], [25, 32], [25, 36], [25, 38], [25, 40], [25, 42], [25, 44], [25, 45], [25, 48], [25, 49], [25, 50], [25, 55], [25, 57], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 34], [26, 39], [26, 41], [26, 43], [26, 55], [26, 56], [27, 31], [27, 36], [27, 39], [27, 41], [27, 47], [27, 48], [27, 53], [27, 54], [27, 57], [28, 29], [28, 34], [28, 48], [28, 54], [28, 56], [29, 36], [29, 37], [29, 41], [29, 42], [29, 50], [29, 56], [30, 34], [30, 40], [30, 42], [30, 43], [30, 46], [30, 47], [30, 49], [30, 55], [31, 34], [31, 36], [31, 38], [31, 44], [31, 47], [31, 49], [31, 51], [31, 54], [31, 55], [31, 57], [32, 35], [32, 45], [32, 52], [32, 55], [32, 56], [33, 39], [33, 41], [33, 44], [33, 46], [33, 51], [33, 54], [33, 57], [34, 35], [34, 39], [34, 42], [34, 46], [34, 47], [34, 51], [34, 53], [35, 37], [35, 38], [35, 39], [35, 41], [35, 45], [35, 49], [35, 54], [35, 58], [36, 39], [36, 41], [36, 44], [36, 48], [36, 57], [37, 42], [37, 47], [37, 52], [37, 56], [38, 44], [38, 50], [38, 52], [38, 59], [39, 41], [39, 42], [39, 47], [39, 51], [39, 55], [39, 56], [40, 41], [40, 47], [40, 48], [40, 49], [40, 55], [41, 42], [41, 43], [41, 45], [41, 46], [41, 47], [41, 51], [41, 53], [41, 55], [41, 58], [41, 59], [42, 46], [42, 54], [42, 55], [42, 59], [43, 44], [43, 48], [43, 53], [43, 54], [43, 55], [44, 46], [44, 47], [44, 51], [44, 55], [44, 56], [45, 48], [45, 51], [45, 55], [45, 58], [46, 47], [46, 48], [46, 51], [46, 52], [46, 53], [46, 58], [47, 50], [47, 58], [48, 49], [48, 50], [48, 52], [48, 57], [48, 59], [49, 52], [49, 53], [49, 54], [49, 57], [50, 53], [51, 56], [51, 57], [52, 53], [52, 55], [52, 57], [53, 58], [54, 55], [54, 59], [55, 57], [56, 58], [57, 58]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l4-s5/tests/run.py b/tasks/construct-mc-max-independent-set-l4-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-independent-set-l4-s5/tests/test.sh b/tasks/construct-mc-max-independent-set-l4-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-number-partitioning-l4-s1/environment/Dockerfile b/tasks/construct-mc-number-partitioning-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l4-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-number-partitioning-l4-s1/environment/instance.json b/tasks/construct-mc-number-partitioning-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..530bfac619daf84c246f61871ae7cd6be8243344
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 27, "k": 3, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l4-s1/solution/solve.sh b/tasks/construct-mc-number-partitioning-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e4770a0dbbb103e4e84cf72fa374a83104504734
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l4-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-number-partitioning-l4-s1/tests/check.py b/tasks/construct-mc-number-partitioning-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..67793721db8ba7d3c3979ea0e1e07091491ffa7e
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l4-s1/tests/check.py
@@ -0,0 +1,14 @@
+"""Partition {1..n} into k subsets of equal sum (MathConstraint number_partitioning, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    x = int_list(ans.get("x"), n, 0, k - 1, "x")
+    target = n * (n + 1) // 2 // k
+    sums = [0] * k
+    for i, s in enumerate(x):
+        sums[s] += i + 1
+    if any(t != target for t in sums):
+        raise Invalid(f"subset sums {sums} are not all {target}")
+    return None, {}
diff --git a/tasks/construct-mc-number-partitioning-l4-s1/tests/instance.json b/tasks/construct-mc-number-partitioning-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..530bfac619daf84c246f61871ae7cd6be8243344
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 27, "k": 3, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l4-s1/tests/run.py b/tasks/construct-mc-number-partitioning-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l4-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-number-partitioning-l4-s1/tests/test.sh b/tasks/construct-mc-number-partitioning-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l4-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-ortholatin-l6-s1/environment/Dockerfile b/tasks/construct-mc-ortholatin-l6-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l6-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-ortholatin-l6-s1/environment/instance.json b/tasks/construct-mc-ortholatin-l6-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e609b56dff83c71d5c78f5c435d67f214f524bec
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l6-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 24, "family": "mc_ortholatin", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ortholatin-l6-s1/solution/solve.sh b/tasks/construct-mc-ortholatin-l6-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6ecb215b41cf68d88d773bcd2b2e534160790ec6
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l6-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16, 17, 15, 19, 20, 18, 22, 23, 21], [2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10, 14, 12, 13, 17, 15, 16, 20, 18, 19, 23, 21, 22], [3, 4, 5, 0, 1, 2, 9, 10, 11, 6, 7, 8, 15, 16, 17, 12, 13, 14, 21, 22, 23, 18, 19, 20], [4, 5, 3, 1, 2, 0, 10, 11, 9, 7, 8, 6, 16, 17, 15, 13, 14, 12, 22, 23, 21, 19, 20, 18], [5, 3, 4, 2, 0, 1, 11, 9, 10, 8, 6, 7, 17, 15, 16, 14, 12, 13, 23, 21, 22, 20, 18, 19], [6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [7, 8, 6, 10, 11, 9, 1, 2, 0, 4, 5, 3, 19, 20, 18, 22, 23, 21, 13, 14, 12, 16, 17, 15], [8, 6, 7, 11, 9, 10, 2, 0, 1, 5, 3, 4, 20, 18, 19, 23, 21, 22, 14, 12, 13, 17, 15, 16], [9, 10, 11, 6, 7, 8, 3, 4, 5, 0, 1, 2, 21, 22, 23, 18, 19, 20, 15, 16, 17, 12, 13, 14], [10, 11, 9, 7, 8, 6, 4, 5, 3, 1, 2, 0, 22, 23, 21, 19, 20, 18, 16, 17, 15, 13, 14, 12], [11, 9, 10, 8, 6, 7, 5, 3, 4, 2, 0, 1, 23, 21, 22, 20, 18, 19, 17, 15, 16, 14, 12, 13], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 12, 16, 17, 15, 19, 20, 18, 22, 23, 21, 1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9], [14, 12, 13, 17, 15, 16, 20, 18, 19, 23, 21, 22, 2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10], [15, 16, 17, 12, 13, 14, 21, 22, 23, 18, 19, 20, 3, 4, 5, 0, 1, 2, 9, 10, 11, 6, 7, 8], [16, 17, 15, 13, 14, 12, 22, 23, 21, 19, 20, 18, 4, 5, 3, 1, 2, 0, 10, 11, 9, 7, 8, 6], [17, 15, 16, 14, 12, 13, 23, 21, 22, 20, 18, 19, 5, 3, 4, 2, 0, 1, 11, 9, 10, 8, 6, 7], [18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5], [19, 20, 18, 22, 23, 21, 13, 14, 12, 16, 17, 15, 7, 8, 6, 10, 11, 9, 1, 2, 0, 4, 5, 3], [20, 18, 19, 23, 21, 22, 14, 12, 13, 17, 15, 16, 8, 6, 7, 11, 9, 10, 2, 0, 1, 5, 3, 4], [21, 22, 23, 18, 19, 20, 15, 16, 17, 12, 13, 14, 9, 10, 11, 6, 7, 8, 3, 4, 5, 0, 1, 2], [22, 23, 21, 19, 20, 18, 16, 17, 15, 13, 14, 12, 10, 11, 9, 7, 8, 6, 4, 5, 3, 1, 2, 0], [23, 21, 22, 20, 18, 19, 17, 15, 16, 14, 12, 13, 11, 9, 10, 8, 6, 7, 5, 3, 4, 2, 0, 1]], "Y": [[0, 2, 1, 3, 5, 4, 6, 8, 7, 9, 11, 10, 12, 14, 13, 15, 17, 16, 18, 20, 19, 21, 23, 22], [1, 0, 2, 4, 3, 5, 7, 6, 8, 10, 9, 11, 13, 12, 14, 16, 15, 17, 19, 18, 20, 22, 21, 23], [2, 1, 0, 5, 4, 3, 8, 7, 6, 11, 10, 9, 14, 13, 12, 17, 16, 15, 20, 19, 18, 23, 22, 21], [6, 8, 7, 9, 11, 10, 0, 2, 1, 3, 5, 4, 18, 20, 19, 21, 23, 22, 12, 14, 13, 15, 17, 16], [7, 6, 8, 10, 9, 11, 1, 0, 2, 4, 3, 5, 19, 18, 20, 22, 21, 23, 13, 12, 14, 16, 15, 17], [8, 7, 6, 11, 10, 9, 2, 1, 0, 5, 4, 3, 20, 19, 18, 23, 22, 21, 14, 13, 12, 17, 16, 15], [12, 14, 13, 15, 17, 16, 18, 20, 19, 21, 23, 22, 0, 2, 1, 3, 5, 4, 6, 8, 7, 9, 11, 10], [13, 12, 14, 16, 15, 17, 19, 18, 20, 22, 21, 23, 1, 0, 2, 4, 3, 5, 7, 6, 8, 10, 9, 11], [14, 13, 12, 17, 16, 15, 20, 19, 18, 23, 22, 21, 2, 1, 0, 5, 4, 3, 8, 7, 6, 11, 10, 9], [18, 20, 19, 21, 23, 22, 12, 14, 13, 15, 17, 16, 6, 8, 7, 9, 11, 10, 0, 2, 1, 3, 5, 4], [19, 18, 20, 22, 21, 23, 13, 12, 14, 16, 15, 17, 7, 6, 8, 10, 9, 11, 1, 0, 2, 4, 3, 5], [20, 19, 18, 23, 22, 21, 14, 13, 12, 17, 16, 15, 8, 7, 6, 11, 10, 9, 2, 1, 0, 5, 4, 3], [9, 11, 10, 6, 8, 7, 3, 5, 4, 0, 2, 1, 21, 23, 22, 18, 20, 19, 15, 17, 16, 12, 14, 13], [10, 9, 11, 7, 6, 8, 4, 3, 5, 1, 0, 2, 22, 21, 23, 19, 18, 20, 16, 15, 17, 13, 12, 14], [11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [3, 5, 4, 0, 2, 1, 9, 11, 10, 6, 8, 7, 15, 17, 16, 12, 14, 13, 21, 23, 22, 18, 20, 19], [4, 3, 5, 1, 0, 2, 10, 9, 11, 7, 6, 8, 16, 15, 17, 13, 12, 14, 22, 21, 23, 19, 18, 20], [5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18], [21, 23, 22, 18, 20, 19, 15, 17, 16, 12, 14, 13, 9, 11, 10, 6, 8, 7, 3, 5, 4, 0, 2, 1], [22, 21, 23, 19, 18, 20, 16, 15, 17, 13, 12, 14, 10, 9, 11, 7, 6, 8, 4, 3, 5, 1, 0, 2], [23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0], [15, 17, 16, 12, 14, 13, 21, 23, 22, 18, 20, 19, 3, 5, 4, 0, 2, 1, 9, 11, 10, 6, 8, 7], [16, 15, 17, 13, 12, 14, 22, 21, 23, 19, 18, 20, 4, 3, 5, 1, 0, 2, 10, 9, 11, 7, 6, 8], [17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ortholatin-l6-s1/tests/check.py b/tasks/construct-mc-ortholatin-l6-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5418a59fae1c86318eee903e90d75b36d8a3306
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l6-s1/tests/check.py
@@ -0,0 +1,25 @@
+"""Pair of orthogonal Latin squares of order n (MathConstraint ortholatin, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def _square(v, n, name):
+    if not isinstance(v, list) or len(v) != n:
+        raise Invalid(f"{name} must be a list of {n} rows")
+    S = [int_list(r, n, 0, n - 1, f"{name} row") for r in v]
+    full = list(range(n))
+    for i in range(n):
+        if sorted(S[i]) != full:
+            raise Invalid(f"{name}: row {i} is not a permutation of 0..{n - 1}")
+        if sorted(S[r][i] for r in range(n)) != full:
+            raise Invalid(f"{name}: column {i} is not a permutation of 0..{n - 1}")
+    return S
+
+
+def check(inst, ans):
+    n = inst["n"]
+    X = _square(ans.get("X"), n, "X")
+    Y = _square(ans.get("Y"), n, "Y")
+    pairs = {(X[i][j], Y[i][j]) for i in range(n) for j in range(n)}
+    if len(pairs) != n * n:
+        raise Invalid("X and Y are not orthogonal (some ordered pair repeats)")
+    return None, {}
diff --git a/tasks/construct-mc-ortholatin-l6-s1/tests/instance.json b/tasks/construct-mc-ortholatin-l6-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e609b56dff83c71d5c78f5c435d67f214f524bec
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l6-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 24, "family": "mc_ortholatin", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ortholatin-l6-s1/tests/run.py b/tasks/construct-mc-ortholatin-l6-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l6-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-ortholatin-l6-s1/tests/test.sh b/tasks/construct-mc-ortholatin-l6-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l6-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l2-s0/environment/Dockerfile b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l2-s0/environment/instance.json b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c26cd06d95850f86bf53fca0e92fffc24f130c2b
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 15, "required_edges": [], "max_chromatic_number": 5, "min_edges": 10, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l2-s0/solution/solve.sh b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ba0a0e451ed96e6080af029e5d2627b86a9c851c
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14]], "coloring": [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/check.py b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/instance.json b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c26cd06d95850f86bf53fca0e92fffc24f130c2b
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 15, "required_edges": [], "max_chromatic_number": 5, "min_edges": 10, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/run.py b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/test.sh b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l2-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-degree-bounds-l2-s0/environment/Dockerfile b/tasks/construct-mc-pysms-degree-bounds-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-degree-bounds-l2-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-degree-bounds-l2-s0/environment/instance.json b/tasks/construct-mc-pysms-degree-bounds-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7e681edec1fe03c22e9a5fd4f096c16b23a30b1d
--- /dev/null
+++ b/tasks/construct-mc-pysms-degree-bounds-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 11, "required_edges": [[2, 8], [2, 6], [2, 10], [3, 8], [0, 10]], "max_degree": 5, "min_degree": 1, "family": "mc_pysms_degree_bounds", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-degree-bounds-l2-s0/solution/solve.sh b/tasks/construct-mc-pysms-degree-bounds-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7253b74e07ee8ae2e02ba7e4bd9370f597e88307
--- /dev/null
+++ b/tasks/construct-mc-pysms-degree-bounds-l2-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 7], [0, 8], [0, 9], [0, 10], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 5], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 8], [4, 9], [4, 10], [5, 6], [5, 7]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/check.py b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/instance.json b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7e681edec1fe03c22e9a5fd4f096c16b23a30b1d
--- /dev/null
+++ b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 11, "required_edges": [[2, 8], [2, 6], [2, 10], [3, 8], [0, 10]], "max_degree": 5, "min_degree": 1, "family": "mc_pysms_degree_bounds", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/run.py b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/test.sh b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-degree-bounds-l2-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-girth-degree-l1-s2/environment/Dockerfile b/tasks/construct-mc-pysms-girth-degree-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l1-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-girth-degree-l1-s2/environment/instance.json b/tasks/construct-mc-pysms-girth-degree-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..080d67234ad3bf2da9c9d18f15844f3b8578dcfa
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 10, "required_edges": [], "max_degree": 3, "min_degree": 2, "min_girth": 5, "family": "mc_pysms_girth_degree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-girth-degree-l1-s2/solution/solve.sh b/tasks/construct-mc-pysms-girth-degree-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..167c50fb47d85c02d46de183e91659859551915c
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l1-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 8], [0, 9], [1, 7], [1, 9], [2, 6], [2, 9], [3, 6], [3, 7], [3, 8], [4, 5], [4, 8], [5, 7]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/check.py b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/instance.json b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..080d67234ad3bf2da9c9d18f15844f3b8578dcfa
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 10, "required_edges": [], "max_degree": 3, "min_degree": 2, "min_girth": 5, "family": "mc_pysms_girth_degree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/run.py b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/test.sh b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l1-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-min-degree-l5-s0/environment/Dockerfile b/tasks/construct-mc-pysms-min-degree-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-degree-l5-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-min-degree-l5-s0/environment/instance.json b/tasks/construct-mc-pysms-min-degree-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ee57ed110ab8b2d79f903cdc59204bc341ace2df
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-degree-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 18, "required_edges": [[3, 15], [11, 13], [13, 17], [2, 11], [11, 17], [2, 12], [7, 17], [9, 17], [3, 5], [0, 16], [1, 14], [7, 9], [0, 9], [6, 11], [3, 11], [0, 2], [1, 17], [4, 8], [5, 15], [1, 15], [2, 15], [15, 17], [4, 16], [0, 8], [4, 6], [8, 13], [13, 14], [2, 10], [6, 13], [9, 12]], "min_degree": 5, "family": "mc_pysms_min_degree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-degree-l5-s0/solution/solve.sh b/tasks/construct-mc-pysms-min-degree-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..eb6e7062cc9837f07c0c2fa725d985e6483a6394
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-degree-l5-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 17], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 17], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [13, 14], [13, 15], [13, 16], [13, 17], [14, 15], [14, 16], [14, 17], [15, 16], [15, 17], [16, 17]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-min-degree-l5-s0/tests/check.py b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-min-degree-l5-s0/tests/instance.json b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ee57ed110ab8b2d79f903cdc59204bc341ace2df
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 18, "required_edges": [[3, 15], [11, 13], [13, 17], [2, 11], [11, 17], [2, 12], [7, 17], [9, 17], [3, 5], [0, 16], [1, 14], [7, 9], [0, 9], [6, 11], [3, 11], [0, 2], [1, 17], [4, 8], [5, 15], [1, 15], [2, 15], [15, 17], [4, 16], [0, 8], [4, 6], [8, 13], [13, 14], [2, 10], [6, 13], [9, 12]], "min_degree": 5, "family": "mc_pysms_min_degree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-degree-l5-s0/tests/run.py b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-min-degree-l5-s0/tests/test.sh b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-degree-l5-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s2/environment/Dockerfile b/tasks/construct-mc-pysms-min-girth-l4-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s2/environment/instance.json b/tasks/construct-mc-pysms-min-girth-l4-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..322b96282d34d7152826d2c428af7e7dac21b55b
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s2/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 17, "required_edges": [], "min_girth": 4, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s2/solution/solve.sh b/tasks/construct-mc-pysms-min-girth-l4-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5d1f37e5d69ab188c08f4a0aba571b2a79b84a86
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 16], [1, 16], [2, 16], [3, 16], [4, 16], [5, 16], [6, 16], [7, 16], [8, 16], [9, 16], [10, 16], [11, 16], [12, 16], [13, 16], [14, 16], [15, 16]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s2/tests/check.py b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s2/tests/instance.json b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..322b96282d34d7152826d2c428af7e7dac21b55b
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 17, "required_edges": [], "min_girth": 4, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s2/tests/run.py b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s2/tests/test.sh b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-quasigroup-idempotent-l1-s0/environment/Dockerfile b/tasks/construct-mc-quasigroup-idempotent-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-quasigroup-idempotent-l1-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-quasigroup-idempotent-l1-s0/environment/instance.json b/tasks/construct-mc-quasigroup-idempotent-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e76a28dd7ae5128cd50a4be1b1690240267b100d
--- /dev/null
+++ b/tasks/construct-mc-quasigroup-idempotent-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 4, "family": "mc_quasigroup_idempotent", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-quasigroup-idempotent-l1-s0/solution/solve.sh b/tasks/construct-mc-quasigroup-idempotent-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..82d1e6cfd8e1c5ff85e4283dae33f99e23a88a7c
--- /dev/null
+++ b/tasks/construct-mc-quasigroup-idempotent-l1-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"table": [[0, 3, 1, 2], [2, 1, 3, 0], [3, 0, 2, 1], [1, 2, 0, 3]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/check.py b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4563f2e9a90050cdd7c56dfc33831acde74c9ef2
--- /dev/null
+++ b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/check.py
@@ -0,0 +1,21 @@
+"""Idempotent quasigroup satisfying QG3, (x*y)*(y*x) = x (MathConstraint quasigroup_idempotent, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    T = ans.get("table")
+    if not isinstance(T, list) or len(T) != n:
+        raise Invalid(f"table must be a list of {n} rows")
+    T = [int_list(r, n, 0, n - 1, "table row") for r in T]
+    full = list(range(n))
+    for i in range(n):
+        if sorted(T[i]) != full or sorted(T[r][i] for r in range(n)) != full:
+            raise Invalid(f"row/column {i} is not a permutation (not a Latin square)")
+        if T[i][i] != i:
+            raise Invalid(f"not idempotent: {i}*{i} = {T[i][i]}")
+    for i in range(n):
+        for j in range(n):
+            if T[T[i][j]][T[j][i]] != i:
+                raise Invalid(f"QG3 fails for (x, y) = ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/instance.json b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e76a28dd7ae5128cd50a4be1b1690240267b100d
--- /dev/null
+++ b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 4, "family": "mc_quasigroup_idempotent", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/run.py b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/test.sh b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-quasigroup-idempotent-l1-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-ramsey-l3-s8/environment/Dockerfile b/tasks/construct-mc-ramsey-l3-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l3-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-ramsey-l3-s8/environment/instance.json b/tasks/construct-mc-ramsey-l3-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..316d0383a487ab0cc58644d613c8c18ca1bcef16
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l3-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 16, "r": 4, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l3-s8/solution/solve.sh b/tasks/construct-mc-ramsey-l3-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f4e87542501bc592a1b342c6158f83dcbc0c3d1b
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l3-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ramsey-l3-s8/tests/check.py b/tasks/construct-mc-ramsey-l3-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l3-s8/tests/check.py
@@ -0,0 +1,31 @@
+"""Two-colouring of the edges of K_n with no colour-0 K_r and no colour-1 K_s (MathConstraint ramsey,
+CC-BY-4.0). Adapted from pilot/grader.py check_ramsey; adds the optional fixed edge colours."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, r, s = inst["n"], inst["r"], inst["s"]
+    edges = list(itertools.combinations(range(n), 2))
+    col = int_list(ans.get("colors"), len(edges), 0, 1, "colors")
+    for name, i, v in inst.get("fixed", []):
+        if col[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    c = {e: col[i] for i, e in enumerate(edges)}
+    for k, colour in ((r, 0), (s, 1)):
+        adj = {v: {u for u in range(n) if u != v and c[(min(u, v), max(u, v))] == colour} for v in range(n)}
+
+        def grow(size, cand):
+            if size == k:
+                return True
+            if size + len(cand) < k:
+                return False
+            for v in sorted(cand):
+                if grow(size + 1, {u for u in cand if u > v} & adj[v]):
+                    return True
+            return False
+
+        if grow(0, set(range(n))):
+            raise Invalid(f"monochromatic K_{k} in colour {colour}")
+    return None, {}
diff --git a/tasks/construct-mc-ramsey-l3-s8/tests/instance.json b/tasks/construct-mc-ramsey-l3-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..316d0383a487ab0cc58644d613c8c18ca1bcef16
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l3-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 16, "r": 4, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l3-s8/tests/run.py b/tasks/construct-mc-ramsey-l3-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l3-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-ramsey-l3-s8/tests/test.sh b/tasks/construct-mc-ramsey-l3-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l3-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-ramsey-l4-s5/environment/Dockerfile b/tasks/construct-mc-ramsey-l4-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-ramsey-l4-s5/environment/instance.json b/tasks/construct-mc-ramsey-l4-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5884b315dafa8c26f6e83509210d29a762c531ad
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 19, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s5/solution/solve.sh b/tasks/construct-mc-ramsey-l4-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..25c054cd2e7076e6717cb776ddd0cb182851d385
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ramsey-l4-s5/tests/check.py b/tasks/construct-mc-ramsey-l4-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s5/tests/check.py
@@ -0,0 +1,31 @@
+"""Two-colouring of the edges of K_n with no colour-0 K_r and no colour-1 K_s (MathConstraint ramsey,
+CC-BY-4.0). Adapted from pilot/grader.py check_ramsey; adds the optional fixed edge colours."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, r, s = inst["n"], inst["r"], inst["s"]
+    edges = list(itertools.combinations(range(n), 2))
+    col = int_list(ans.get("colors"), len(edges), 0, 1, "colors")
+    for name, i, v in inst.get("fixed", []):
+        if col[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    c = {e: col[i] for i, e in enumerate(edges)}
+    for k, colour in ((r, 0), (s, 1)):
+        adj = {v: {u for u in range(n) if u != v and c[(min(u, v), max(u, v))] == colour} for v in range(n)}
+
+        def grow(size, cand):
+            if size == k:
+                return True
+            if size + len(cand) < k:
+                return False
+            for v in sorted(cand):
+                if grow(size + 1, {u for u in cand if u > v} & adj[v]):
+                    return True
+            return False
+
+        if grow(0, set(range(n))):
+            raise Invalid(f"monochromatic K_{k} in colour {colour}")
+    return None, {}
diff --git a/tasks/construct-mc-ramsey-l4-s5/tests/instance.json b/tasks/construct-mc-ramsey-l4-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5884b315dafa8c26f6e83509210d29a762c531ad
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 19, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s5/tests/run.py b/tasks/construct-mc-ramsey-l4-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-ramsey-l4-s5/tests/test.sh b/tasks/construct-mc-ramsey-l4-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-social-golfers-l2-s2/environment/Dockerfile b/tasks/construct-mc-social-golfers-l2-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l2-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-social-golfers-l2-s2/environment/instance.json b/tasks/construct-mc-social-golfers-l2-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..327bd0cebcd1bcb4e7576b287405e72f6aea830c
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l2-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n_groups": 9, "group_size": 3, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l2-s2/solution/solve.sh b/tasks/construct-mc-social-golfers-l2-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..005d1c3dfff77496849d5ec5897fbd39789ff90a
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l2-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8], [0, 1, 2, 2, 3, 4, 3, 4, 5, 3, 4, 5, 5, 6, 7, 6, 7, 8, 6, 8, 7, 1, 0, 2, 8, 1, 0], [1, 0, 2, 3, 2, 4, 3, 5, 4, 4, 3, 5, 6, 5, 7, 7, 8, 6, 8, 7, 6, 1, 8, 0, 1, 2, 0], [2, 3, 4, 3, 2, 4, 4, 5, 6, 5, 7, 8, 7, 6, 8, 7, 5, 6, 8, 0, 1, 0, 1, 2, 3, 1, 0], [2, 1, 3, 2, 4, 5, 6, 3, 4, 7, 8, 5, 6, 8, 7, 5, 8, 7, 6, 1, 0, 4, 1, 0, 0, 2, 3], [0, 1, 2, 3, 1, 0, 4, 1, 2, 3, 2, 4, 0, 3, 5, 6, 4, 7, 7, 8, 6, 6, 5, 8, 5, 8, 7]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-social-golfers-l2-s2/tests/check.py b/tasks/construct-mc-social-golfers-l2-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..73977815b7b6094a8491075b6dc2ae1293e44930
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l2-s2/tests/check.py
@@ -0,0 +1,25 @@
+"""Social golfer problem (MathConstraint social_golfers, CSPLib prob010, CC-BY-4.0): each week partition
+the g*s players into g groups of size s; no two players share a group in more than one week."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    g, s, w = inst["n_groups"], inst["group_size"], inst["n_weeks"]
+    P = g * s
+    sched = ans.get("schedule")
+    if not isinstance(sched, list) or len(sched) != w:
+        raise Invalid(f"schedule must be a list of {w} weeks")
+    met = set()
+    for wk, row in enumerate(sched):
+        row = int_list(row, P, 0, g - 1, f"week {wk}")
+        groups = [[p for p in range(P) if row[p] == grp] for grp in range(g)]
+        for grp, mem in enumerate(groups):
+            if len(mem) != s:
+                raise Invalid(f"week {wk}: group {grp} has {len(mem)} players, need {s}")
+            for i in range(s):
+                for j in range(i + 1, s):
+                    pr = (mem[i], mem[j])
+                    if pr in met:
+                        raise Invalid(f"players {pr} play together in more than one week")
+                    met.add(pr)
+    return None, {}
diff --git a/tasks/construct-mc-social-golfers-l2-s2/tests/instance.json b/tasks/construct-mc-social-golfers-l2-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..327bd0cebcd1bcb4e7576b287405e72f6aea830c
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l2-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n_groups": 9, "group_size": 3, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l2-s2/tests/run.py b/tasks/construct-mc-social-golfers-l2-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l2-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-social-golfers-l2-s2/tests/test.sh b/tasks/construct-mc-social-golfers-l2-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l2-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-social-golfers-l5-s1/environment/Dockerfile b/tasks/construct-mc-social-golfers-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l5-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-social-golfers-l5-s1/environment/instance.json b/tasks/construct-mc-social-golfers-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..96f60a74e9c90573744da99cf89df7493498bdf9
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n_groups": 8, "group_size": 4, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l5-s1/solution/solve.sh b/tasks/construct-mc-social-golfers-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d9149ee6fbdff33756ac05a1d40908745f836084
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l5-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"schedule": [[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7], [6, 4, 7, 2, 5, 1, 2, 4, 7, 5, 3, 0, 0, 6, 1, 2, 7, 3, 1, 0, 6, 4, 7, 5, 0, 1, 2, 3, 6, 5, 4, 3], [7, 5, 6, 4, 5, 3, 6, 0, 3, 7, 4, 6, 1, 0, 2, 7, 2, 0, 1, 3, 5, 4, 1, 2, 7, 4, 2, 1, 6, 0, 3, 5], [1, 0, 2, 6, 1, 3, 0, 2, 1, 2, 0, 4, 7, 3, 6, 4, 3, 6, 4, 5, 7, 5, 6, 0, 3, 7, 5, 1, 5, 7, 4, 2], [5, 1, 7, 3, 4, 2, 0, 5, 6, 1, 2, 3, 4, 3, 0, 2, 4, 6, 1, 5, 0, 4, 5, 7, 0, 6, 1, 7, 6, 2, 7, 3], [0, 5, 1, 2, 1, 3, 0, 2, 2, 3, 1, 5, 4, 1, 5, 7, 0, 4, 6, 7, 2, 6, 3, 7, 6, 7, 4, 5, 3, 6, 4, 0], [3, 7, 0, 4, 4, 3, 6, 2, 5, 6, 2, 3, 5, 7, 0, 1, 1, 6, 2, 0, 1, 6, 7, 5, 4, 7, 3, 1, 2, 0, 4, 5]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-social-golfers-l5-s1/tests/check.py b/tasks/construct-mc-social-golfers-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..73977815b7b6094a8491075b6dc2ae1293e44930
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l5-s1/tests/check.py
@@ -0,0 +1,25 @@
+"""Social golfer problem (MathConstraint social_golfers, CSPLib prob010, CC-BY-4.0): each week partition
+the g*s players into g groups of size s; no two players share a group in more than one week."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    g, s, w = inst["n_groups"], inst["group_size"], inst["n_weeks"]
+    P = g * s
+    sched = ans.get("schedule")
+    if not isinstance(sched, list) or len(sched) != w:
+        raise Invalid(f"schedule must be a list of {w} weeks")
+    met = set()
+    for wk, row in enumerate(sched):
+        row = int_list(row, P, 0, g - 1, f"week {wk}")
+        groups = [[p for p in range(P) if row[p] == grp] for grp in range(g)]
+        for grp, mem in enumerate(groups):
+            if len(mem) != s:
+                raise Invalid(f"week {wk}: group {grp} has {len(mem)} players, need {s}")
+            for i in range(s):
+                for j in range(i + 1, s):
+                    pr = (mem[i], mem[j])
+                    if pr in met:
+                        raise Invalid(f"players {pr} play together in more than one week")
+                    met.add(pr)
+    return None, {}
diff --git a/tasks/construct-mc-social-golfers-l5-s1/tests/instance.json b/tasks/construct-mc-social-golfers-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..96f60a74e9c90573744da99cf89df7493498bdf9
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n_groups": 8, "group_size": 4, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l5-s1/tests/run.py b/tasks/construct-mc-social-golfers-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l5-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-social-golfers-l5-s1/tests/test.sh b/tasks/construct-mc-social-golfers-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l5-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-van-der-waerden-l4-s7/environment/Dockerfile b/tasks/construct-mc-van-der-waerden-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l4-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-van-der-waerden-l4-s7/environment/instance.json b/tasks/construct-mc-van-der-waerden-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..50029443d55ba8cc8ceb3128fc6f516b5e9ee3dc
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"k": 3, "L": 4, "n": 80, "family": "mc_van_der_waerden", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-van-der-waerden-l4-s7/solution/solve.sh b/tasks/construct-mc-van-der-waerden-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..79315f39cfe7d3811a1cf7cdb45f0b675e492826
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l4-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 0, 2, 1, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-van-der-waerden-l4-s7/tests/check.py b/tasks/construct-mc-van-der-waerden-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..9853b089b6ac1773d80eac8e9e02ceb4019ad41f
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l4-s7/tests/check.py
@@ -0,0 +1,15 @@
+"""k-colouring of {1..n} with no monochromatic L-term arithmetic progression (MathConstraint
+van_der_waerden, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k, L = inst["n"], inst["k"], inst["L"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    for a in range(n):
+        for d in range(1, n):
+            if a + (L - 1) * d >= n:
+                break
+            if all(c[a + j * d] == c[a] for j in range(1, L)):
+                raise Invalid(f"monochromatic progression {[a + 1 + j * d for j in range(L)]}")
+    return None, {}
diff --git a/tasks/construct-mc-van-der-waerden-l4-s7/tests/instance.json b/tasks/construct-mc-van-der-waerden-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..50029443d55ba8cc8ceb3128fc6f516b5e9ee3dc
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"k": 3, "L": 4, "n": 80, "family": "mc_van_der_waerden", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-van-der-waerden-l4-s7/tests/run.py b/tasks/construct-mc-van-der-waerden-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l4-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-van-der-waerden-l4-s7/tests/test.sh b/tasks/construct-mc-van-der-waerden-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l4-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-vertex-cover-l1-s1/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-vertex-cover-l1-s1/environment/instance.json b/tasks/construct-mc-vertex-cover-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..171ff053c4812623b7c9557123031c3ec59f2740
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 11, "edges": [[0, 6], [1, 4], [1, 12], [2, 7], [3, 9], [3, 12], [3, 17], [3, 18], [4, 6], [4, 10], [4, 14], [5, 6], [5, 19], [6, 7], [6, 11], [6, 15], [6, 16], [7, 11], [7, 16], [7, 17], [8, 14], [8, 16], [9, 12], [9, 13], [9, 19], [10, 12], [10, 18], [12, 17], [13, 15], [13, 16], [15, 16]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l1-s1/solution/solve.sh b/tasks/construct-mc-vertex-cover-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ecc03877a8c2197fd5c02b488452bf7a508ef8d3
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [3, 4, 6, 7, 10, 12, 13, 14, 15, 16, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l1-s1/tests/check.py b/tasks/construct-mc-vertex-cover-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s1/tests/check.py
@@ -0,0 +1,16 @@
+"""Vertex cover of size <= k in a given graph (MathConstraint vertex_cover, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) > k:
+        raise Invalid(f"cover has {len(S)} vertices, at most {k} allowed")
+    C = set(S)
+    for u, v in inst["edges"]:
+        if u not in C and v not in C:
+            raise Invalid(f"edge ({u},{v}) is not covered")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-vertex-cover-l1-s1/tests/instance.json b/tasks/construct-mc-vertex-cover-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..171ff053c4812623b7c9557123031c3ec59f2740
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 11, "edges": [[0, 6], [1, 4], [1, 12], [2, 7], [3, 9], [3, 12], [3, 17], [3, 18], [4, 6], [4, 10], [4, 14], [5, 6], [5, 19], [6, 7], [6, 11], [6, 15], [6, 16], [7, 11], [7, 16], [7, 17], [8, 14], [8, 16], [9, 12], [9, 13], [9, 19], [10, 12], [10, 18], [12, 17], [13, 15], [13, 16], [15, 16]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l1-s1/tests/run.py b/tasks/construct-mc-vertex-cover-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-vertex-cover-l1-s1/tests/test.sh b/tasks/construct-mc-vertex-cover-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-vertex-cover-l1-s6/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l1-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-vertex-cover-l1-s6/environment/instance.json b/tasks/construct-mc-vertex-cover-l1-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..293fda8b2b3ded740968e08f3bd6385b8f5f4803
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 11, "edges": [[0, 2], [0, 7], [0, 13], [0, 15], [1, 5], [1, 7], [1, 10], [1, 17], [3, 6], [3, 12], [3, 16], [3, 19], [4, 6], [4, 18], [4, 19], [5, 6], [5, 12], [5, 17], [7, 11], [7, 19], [8, 10], [8, 11], [10, 12], [10, 16], [11, 16], [11, 17], [12, 13], [12, 16], [13, 16], [14, 18], [15, 19], [16, 17]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l1-s6/solution/solve.sh b/tasks/construct-mc-vertex-cover-l1-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..dea19085aa195063d360c7347d3af92448618b4e
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 1, 4, 6, 7, 8, 12, 16, 17, 18, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l1-s6/tests/check.py b/tasks/construct-mc-vertex-cover-l1-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s6/tests/check.py
@@ -0,0 +1,16 @@
+"""Vertex cover of size <= k in a given graph (MathConstraint vertex_cover, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) > k:
+        raise Invalid(f"cover has {len(S)} vertices, at most {k} allowed")
+    C = set(S)
+    for u, v in inst["edges"]:
+        if u not in C and v not in C:
+            raise Invalid(f"edge ({u},{v}) is not covered")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-vertex-cover-l1-s6/tests/instance.json b/tasks/construct-mc-vertex-cover-l1-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..293fda8b2b3ded740968e08f3bd6385b8f5f4803
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 11, "edges": [[0, 2], [0, 7], [0, 13], [0, 15], [1, 5], [1, 7], [1, 10], [1, 17], [3, 6], [3, 12], [3, 16], [3, 19], [4, 6], [4, 18], [4, 19], [5, 6], [5, 12], [5, 17], [7, 11], [7, 19], [8, 10], [8, 11], [10, 12], [10, 16], [11, 16], [11, 17], [12, 13], [12, 16], [13, 16], [14, 18], [15, 19], [16, 17]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l1-s6/tests/run.py b/tasks/construct-mc-vertex-cover-l1-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-vertex-cover-l1-s6/tests/test.sh b/tasks/construct-mc-vertex-cover-l1-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-vertex-cover-l1-s8/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l1-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-vertex-cover-l1-s8/environment/instance.json b/tasks/construct-mc-vertex-cover-l1-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..16ee1a5003266b538ffe1e1b7b1c7a4350eafd15
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 11, "edges": [[0, 4], [0, 7], [0, 9], [0, 10], [1, 17], [2, 8], [2, 11], [3, 15], [4, 6], [4, 7], [4, 12], [4, 19], [5, 13], [6, 12], [6, 18], [7, 11], [7, 16], [8, 16], [9, 12], [9, 13], [9, 15], [10, 13], [10, 18], [11, 12], [11, 13], [12, 17], [13, 14], [13, 19], [16, 17], [17, 19]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l1-s8/solution/solve.sh b/tasks/construct-mc-vertex-cover-l1-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c8cd8ddb7c5bb809a4f5765a180bee5136ed3171
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 1, 2, 4, 7, 12, 13, 15, 16, 18, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l1-s8/tests/check.py b/tasks/construct-mc-vertex-cover-l1-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s8/tests/check.py
@@ -0,0 +1,16 @@
+"""Vertex cover of size <= k in a given graph (MathConstraint vertex_cover, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) > k:
+        raise Invalid(f"cover has {len(S)} vertices, at most {k} allowed")
+    C = set(S)
+    for u, v in inst["edges"]:
+        if u not in C and v not in C:
+            raise Invalid(f"edge ({u},{v}) is not covered")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-vertex-cover-l1-s8/tests/instance.json b/tasks/construct-mc-vertex-cover-l1-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..16ee1a5003266b538ffe1e1b7b1c7a4350eafd15
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 11, "edges": [[0, 4], [0, 7], [0, 9], [0, 10], [1, 17], [2, 8], [2, 11], [3, 15], [4, 6], [4, 7], [4, 12], [4, 19], [5, 13], [6, 12], [6, 18], [7, 11], [7, 16], [8, 16], [9, 12], [9, 13], [9, 15], [10, 13], [10, 18], [11, 12], [11, 13], [12, 17], [13, 14], [13, 19], [16, 17], [17, 19]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l1-s8/tests/run.py b/tasks/construct-mc-vertex-cover-l1-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-vertex-cover-l1-s8/tests/test.sh b/tasks/construct-mc-vertex-cover-l1-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l1-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-vertex-cover-l5-s7/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l5-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-vertex-cover-l5-s7/environment/instance.json b/tasks/construct-mc-vertex-cover-l5-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ff6ac17bba87435db2aeef49daafbce7b8881879
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 2], [0, 5], [0, 6], [0, 22], [0, 26], [0, 46], [0, 54], [0, 55], [0, 60], [0, 83], [0, 84], [1, 4], [1, 11], [1, 12], [1, 19], [1, 20], [1, 36], [1, 42], [1, 44], [1, 53], [1, 54], [1, 55], [1, 56], [1, 58], [1, 62], [1, 73], [1, 79], [1, 83], [1, 84], [1, 86], [2, 18], [2, 28], [2, 33], [2, 44], [2, 57], [2, 75], [3, 5], [3, 7], [3, 23], [3, 27], [3, 31], [3, 35], [3, 39], [3, 42], [3, 52], [3, 59], [3, 62], [3, 64], [3, 70], [3, 87], [4, 9], [4, 18], [4, 19], [4, 42], [4, 43], [4, 58], [4, 60], [4, 63], [4, 71], [4, 72], [4, 73], [4, 74], [4, 81], [4, 84], [4, 86], [5, 10], [5, 13], [5, 18], [5, 23], [5, 28], [5, 34], [5, 42], [5, 46], [5, 50], [5, 53], [5, 54], [5, 60], [5, 62], [5, 72], [5, 73], [5, 79], [5, 84], [5, 87], [5, 88], [5, 89], [6, 9], [6, 10], [6, 12], [6, 14], [6, 17], [6, 24], [6, 25], [6, 27], [6, 32], [6, 35], [6, 47], [6, 51], [6, 52], [6, 60], [6, 67], [6, 69], [6, 76], [6, 82], [7, 26], [7, 39], [7, 41], [7, 42], [7, 78], [8, 17], [8, 40], [8, 48], [9, 12], [9, 13], [9, 17], [9, 21], [9, 22], [9, 24], [9, 28], [9, 35], [9, 49], [9, 50], [9, 52], [9, 61], [9, 71], [9, 73], [9, 79], [10, 44], [10, 47], [10, 51], [10, 53], [10, 63], [10, 69], [11, 14], [11, 22], [11, 26], [11, 38], [11, 44], [11, 59], [11, 61], [11, 82], [11, 85], [12, 18], [12, 19], [12, 36], [12, 37], [12, 42], [12, 44], [12, 47], [12, 51], [12, 67], [12, 72], [13, 26], [13, 35], [13, 36], [13, 51], [13, 66], [13, 78], [13, 79], [13, 81], [13, 84], [13, 86], [14, 15], [14, 26], [14, 30], [14, 34], [14, 39], [14, 44], [14, 76], [14, 77], [14, 81], [14, 82], [15, 22], [15, 50], [15, 51], [15, 52], [15, 53], [15, 54], [15, 69], [15, 83], [16, 22], [16, 37], [16, 54], [16, 56], [16, 73], [16, 79], [16, 84], [16, 85], [17, 21], [17, 22], [17, 43], [17, 54], [17, 75], [17, 86], [17, 88], [18, 32], [18, 34], [18, 37], [18, 41], [18, 50], [18, 55], [18, 56], [18, 69], [18, 82], [19, 26], [19, 27], [19, 28], [19, 46], [19, 77], [19, 86], [20, 40], [20, 57], [20, 86], [21, 22], [21, 29], [21, 34], [21, 44], [21, 46], [21, 50], [21, 60], [21, 67], [21, 75], [21, 81], [21, 89], [22, 25], [22, 27], [22, 55], [22, 56], [22, 62], [22, 72], [22, 74], [22, 75], [22, 82], [23, 34], [23, 43], [23, 45], [23, 49], [23, 58], [23, 63], [23, 67], [23, 74], [23, 89], [24, 25], [24, 26], [24, 31], [24, 32], [24, 35], [24, 50], [24, 61], [24, 69], [24, 77], [24, 78], [24, 81], [24, 85], [25, 31], [25, 32], [25, 48], [25, 54], [25, 76], [25, 80], [25, 84], [25, 89], [26, 29], [26, 39], [26, 40], [26, 46], [26, 49], [26, 59], [26, 61], [26, 63], [26, 70], [26, 71], [26, 88], [27, 42], [27, 52], [27, 60], [27, 65], [27, 66], [27, 86], [28, 30], [28, 38], [28, 43], [28, 45], [28, 49], [28, 56], [28, 58], [28, 71], [28, 75], [28, 82], [28, 86], [28, 87], [29, 31], [29, 34], [29, 36], [29, 38], [29, 39], [29, 43], [29, 46], [29, 51], [29, 52], [29, 68], [29, 77], [29, 84], [29, 87], [30, 31], [30, 37], [30, 39], [30, 41], [30, 44], [30, 48], [30, 49], [30, 52], [30, 56], [30, 57], [30, 63], [30, 78], [30, 83], [31, 32], [31, 42], [31, 44], [31, 45], [31, 58], [31, 63], [31, 65], [31, 73], [31, 81], [32, 33], [32, 36], [32, 37], [32, 39], [32, 41], [32, 51], [32, 59], [32, 76], [32, 81], [33, 51], [33, 53], [33, 54], [33, 65], [33, 66], [33, 78], [33, 80], [33, 81], [33, 88], [34, 37], [34, 41], [34, 43], [34, 47], [34, 48], [34, 63], [34, 75], [34, 77], [35, 41], [35, 58], [35, 67], [35, 73], [35, 81], [36, 38], [36, 51], [36, 58], [36, 60], [36, 64], [36, 66], [36, 80], [37, 39], [37, 56], [37, 58], [37, 61], [37, 66], [37, 69], [37, 81], [38, 48], [38, 52], [38, 67], [38, 68], [38, 74], [38, 76], [38, 78], [38, 80], [38, 84], [38, 85], [39, 43], [39, 47], [39, 48], [39, 49], [39, 50], [39, 55], [39, 63], [39, 69], [39, 74], [39, 81], [39, 82], [40, 44], [40, 50], [40, 54], [40, 56], [40, 58], [40, 68], [40, 69], [40, 73], [40, 88], [40, 89], [41, 49], [41, 54], [41, 62], [41, 63], [41, 67], [41, 89], [42, 46], [42, 58], [42, 65], [42, 66], [42, 69], [42, 77], [42, 82], [43, 50], [43, 59], [44, 45], [44, 61], [44, 65], [44, 67], [44, 72], [44, 74], [44, 78], [45, 76], [45, 86], [46, 60], [46, 77], [47, 57], [47, 58], [47, 70], [47, 71], [47, 73], [47, 75], [48, 52], [48, 56], [48, 71], [48, 78], [48, 80], [48, 84], [48, 86], [49, 50], [49, 58], [49, 77], [50, 52], [50, 71], [50, 73], [50, 85], [50, 86], [51, 61], [51, 86], [52, 73], [52, 75], [52, 80], [53, 57], [53, 58], [53, 77], [54, 58], [54, 60], [54, 63], [54, 72], [54, 74], [55, 74], [55, 84], [56, 58], [56, 60], [56, 61], [56, 67], [56, 70], [56, 75], [56, 76], [56, 80], [56, 88], [57, 67], [57, 69], [57, 70], [57, 73], [57, 74], [57, 86], [58, 62], [58, 64], [58, 65], [58, 68], [58, 74], [58, 78], [58, 81], [58, 85], [59, 80], [59, 81], [59, 84], [59, 89], [60, 62], [60, 63], [60, 83], [61, 75], [61, 79], [61, 82], [61, 87], [62, 67], [62, 85], [63, 73], [63, 81], [63, 88], [64, 88], [65, 68], [65, 69], [66, 71], [66, 73], [66, 77], [66, 86], [66, 88], [67, 69], [67, 74], [67, 77], [68, 85], [70, 71], [70, 80], [70, 81], [70, 86], [70, 88], [71, 72], [71, 73], [71, 79], [71, 81], [72, 74], [72, 89], [73, 75], [73, 78], [73, 79], [73, 82], [73, 89], [74, 77], [74, 84], [74, 87], [75, 76], [75, 79], [75, 85], [75, 89], [76, 83], [77, 83], [78, 83], [79, 85], [80, 88], [82, 87], [84, 89]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s7/solution/solve.sh b/tasks/construct-mc-vertex-cover-l5-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5c34b0cb4bf01363a44b9e84e082cb337ef85f57
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 1, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 48, 50, 54, 57, 58, 60, 61, 65, 67, 70, 71, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 89]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l5-s7/tests/check.py b/tasks/construct-mc-vertex-cover-l5-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s7/tests/check.py
@@ -0,0 +1,16 @@
+"""Vertex cover of size <= k in a given graph (MathConstraint vertex_cover, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) > k:
+        raise Invalid(f"cover has {len(S)} vertices, at most {k} allowed")
+    C = set(S)
+    for u, v in inst["edges"]:
+        if u not in C and v not in C:
+            raise Invalid(f"edge ({u},{v}) is not covered")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-vertex-cover-l5-s7/tests/instance.json b/tasks/construct-mc-vertex-cover-l5-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ff6ac17bba87435db2aeef49daafbce7b8881879
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 2], [0, 5], [0, 6], [0, 22], [0, 26], [0, 46], [0, 54], [0, 55], [0, 60], [0, 83], [0, 84], [1, 4], [1, 11], [1, 12], [1, 19], [1, 20], [1, 36], [1, 42], [1, 44], [1, 53], [1, 54], [1, 55], [1, 56], [1, 58], [1, 62], [1, 73], [1, 79], [1, 83], [1, 84], [1, 86], [2, 18], [2, 28], [2, 33], [2, 44], [2, 57], [2, 75], [3, 5], [3, 7], [3, 23], [3, 27], [3, 31], [3, 35], [3, 39], [3, 42], [3, 52], [3, 59], [3, 62], [3, 64], [3, 70], [3, 87], [4, 9], [4, 18], [4, 19], [4, 42], [4, 43], [4, 58], [4, 60], [4, 63], [4, 71], [4, 72], [4, 73], [4, 74], [4, 81], [4, 84], [4, 86], [5, 10], [5, 13], [5, 18], [5, 23], [5, 28], [5, 34], [5, 42], [5, 46], [5, 50], [5, 53], [5, 54], [5, 60], [5, 62], [5, 72], [5, 73], [5, 79], [5, 84], [5, 87], [5, 88], [5, 89], [6, 9], [6, 10], [6, 12], [6, 14], [6, 17], [6, 24], [6, 25], [6, 27], [6, 32], [6, 35], [6, 47], [6, 51], [6, 52], [6, 60], [6, 67], [6, 69], [6, 76], [6, 82], [7, 26], [7, 39], [7, 41], [7, 42], [7, 78], [8, 17], [8, 40], [8, 48], [9, 12], [9, 13], [9, 17], [9, 21], [9, 22], [9, 24], [9, 28], [9, 35], [9, 49], [9, 50], [9, 52], [9, 61], [9, 71], [9, 73], [9, 79], [10, 44], [10, 47], [10, 51], [10, 53], [10, 63], [10, 69], [11, 14], [11, 22], [11, 26], [11, 38], [11, 44], [11, 59], [11, 61], [11, 82], [11, 85], [12, 18], [12, 19], [12, 36], [12, 37], [12, 42], [12, 44], [12, 47], [12, 51], [12, 67], [12, 72], [13, 26], [13, 35], [13, 36], [13, 51], [13, 66], [13, 78], [13, 79], [13, 81], [13, 84], [13, 86], [14, 15], [14, 26], [14, 30], [14, 34], [14, 39], [14, 44], [14, 76], [14, 77], [14, 81], [14, 82], [15, 22], [15, 50], [15, 51], [15, 52], [15, 53], [15, 54], [15, 69], [15, 83], [16, 22], [16, 37], [16, 54], [16, 56], [16, 73], [16, 79], [16, 84], [16, 85], [17, 21], [17, 22], [17, 43], [17, 54], [17, 75], [17, 86], [17, 88], [18, 32], [18, 34], [18, 37], [18, 41], [18, 50], [18, 55], [18, 56], [18, 69], [18, 82], [19, 26], [19, 27], [19, 28], [19, 46], [19, 77], [19, 86], [20, 40], [20, 57], [20, 86], [21, 22], [21, 29], [21, 34], [21, 44], [21, 46], [21, 50], [21, 60], [21, 67], [21, 75], [21, 81], [21, 89], [22, 25], [22, 27], [22, 55], [22, 56], [22, 62], [22, 72], [22, 74], [22, 75], [22, 82], [23, 34], [23, 43], [23, 45], [23, 49], [23, 58], [23, 63], [23, 67], [23, 74], [23, 89], [24, 25], [24, 26], [24, 31], [24, 32], [24, 35], [24, 50], [24, 61], [24, 69], [24, 77], [24, 78], [24, 81], [24, 85], [25, 31], [25, 32], [25, 48], [25, 54], [25, 76], [25, 80], [25, 84], [25, 89], [26, 29], [26, 39], [26, 40], [26, 46], [26, 49], [26, 59], [26, 61], [26, 63], [26, 70], [26, 71], [26, 88], [27, 42], [27, 52], [27, 60], [27, 65], [27, 66], [27, 86], [28, 30], [28, 38], [28, 43], [28, 45], [28, 49], [28, 56], [28, 58], [28, 71], [28, 75], [28, 82], [28, 86], [28, 87], [29, 31], [29, 34], [29, 36], [29, 38], [29, 39], [29, 43], [29, 46], [29, 51], [29, 52], [29, 68], [29, 77], [29, 84], [29, 87], [30, 31], [30, 37], [30, 39], [30, 41], [30, 44], [30, 48], [30, 49], [30, 52], [30, 56], [30, 57], [30, 63], [30, 78], [30, 83], [31, 32], [31, 42], [31, 44], [31, 45], [31, 58], [31, 63], [31, 65], [31, 73], [31, 81], [32, 33], [32, 36], [32, 37], [32, 39], [32, 41], [32, 51], [32, 59], [32, 76], [32, 81], [33, 51], [33, 53], [33, 54], [33, 65], [33, 66], [33, 78], [33, 80], [33, 81], [33, 88], [34, 37], [34, 41], [34, 43], [34, 47], [34, 48], [34, 63], [34, 75], [34, 77], [35, 41], [35, 58], [35, 67], [35, 73], [35, 81], [36, 38], [36, 51], [36, 58], [36, 60], [36, 64], [36, 66], [36, 80], [37, 39], [37, 56], [37, 58], [37, 61], [37, 66], [37, 69], [37, 81], [38, 48], [38, 52], [38, 67], [38, 68], [38, 74], [38, 76], [38, 78], [38, 80], [38, 84], [38, 85], [39, 43], [39, 47], [39, 48], [39, 49], [39, 50], [39, 55], [39, 63], [39, 69], [39, 74], [39, 81], [39, 82], [40, 44], [40, 50], [40, 54], [40, 56], [40, 58], [40, 68], [40, 69], [40, 73], [40, 88], [40, 89], [41, 49], [41, 54], [41, 62], [41, 63], [41, 67], [41, 89], [42, 46], [42, 58], [42, 65], [42, 66], [42, 69], [42, 77], [42, 82], [43, 50], [43, 59], [44, 45], [44, 61], [44, 65], [44, 67], [44, 72], [44, 74], [44, 78], [45, 76], [45, 86], [46, 60], [46, 77], [47, 57], [47, 58], [47, 70], [47, 71], [47, 73], [47, 75], [48, 52], [48, 56], [48, 71], [48, 78], [48, 80], [48, 84], [48, 86], [49, 50], [49, 58], [49, 77], [50, 52], [50, 71], [50, 73], [50, 85], [50, 86], [51, 61], [51, 86], [52, 73], [52, 75], [52, 80], [53, 57], [53, 58], [53, 77], [54, 58], [54, 60], [54, 63], [54, 72], [54, 74], [55, 74], [55, 84], [56, 58], [56, 60], [56, 61], [56, 67], [56, 70], [56, 75], [56, 76], [56, 80], [56, 88], [57, 67], [57, 69], [57, 70], [57, 73], [57, 74], [57, 86], [58, 62], [58, 64], [58, 65], [58, 68], [58, 74], [58, 78], [58, 81], [58, 85], [59, 80], [59, 81], [59, 84], [59, 89], [60, 62], [60, 63], [60, 83], [61, 75], [61, 79], [61, 82], [61, 87], [62, 67], [62, 85], [63, 73], [63, 81], [63, 88], [64, 88], [65, 68], [65, 69], [66, 71], [66, 73], [66, 77], [66, 86], [66, 88], [67, 69], [67, 74], [67, 77], [68, 85], [70, 71], [70, 80], [70, 81], [70, 86], [70, 88], [71, 72], [71, 73], [71, 79], [71, 81], [72, 74], [72, 89], [73, 75], [73, 78], [73, 79], [73, 82], [73, 89], [74, 77], [74, 84], [74, 87], [75, 76], [75, 79], [75, 85], [75, 89], [76, 83], [77, 83], [78, 83], [79, 85], [80, 88], [82, 87], [84, 89]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s7/tests/run.py b/tasks/construct-mc-vertex-cover-l5-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-vertex-cover-l5-s7/tests/test.sh b/tasks/construct-mc-vertex-cover-l5-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-vertex-cover-l5-s9/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l5-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-vertex-cover-l5-s9/environment/instance.json b/tasks/construct-mc-vertex-cover-l5-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2cfc444030a585f8ea912667ea9bcc84d10eebd2
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 14], [0, 16], [0, 31], [0, 39], [0, 44], [0, 46], [0, 57], [0, 60], [0, 71], [0, 74], [0, 76], [0, 80], [0, 81], [1, 7], [1, 10], [1, 11], [1, 15], [1, 30], [1, 31], [1, 44], [1, 45], [1, 53], [1, 58], [1, 62], [1, 64], [1, 71], [2, 7], [2, 11], [2, 22], [2, 23], [2, 38], [2, 40], [2, 49], [2, 58], [2, 59], [2, 63], [2, 76], [3, 6], [3, 12], [3, 16], [3, 36], [3, 47], [3, 56], [3, 57], [3, 70], [3, 75], [3, 78], [3, 86], [4, 28], [4, 47], [4, 57], [4, 62], [4, 79], [4, 84], [4, 87], [4, 88], [5, 9], [5, 14], [5, 16], [5, 25], [5, 29], [5, 34], [5, 41], [5, 46], [5, 50], [5, 51], [5, 54], [5, 55], [5, 57], [5, 69], [5, 74], [5, 80], [5, 87], [6, 16], [6, 22], [6, 26], [6, 28], [6, 36], [6, 37], [6, 43], [7, 18], [7, 22], [7, 25], [7, 27], [7, 31], [7, 32], [7, 34], [7, 36], [7, 46], [7, 58], [7, 63], [7, 64], [7, 70], [7, 75], [7, 84], [8, 21], [8, 25], [8, 26], [8, 39], [8, 40], [8, 41], [8, 42], [8, 43], [8, 44], [8, 53], [8, 59], [8, 60], [8, 61], [8, 65], [8, 67], [8, 70], [8, 89], [9, 10], [9, 11], [9, 20], [9, 34], [9, 35], [9, 37], [9, 40], [9, 43], [9, 57], [9, 59], [9, 63], [9, 69], [9, 72], [9, 73], [9, 79], [9, 84], [10, 14], [10, 26], [10, 29], [10, 40], [10, 45], [10, 64], [10, 74], [10, 83], [11, 12], [11, 13], [11, 29], [11, 30], [11, 42], [11, 52], [11, 65], [11, 69], [11, 71], [11, 78], [11, 89], [12, 13], [12, 17], [12, 19], [12, 20], [12, 22], [12, 38], [12, 40], [12, 48], [12, 52], [12, 53], [12, 57], [12, 61], [12, 62], [12, 65], [12, 67], [12, 72], [12, 73], [12, 82], [12, 87], [12, 88], [13, 22], [13, 23], [13, 24], [13, 28], [13, 34], [13, 42], [13, 47], [13, 48], [13, 52], [13, 56], [13, 75], [13, 81], [13, 88], [14, 30], [14, 32], [14, 34], [14, 40], [14, 44], [14, 45], [14, 47], [14, 57], [14, 59], [14, 64], [14, 68], [14, 82], [15, 17], [15, 20], [15, 29], [15, 34], [15, 36], [15, 42], [15, 44], [15, 52], [15, 53], [15, 67], [15, 68], [15, 74], [15, 80], [15, 82], [16, 30], [16, 35], [16, 36], [16, 37], [16, 41], [16, 53], [16, 71], [16, 73], [16, 83], [16, 89], [17, 38], [17, 39], [17, 44], [17, 47], [17, 78], [17, 87], [17, 88], [18, 20], [18, 22], [18, 32], [18, 34], [18, 36], [18, 41], [18, 45], [18, 47], [18, 49], [18, 57], [18, 67], [18, 84], [18, 87], [18, 88], [19, 34], [19, 37], [19, 45], [19, 64], [19, 71], [19, 73], [19, 81], [20, 34], [20, 36], [20, 41], [20, 42], [20, 46], [20, 48], [20, 56], [20, 58], [20, 83], [20, 86], [21, 23], [21, 29], [21, 30], [21, 31], [21, 32], [21, 45], [21, 49], [21, 56], [21, 57], [21, 58], [21, 66], [21, 70], [21, 84], [21, 87], [22, 23], [22, 27], [22, 32], [22, 34], [22, 37], [22, 38], [22, 48], [22, 54], [22, 57], [22, 64], [22, 66], [22, 68], [22, 77], [22, 78], [23, 27], [23, 36], [23, 44], [23, 51], [23, 61], [23, 75], [24, 52], [24, 53], [24, 61], [24, 85], [24, 87], [25, 28], [25, 37], [25, 49], [25, 51], [25, 54], [25, 64], [25, 70], [25, 83], [26, 32], [26, 36], [26, 42], [26, 79], [26, 84], [27, 49], [27, 52], [27, 79], [27, 89], [28, 41], [28, 64], [29, 30], [29, 33], [29, 35], [29, 40], [29, 41], [29, 42], [29, 45], [29, 55], [29, 70], [29, 72], [29, 77], [29, 80], [29, 81], [29, 88], [30, 31], [30, 36], [30, 37], [30, 41], [30, 52], [30, 56], [30, 58], [30, 61], [30, 65], [30, 79], [30, 81], [30, 83], [31, 34], [31, 44], [31, 46], [31, 47], [31, 55], [31, 57], [31, 75], [31, 78], [31, 86], [32, 41], [32, 45], [32, 52], [32, 60], [32, 63], [32, 67], [32, 70], [32, 72], [32, 78], [32, 79], [32, 81], [33, 36], [33, 42], [33, 55], [33, 56], [33, 62], [33, 69], [33, 82], [34, 39], [34, 45], [34, 54], [34, 61], [34, 62], [34, 66], [34, 72], [34, 76], [34, 78], [34, 81], [34, 83], [34, 84], [34, 86], [34, 89], [35, 43], [35, 45], [35, 52], [35, 59], [35, 69], [35, 72], [35, 79], [35, 81], [35, 84], [35, 89], [36, 38], [36, 48], [36, 56], [36, 59], [36, 62], [36, 63], [36, 64], [36, 68], [36, 80], [36, 84], [37, 45], [37, 61], [37, 77], [37, 84], [38, 42], [38, 64], [39, 41], [39, 52], [39, 61], [39, 83], [39, 88], [40, 41], [40, 51], [40, 54], [40, 57], [40, 58], [40, 63], [40, 72], [40, 76], [40, 79], [40, 83], [40, 86], [41, 46], [41, 49], [41, 52], [41, 66], [41, 83], [42, 45], [42, 49], [42, 55], [42, 56], [42, 65], [42, 72], [42, 73], [42, 74], [42, 79], [42, 83], [42, 86], [43, 68], [43, 79], [43, 85], [43, 87], [43, 89], [44, 48], [44, 75], [44, 87], [45, 46], [45, 52], [45, 55], [45, 60], [45, 65], [45, 79], [45, 84], [46, 48], [46, 61], [46, 76], [46, 83], [46, 88], [47, 50], [47, 53], [47, 59], [47, 66], [47, 69], [47, 83], [47, 84], [48, 53], [48, 58], [48, 59], [48, 62], [48, 71], [48, 72], [48, 73], [48, 81], [48, 87], [49, 55], [49, 63], [49, 64], [49, 66], [49, 71], [49, 79], [49, 87], [49, 89], [50, 88], [51, 52], [51, 57], [51, 61], [51, 66], [51, 68], [51, 74], [51, 77], [51, 80], [51, 87], [52, 64], [52, 70], [52, 72], [52, 83], [52, 84], [52, 86], [52, 88], [53, 57], [53, 58], [53, 67], [53, 72], [53, 75], [53, 82], [54, 65], [54, 69], [54, 78], [54, 80], [55, 62], [55, 64], [55, 73], [55, 78], [56, 58], [56, 66], [56, 71], [56, 73], [56, 81], [56, 88], [57, 67], [57, 72], [57, 77], [58, 68], [58, 74], [58, 75], [58, 86], [59, 64], [59, 78], [59, 82], [59, 89], [61, 67], [61, 70], [61, 74], [61, 80], [62, 67], [62, 69], [62, 78], [62, 80], [62, 84], [63, 71], [63, 84], [63, 89], [64, 76], [64, 84], [64, 89], [66, 74], [67, 77], [68, 69], [68, 85], [68, 89], [69, 73], [69, 82], [70, 73], [70, 78], [70, 79], [70, 82], [71, 87], [71, 88], [72, 81], [72, 84], [73, 75], [73, 76], [73, 77], [75, 79], [76, 82], [76, 85], [76, 87], [77, 81], [77, 88], [78, 79], [78, 83], [81, 82], [81, 84], [81, 89], [82, 87], [83, 85], [85, 87], [85, 88]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s9/solution/solve.sh b/tasks/construct-mc-vertex-cover-l5-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6c7c0a88d181ade07fbd69f8838b91c4e97020e3
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 20, 21, 22, 23, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 53, 54, 57, 58, 59, 61, 62, 64, 66, 67, 68, 71, 73, 76, 78, 79, 81, 82, 83, 84, 85, 87, 88, 89]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l5-s9/tests/check.py b/tasks/construct-mc-vertex-cover-l5-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s9/tests/check.py
@@ -0,0 +1,16 @@
+"""Vertex cover of size <= k in a given graph (MathConstraint vertex_cover, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) > k:
+        raise Invalid(f"cover has {len(S)} vertices, at most {k} allowed")
+    C = set(S)
+    for u, v in inst["edges"]:
+        if u not in C and v not in C:
+            raise Invalid(f"edge ({u},{v}) is not covered")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-vertex-cover-l5-s9/tests/instance.json b/tasks/construct-mc-vertex-cover-l5-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2cfc444030a585f8ea912667ea9bcc84d10eebd2
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 14], [0, 16], [0, 31], [0, 39], [0, 44], [0, 46], [0, 57], [0, 60], [0, 71], [0, 74], [0, 76], [0, 80], [0, 81], [1, 7], [1, 10], [1, 11], [1, 15], [1, 30], [1, 31], [1, 44], [1, 45], [1, 53], [1, 58], [1, 62], [1, 64], [1, 71], [2, 7], [2, 11], [2, 22], [2, 23], [2, 38], [2, 40], [2, 49], [2, 58], [2, 59], [2, 63], [2, 76], [3, 6], [3, 12], [3, 16], [3, 36], [3, 47], [3, 56], [3, 57], [3, 70], [3, 75], [3, 78], [3, 86], [4, 28], [4, 47], [4, 57], [4, 62], [4, 79], [4, 84], [4, 87], [4, 88], [5, 9], [5, 14], [5, 16], [5, 25], [5, 29], [5, 34], [5, 41], [5, 46], [5, 50], [5, 51], [5, 54], [5, 55], [5, 57], [5, 69], [5, 74], [5, 80], [5, 87], [6, 16], [6, 22], [6, 26], [6, 28], [6, 36], [6, 37], [6, 43], [7, 18], [7, 22], [7, 25], [7, 27], [7, 31], [7, 32], [7, 34], [7, 36], [7, 46], [7, 58], [7, 63], [7, 64], [7, 70], [7, 75], [7, 84], [8, 21], [8, 25], [8, 26], [8, 39], [8, 40], [8, 41], [8, 42], [8, 43], [8, 44], [8, 53], [8, 59], [8, 60], [8, 61], 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[28, 41], [28, 64], [29, 30], [29, 33], [29, 35], [29, 40], [29, 41], [29, 42], [29, 45], [29, 55], [29, 70], [29, 72], [29, 77], [29, 80], [29, 81], [29, 88], [30, 31], [30, 36], [30, 37], [30, 41], [30, 52], [30, 56], [30, 58], [30, 61], [30, 65], [30, 79], [30, 81], [30, 83], [31, 34], [31, 44], [31, 46], [31, 47], [31, 55], [31, 57], [31, 75], [31, 78], [31, 86], [32, 41], [32, 45], [32, 52], [32, 60], [32, 63], [32, 67], [32, 70], [32, 72], [32, 78], [32, 79], [32, 81], [33, 36], [33, 42], [33, 55], [33, 56], [33, 62], [33, 69], [33, 82], [34, 39], [34, 45], [34, 54], [34, 61], [34, 62], [34, 66], [34, 72], [34, 76], [34, 78], [34, 81], [34, 83], [34, 84], [34, 86], [34, 89], [35, 43], [35, 45], [35, 52], [35, 59], [35, 69], [35, 72], [35, 79], [35, 81], [35, 84], [35, 89], [36, 38], [36, 48], [36, 56], [36, 59], [36, 62], [36, 63], [36, 64], [36, 68], [36, 80], [36, 84], [37, 45], [37, 61], [37, 77], [37, 84], [38, 42], [38, 64], [39, 41], [39, 52], [39, 61], [39, 83], [39, 88], [40, 41], [40, 51], [40, 54], [40, 57], [40, 58], [40, 63], [40, 72], [40, 76], [40, 79], [40, 83], [40, 86], [41, 46], [41, 49], [41, 52], [41, 66], [41, 83], [42, 45], [42, 49], [42, 55], [42, 56], [42, 65], [42, 72], [42, 73], [42, 74], [42, 79], [42, 83], [42, 86], [43, 68], [43, 79], [43, 85], [43, 87], [43, 89], [44, 48], [44, 75], [44, 87], [45, 46], [45, 52], [45, 55], [45, 60], [45, 65], [45, 79], [45, 84], [46, 48], [46, 61], [46, 76], [46, 83], [46, 88], [47, 50], [47, 53], [47, 59], [47, 66], [47, 69], [47, 83], [47, 84], [48, 53], [48, 58], [48, 59], [48, 62], [48, 71], [48, 72], [48, 73], [48, 81], [48, 87], [49, 55], [49, 63], [49, 64], [49, 66], [49, 71], [49, 79], [49, 87], [49, 89], [50, 88], [51, 52], [51, 57], [51, 61], [51, 66], [51, 68], [51, 74], [51, 77], [51, 80], [51, 87], [52, 64], [52, 70], [52, 72], [52, 83], [52, 84], [52, 86], [52, 88], [53, 57], [53, 58], [53, 67], [53, 72], [53, 75], [53, 82], [54, 65], [54, 69], [54, 78], [54, 80], [55, 62], [55, 64], [55, 73], [55, 78], [56, 58], [56, 66], [56, 71], [56, 73], [56, 81], [56, 88], [57, 67], [57, 72], [57, 77], [58, 68], [58, 74], [58, 75], [58, 86], [59, 64], [59, 78], [59, 82], [59, 89], [61, 67], [61, 70], [61, 74], [61, 80], [62, 67], [62, 69], [62, 78], [62, 80], [62, 84], [63, 71], [63, 84], [63, 89], [64, 76], [64, 84], [64, 89], [66, 74], [67, 77], [68, 69], [68, 85], [68, 89], [69, 73], [69, 82], [70, 73], [70, 78], [70, 79], [70, 82], [71, 87], [71, 88], [72, 81], [72, 84], [73, 75], [73, 76], [73, 77], [75, 79], [76, 82], [76, 85], [76, 87], [77, 81], [77, 88], [78, 79], [78, 83], [81, 82], [81, 84], [81, 89], [82, 87], [83, 85], [85, 87], [85, 88]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s9/tests/run.py b/tasks/construct-mc-vertex-cover-l5-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-vertex-cover-l5-s9/tests/test.sh b/tasks/construct-mc-vertex-cover-l5-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-vertex-cover-l6-s2/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-vertex-cover-l6-s2/environment/instance.json b/tasks/construct-mc-vertex-cover-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..64877d8e5aec2ea9897ccc3928c8f1126d4a9a56
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 140, "k": 107, "edges": [[0, 5], [0, 14], [0, 23], [0, 45], [0, 47], [0, 60], [0, 61], [0, 69], [0, 73], [0, 86], [0, 87], [0, 98], [0, 100], [0, 106], [0, 115], [0, 116], [0, 117], [0, 132], [1, 10], [1, 19], [1, 55], [1, 60], [1, 86], [1, 91], [1, 95], [1, 99], [1, 102], [1, 108], [1, 109], [1, 113], [1, 135], [1, 136], [2, 8], [2, 9], [2, 11], [2, 14], [2, 18], [2, 19], [2, 32], [2, 34], [2, 52], [2, 68], [2, 101], [2, 102], [2, 103], [2, 106], [2, 116], [2, 118], [2, 121], [2, 122], [2, 128], [2, 136], [3, 10], [3, 13], [3, 14], [3, 38], [3, 47], [3, 49], [3, 50], [3, 56], [3, 68], [3, 81], [3, 96], [3, 105], [3, 107], [3, 116], [3, 129], [3, 130], [3, 134], [3, 135], [4, 13], [4, 29], [4, 38], [4, 39], [4, 46], [4, 56], [4, 66], [4, 76], [4, 78], [4, 89], [4, 92], [4, 94], [4, 97], [4, 101], [4, 109], [4, 113], [4, 120], [4, 139], [5, 29], [5, 30], [5, 32], [5, 36], [5, 49], [5, 53], [5, 58], [5, 67], [5, 70], [5, 82], [5, 85], [5, 95], [5, 102], [5, 106], [5, 110], [5, 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138], [122, 125], [123, 126], [123, 128], [127, 128], [127, 131], [127, 134], [127, 139], [128, 130], [128, 134], [129, 133], [129, 136], [130, 137], [131, 132], [131, 139], [133, 136], [133, 137], [133, 139], [135, 136], [135, 138], [136, 139]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l6-s2/solution/solve.sh b/tasks/construct-mc-vertex-cover-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..13142897e184f396c3b9d6100845faa9f09ef7b2
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 31, 33, 35, 36, 37, 38, 39, 40, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 72, 73, 74, 76, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 118, 119, 121, 122, 125, 126, 127, 128, 129, 130, 131, 132, 136, 137, 138, 139]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l6-s2/tests/check.py b/tasks/construct-mc-vertex-cover-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l6-s2/tests/check.py
@@ -0,0 +1,16 @@
+"""Vertex cover of size <= k in a given graph (MathConstraint vertex_cover, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) > k:
+        raise Invalid(f"cover has {len(S)} vertices, at most {k} allowed")
+    C = set(S)
+    for u, v in inst["edges"]:
+        if u not in C and v not in C:
+            raise Invalid(f"edge ({u},{v}) is not covered")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-vertex-cover-l6-s2/tests/instance.json b/tasks/construct-mc-vertex-cover-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..64877d8e5aec2ea9897ccc3928c8f1126d4a9a56
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 140, "k": 107, "edges": [[0, 5], [0, 14], [0, 23], [0, 45], [0, 47], [0, 60], [0, 61], [0, 69], [0, 73], [0, 86], [0, 87], [0, 98], [0, 100], [0, 106], [0, 115], [0, 116], [0, 117], [0, 132], [1, 10], [1, 19], [1, 55], [1, 60], [1, 86], [1, 91], [1, 95], [1, 99], [1, 102], [1, 108], [1, 109], [1, 113], [1, 135], [1, 136], [2, 8], [2, 9], [2, 11], [2, 14], [2, 18], [2, 19], [2, 32], [2, 34], [2, 52], [2, 68], [2, 101], [2, 102], [2, 103], [2, 106], [2, 116], [2, 118], [2, 121], [2, 122], [2, 128], [2, 136], [3, 10], [3, 13], [3, 14], [3, 38], [3, 47], [3, 49], [3, 50], [3, 56], [3, 68], [3, 81], [3, 96], [3, 105], [3, 107], [3, 116], [3, 129], [3, 130], [3, 134], [3, 135], [4, 13], [4, 29], [4, 38], [4, 39], [4, 46], [4, 56], [4, 66], [4, 76], [4, 78], [4, 89], [4, 92], [4, 94], [4, 97], [4, 101], [4, 109], [4, 113], [4, 120], [4, 139], [5, 29], [5, 30], [5, 32], [5, 36], [5, 49], [5, 53], [5, 58], [5, 67], [5, 70], [5, 82], [5, 85], [5, 95], [5, 102], [5, 106], [5, 110], [5, 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131], [101, 115], [101, 130], [102, 111], [102, 118], [102, 138], [103, 110], [103, 118], [103, 127], [104, 105], [104, 114], [104, 115], [104, 117], [104, 121], [105, 107], [105, 111], [105, 112], [105, 116], [105, 120], [105, 138], [105, 139], [106, 127], [107, 109], [107, 120], [107, 123], [107, 126], [107, 130], [108, 113], [108, 115], [108, 123], [108, 125], [108, 126], [108, 134], [108, 137], [108, 138], [108, 139], [109, 128], [109, 130], [109, 133], [109, 139], [110, 121], [110, 124], [110, 131], [111, 112], [111, 119], [111, 121], [112, 113], [112, 116], [112, 121], [112, 122], [112, 134], [112, 138], [113, 114], [113, 122], [113, 126], [113, 135], [114, 122], [114, 126], [114, 128], [114, 131], [114, 132], [115, 120], [115, 121], [115, 122], [115, 128], [115, 135], [116, 119], [116, 135], [117, 120], [117, 125], [117, 139], [118, 122], [118, 128], [118, 135], [118, 136], [118, 138], [119, 120], [119, 128], [119, 132], [119, 134], [121, 124], [121, 125], [121, 130], [121, 138], [122, 125], [123, 126], [123, 128], [127, 128], [127, 131], [127, 134], [127, 139], [128, 130], [128, 134], [129, 133], [129, 136], [130, 137], [131, 132], [131, 139], [133, 136], [133, 137], [133, 139], [135, 136], [135, 138], [136, 139]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l6-s2/tests/run.py b/tasks/construct-mc-vertex-cover-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-vertex-cover-l6-s2/tests/test.sh b/tasks/construct-mc-vertex-cover-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-3col-l5-s0/environment/Dockerfile b/tasks/construct-nppc-3col-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-3col-l5-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-3col-l5-s0/environment/instance.json b/tasks/construct-nppc-3col-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..144fbb0e73861c70c359327b15065c9bd79fd5da
--- /dev/null
+++ b/tasks/construct-nppc-3col-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 60, "edges": [[0, 3], [0, 10], [0, 24], [0, 30], [0, 39], [0, 41], [0, 44], [0, 48], [1, 7], [1, 21], [1, 22], [1, 33], [1, 34], [1, 39], [2, 12], [2, 43], [2, 49], [3, 13], [3, 48], [3, 55], [3, 57], [4, 5], [4, 7], [4, 20], [4, 21], [4, 32], [4, 42], [4, 52], [5, 15], [5, 18], [5, 19], [5, 29], [5, 33], [5, 35], [5, 47], [5, 58], [6, 16], [6, 29], [6, 44], [6, 52], [6, 53], [6, 59], [7, 8], [7, 12], [7, 13], [7, 26], [7, 29], [7, 35], [7, 50], [7, 54], [7, 56], [8, 11], [8, 24], [8, 50], [8, 51], [9, 29], [9, 34], [9, 49], [9, 50], [9, 59], [10, 12], [10, 13], [10, 14], [10, 36], [10, 37], [10, 41], [10, 44], [10, 50], [11, 24], [11, 26], [11, 27], [11, 36], [11, 38], [12, 17], [12, 18], [12, 25], [12, 27], [12, 28], [12, 32], [12, 37], [12, 38], [13, 14], [13, 22], [13, 26], [13, 36], [13, 37], [14, 31], [14, 50], [14, 55], [14, 57], [14, 58], [15, 29], [15, 32], [15, 34], [15, 36], [15, 37], [15, 59], [16, 33], [16, 43], [16, 51], [16, 58], [16, 59], [17, 23], [18, 32], [18, 35], [18, 44], [18, 53], [18, 58], [19, 34], [19, 36], [19, 37], [19, 40], [19, 50], [20, 31], [20, 47], [20, 49], [21, 27], [21, 33], [21, 43], [21, 45], [21, 50], [22, 29], [22, 43], [22, 50], [22, 51], [23, 58], [24, 26], [24, 29], [24, 30], [24, 36], [24, 44], [24, 56], [25, 30], [25, 32], [25, 34], [25, 35], [25, 51], [26, 38], [26, 45], [26, 56], [27, 31], [27, 34], [27, 59], [28, 29], [28, 43], [28, 53], [28, 56], [29, 32], [30, 42], [30, 45], [30, 56], [31, 45], [31, 55], [31, 57], [32, 48], [32, 50], [33, 37], [33, 46], [33, 50], [33, 53], [33, 56], [33, 59], [34, 43], [34, 51], [34, 57], [35, 55], [36, 42], [36, 43], [36, 49], [36, 54], [36, 58], [37, 48], [37, 53], [37, 56], [38, 43], [38, 46], [38, 47], [38, 49], [38, 51], [38, 53], [38, 58], [39, 56], [40, 48], [41, 49], [42, 44], [43, 55], [44, 45], [44, 55], [44, 58], [44, 59], [46, 48], [46, 54], [46, 55], [46, 58], [48, 49], [48, 59], [49, 55], [51, 57], [52, 55], [52, 57]], "family": "nppc_three_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-3col-l5-s0/solution/solve.sh b/tasks/construct-nppc-3col-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..53ebb2398444e2bef3420dcdaa48b681c8e5a31f
--- /dev/null
+++ b/tasks/construct-nppc-3col-l5-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"coloring": [1, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1, 0, 1, 0, 2, 0, 1, 0, 0, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-3col-l5-s0/tests/check.py b/tasks/construct-nppc-3col-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..72362ed9180250b6c53ce0c71867ca476ac2af20
--- /dev/null
+++ b/tasks/construct-nppc-3col-l5-s0/tests/check.py
@@ -0,0 +1,12 @@
+"""Proper 3-colouring of a given graph. Accepts any valid colouring."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["num_nodes"]
+    # upstream NPPC verifier skips the range/length check, so an all-distinct colouring passed it
+    c = int_list(ans.get("coloring"), n, 0, 2, "coloring")
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"edge ({u},{v}) is monochromatic")
+    return None, {}
diff --git a/tasks/construct-nppc-3col-l5-s0/tests/instance.json b/tasks/construct-nppc-3col-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..144fbb0e73861c70c359327b15065c9bd79fd5da
--- /dev/null
+++ b/tasks/construct-nppc-3col-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 60, "edges": [[0, 3], [0, 10], [0, 24], [0, 30], [0, 39], [0, 41], [0, 44], [0, 48], [1, 7], [1, 21], [1, 22], [1, 33], [1, 34], [1, 39], [2, 12], [2, 43], [2, 49], [3, 13], [3, 48], [3, 55], [3, 57], [4, 5], [4, 7], [4, 20], [4, 21], [4, 32], [4, 42], [4, 52], [5, 15], [5, 18], [5, 19], [5, 29], [5, 33], [5, 35], [5, 47], [5, 58], [6, 16], [6, 29], [6, 44], [6, 52], [6, 53], [6, 59], [7, 8], [7, 12], [7, 13], [7, 26], [7, 29], [7, 35], [7, 50], [7, 54], [7, 56], [8, 11], [8, 24], [8, 50], [8, 51], [9, 29], [9, 34], [9, 49], [9, 50], [9, 59], [10, 12], [10, 13], [10, 14], [10, 36], [10, 37], [10, 41], [10, 44], [10, 50], [11, 24], [11, 26], [11, 27], [11, 36], [11, 38], [12, 17], [12, 18], [12, 25], [12, 27], [12, 28], [12, 32], [12, 37], [12, 38], [13, 14], [13, 22], [13, 26], [13, 36], [13, 37], [14, 31], [14, 50], [14, 55], [14, 57], [14, 58], [15, 29], [15, 32], [15, 34], [15, 36], [15, 37], [15, 59], [16, 33], [16, 43], [16, 51], [16, 58], [16, 59], [17, 23], [18, 32], [18, 35], [18, 44], [18, 53], [18, 58], [19, 34], [19, 36], [19, 37], [19, 40], [19, 50], [20, 31], [20, 47], [20, 49], [21, 27], [21, 33], [21, 43], [21, 45], [21, 50], [22, 29], [22, 43], [22, 50], [22, 51], [23, 58], [24, 26], [24, 29], [24, 30], [24, 36], [24, 44], [24, 56], [25, 30], [25, 32], [25, 34], [25, 35], [25, 51], [26, 38], [26, 45], [26, 56], [27, 31], [27, 34], [27, 59], [28, 29], [28, 43], [28, 53], [28, 56], [29, 32], [30, 42], [30, 45], [30, 56], [31, 45], [31, 55], [31, 57], [32, 48], [32, 50], [33, 37], [33, 46], [33, 50], [33, 53], [33, 56], [33, 59], [34, 43], [34, 51], [34, 57], [35, 55], [36, 42], [36, 43], [36, 49], [36, 54], [36, 58], [37, 48], [37, 53], [37, 56], [38, 43], [38, 46], [38, 47], [38, 49], [38, 51], [38, 53], [38, 58], [39, 56], [40, 48], [41, 49], [42, 44], [43, 55], [44, 45], [44, 55], [44, 58], [44, 59], [46, 48], [46, 54], [46, 55], [46, 58], [48, 49], [48, 59], [49, 55], [51, 57], [52, 55], [52, 57]], "family": "nppc_three_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-3col-l5-s0/tests/run.py b/tasks/construct-nppc-3col-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-3col-l5-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-3col-l5-s0/tests/test.sh b/tasks/construct-nppc-3col-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-3col-l5-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l3-s2/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l3-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l3-s2/environment/instance.json b/tasks/construct-nppc-bandwidth-l3-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e73639d73c8d9ce5fa181533b10acce5b051bb59
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s2/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 2], [0, 3], [1, 3], [2, 7], [3, 4], [3, 6], [4, 7], [5, 6]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s2/solution/solve.sh b/tasks/construct-nppc-bandwidth-l3-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..76dcd8aa4b2b3d9e20c5394fcad73635963414f1
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [2, 5, 0, 4, 3, 7, 6, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l3-s2/tests/check.py b/tasks/construct-nppc-bandwidth-l3-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s2/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l3-s2/tests/instance.json b/tasks/construct-nppc-bandwidth-l3-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e73639d73c8d9ce5fa181533b10acce5b051bb59
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s2/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 2], [0, 3], [1, 3], [2, 7], [3, 4], [3, 6], [4, 7], [5, 6]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s2/tests/run.py b/tasks/construct-nppc-bandwidth-l3-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l3-s2/tests/test.sh b/tasks/construct-nppc-bandwidth-l3-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l3-s5/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l3-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l3-s5/environment/instance.json b/tasks/construct-nppc-bandwidth-l3-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..739eab8010298722ab7c503d51b2025574b30343
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s5/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 2], [0, 3], [0, 7], [1, 2], [2, 3], [3, 5], [4, 7], [5, 6]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s5/solution/solve.sh b/tasks/construct-nppc-bandwidth-l3-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..405262658a5a5ff6e3f1fd5fa1c96962e0ba1710
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [5, 1, 3, 4, 7, 2, 0, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l3-s5/tests/check.py b/tasks/construct-nppc-bandwidth-l3-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s5/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l3-s5/tests/instance.json b/tasks/construct-nppc-bandwidth-l3-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..739eab8010298722ab7c503d51b2025574b30343
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s5/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 2], [0, 3], [0, 7], [1, 2], [2, 3], [3, 5], [4, 7], [5, 6]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s5/tests/run.py b/tasks/construct-nppc-bandwidth-l3-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l3-s5/tests/test.sh b/tasks/construct-nppc-bandwidth-l3-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l4-s1/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l4-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l4-s1/environment/instance.json b/tasks/construct-nppc-bandwidth-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bd5aa613037bde488dadcb7bdacff9c24343111f
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "bandwidth": 3, "edges": [[0, 4], [0, 6], [0, 7], [0, 8], [0, 12], [0, 16], [1, 2], [1, 15], [1, 19], [2, 13], [2, 15], [3, 5], [3, 8], [3, 11], [4, 6], [4, 8], [4, 12], [4, 16], [4, 18], [5, 11], [6, 8], [6, 11], [7, 10], [7, 12], [7, 19], [8, 11], [9, 13], [9, 14], [9, 17], [9, 19], [10, 12], [10, 14], [10, 16], [10, 19], [11, 18], [12, 16], [13, 15], [14, 16], [14, 17], [17, 19]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l4-s1/solution/solve.sh b/tasks/construct-nppc-bandwidth-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..dfd495a79d10fc2d26a28c4f3499a93f83e4d8bb
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l4-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [12, 3, 0, 18, 13, 19, 14, 9, 15, 4, 8, 17, 11, 2, 7, 1, 10, 5, 16, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l4-s1/tests/check.py b/tasks/construct-nppc-bandwidth-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l4-s1/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l4-s1/tests/instance.json b/tasks/construct-nppc-bandwidth-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bd5aa613037bde488dadcb7bdacff9c24343111f
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "bandwidth": 3, "edges": [[0, 4], [0, 6], [0, 7], [0, 8], [0, 12], [0, 16], [1, 2], [1, 15], [1, 19], [2, 13], [2, 15], [3, 5], [3, 8], [3, 11], [4, 6], [4, 8], [4, 12], [4, 16], [4, 18], [5, 11], [6, 8], [6, 11], [7, 10], [7, 12], [7, 19], [8, 11], [9, 13], [9, 14], [9, 17], [9, 19], [10, 12], [10, 14], [10, 16], [10, 19], [11, 18], [12, 16], [13, 15], [14, 16], [14, 17], [17, 19]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l4-s1/tests/run.py b/tasks/construct-nppc-bandwidth-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l4-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l4-s1/tests/test.sh b/tasks/construct-nppc-bandwidth-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l4-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-clique-l1-s7/environment/Dockerfile b/tasks/construct-nppc-clique-l1-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-l1-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-clique-l1-s7/environment/instance.json b/tasks/construct-nppc-clique-l1-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c2e4e4dd88c0233d49f9d8ab6377c54256d300f6
--- /dev/null
+++ b/tasks/construct-nppc-clique-l1-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "k": 4, "edges": [[0, 1], [0, 3], [0, 6], [1, 3], [1, 4], [1, 6], [1, 7], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 6], [3, 7], [4, 6], [4, 7], [5, 6], [6, 7]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l1-s7/solution/solve.sh b/tasks/construct-nppc-clique-l1-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f73949fa6859640ede79684da0f756779f6ab224
--- /dev/null
+++ b/tasks/construct-nppc-clique-l1-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 1, 3, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l1-s7/tests/check.py b/tasks/construct-nppc-clique-l1-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l1-s7/tests/check.py
@@ -0,0 +1,19 @@
+"""Clique of size >= k. Accepts any valid clique."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    # upstream NPPC verifier checks len(list) >= k but only tests pairs u < v, so [v, v, ..., v] passed
+    if len(set(c)) != len(c):
+        raise Invalid("clique contains duplicates")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(c), 2):
+        if (u, v) not in es:
+            raise Invalid(f"no edge between {u} and {v}")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-clique-l1-s7/tests/instance.json b/tasks/construct-nppc-clique-l1-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c2e4e4dd88c0233d49f9d8ab6377c54256d300f6
--- /dev/null
+++ b/tasks/construct-nppc-clique-l1-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "k": 4, "edges": [[0, 1], [0, 3], [0, 6], [1, 3], [1, 4], [1, 6], [1, 7], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 6], [3, 7], [4, 6], [4, 7], [5, 6], [6, 7]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l1-s7/tests/run.py b/tasks/construct-nppc-clique-l1-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l1-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-clique-l1-s7/tests/test.sh b/tasks/construct-nppc-clique-l1-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-l1-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-clique-l2-s5/environment/Dockerfile b/tasks/construct-nppc-clique-l2-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-clique-l2-s5/environment/instance.json b/tasks/construct-nppc-clique-l2-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..29db8b9c022e1c8229154ca4ca14c3a9174e800f
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s5/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 14, "k": 7, "edges": [[0, 2], [0, 3], [0, 4], [0, 6], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [1, 3], [1, 6], [1, 7], [1, 8], [1, 10], [2, 6], [2, 11], [2, 13], [3, 8], [3, 10], [3, 11], [3, 12], [3, 13], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 11], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [7, 8], [7, 9], [7, 11], [8, 9], [8, 10], [8, 11], [8, 12], [9, 10], [9, 11], [9, 12], [9, 13], [10, 12]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l2-s5/solution/solve.sh b/tasks/construct-nppc-clique-l2-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d27345102c54895f7556e7a66be1310ead272ebb
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 4, 6, 8, 9, 10, 12]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l2-s5/tests/check.py b/tasks/construct-nppc-clique-l2-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s5/tests/check.py
@@ -0,0 +1,19 @@
+"""Clique of size >= k. Accepts any valid clique."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    # upstream NPPC verifier checks len(list) >= k but only tests pairs u < v, so [v, v, ..., v] passed
+    if len(set(c)) != len(c):
+        raise Invalid("clique contains duplicates")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(c), 2):
+        if (u, v) not in es:
+            raise Invalid(f"no edge between {u} and {v}")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-clique-l2-s5/tests/instance.json b/tasks/construct-nppc-clique-l2-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..29db8b9c022e1c8229154ca4ca14c3a9174e800f
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s5/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 14, "k": 7, "edges": [[0, 2], [0, 3], [0, 4], [0, 6], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [1, 3], [1, 6], [1, 7], [1, 8], [1, 10], [2, 6], [2, 11], [2, 13], [3, 8], [3, 10], [3, 11], [3, 12], [3, 13], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 11], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [7, 8], [7, 9], [7, 11], [8, 9], [8, 10], [8, 11], [8, 12], [9, 10], [9, 11], [9, 12], [9, 13], [10, 12]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l2-s5/tests/run.py b/tasks/construct-nppc-clique-l2-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-clique-l2-s5/tests/test.sh b/tasks/construct-nppc-clique-l2-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-clique-l6-s3/environment/Dockerfile b/tasks/construct-nppc-clique-l6-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-clique-l6-s3/environment/instance.json b/tasks/construct-nppc-clique-l6-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..65f36f7193d97913ad8a8578478ca7f8f24d1d5b
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s3/environment/instance.json
@@ -0,0 +1 @@
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88], [87, 90], [87, 93], [87, 99], [88, 89], [88, 91], [88, 96], [89, 96], [89, 97], [90, 91], [90, 92], [90, 96], [90, 97], [90, 99], [91, 92], [91, 93], [91, 94], [91, 95], [91, 96], [91, 97], [92, 93], [92, 95], [92, 96], [93, 94], [93, 96], [93, 99], [94, 95], [94, 97], [94, 99], [95, 96], [95, 98], [95, 99], [96, 97], [97, 99], [98, 99]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l6-s3/solution/solve.sh b/tasks/construct-nppc-clique-l6-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..911827931f86be6cf499ab389a12c74fd9943aea
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [10, 15, 26, 28, 30, 31, 51, 60, 65, 68, 69, 74, 76, 80, 81, 84, 85, 90, 91, 92]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l6-s3/tests/check.py b/tasks/construct-nppc-clique-l6-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s3/tests/check.py
@@ -0,0 +1,19 @@
+"""Clique of size >= k. Accepts any valid clique."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    # upstream NPPC verifier checks len(list) >= k but only tests pairs u < v, so [v, v, ..., v] passed
+    if len(set(c)) != len(c):
+        raise Invalid("clique contains duplicates")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(c), 2):
+        if (u, v) not in es:
+            raise Invalid(f"no edge between {u} and {v}")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-clique-l6-s3/tests/instance.json b/tasks/construct-nppc-clique-l6-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..65f36f7193d97913ad8a8578478ca7f8f24d1d5b
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s3/tests/instance.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l6-s3/tests/run.py b/tasks/construct-nppc-clique-l6-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-clique-l6-s3/tests/test.sh b/tasks/construct-nppc-clique-l6-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-clique-l6-s4/environment/Dockerfile b/tasks/construct-nppc-clique-l6-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-clique-l6-s4/environment/instance.json b/tasks/construct-nppc-clique-l6-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9847518742ab49cd0c26f8a4b7ddd67e10cf01c8
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s4/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 13], [0, 15], [0, 19], [0, 21], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 38], [0, 40], [0, 41], [0, 42], [0, 44], [0, 45], [0, 46], [0, 47], [0, 51], [0, 54], [0, 55], [0, 57], [0, 58], [0, 61], [0, 63], [0, 64], [0, 65], [0, 66], [0, 68], [0, 71], [0, 72], [0, 73], [0, 75], [0, 76], [0, 77], [0, 78], [0, 79], [0, 80], [0, 81], [0, 84], [0, 85], [0, 87], [0, 88], [0, 89], [0, 91], [0, 92], [0, 93], [0, 95], [0, 97], [0, 98], [1, 3], [1, 4], [1, 13], [1, 14], [1, 18], [1, 26], [1, 27], [1, 29], [1, 32], [1, 34], [1, 35], [1, 37], [1, 38], [1, 42], [1, 45], [1, 48], [1, 50], [1, 52], [1, 54], [1, 56], [1, 58], [1, 59], [1, 67], [1, 68], [1, 69], [1, 70], [1, 73], [1, 78], [1, 81], [1, 84], [1, 87], [1, 88], [1, 89], [1, 90], [1, 91], [1, 94], [1, 97], [1, 98], [2, 4], [2, 5], [2, 8], [2, 10], [2, 12], [2, 15], [2, 21], [2, 22], [2, 23], 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[95, 98], [96, 98], [97, 98], [97, 99], [98, 99]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l6-s4/solution/solve.sh b/tasks/construct-nppc-clique-l6-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c31cd92447c858fc425efdad24d14e923d17f05a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 4, 5, 6, 7, 11, 15, 19, 21, 28, 30, 31, 38, 41, 46, 65, 77, 78, 85, 98]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l6-s4/tests/check.py b/tasks/construct-nppc-clique-l6-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s4/tests/check.py
@@ -0,0 +1,19 @@
+"""Clique of size >= k. Accepts any valid clique."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    # upstream NPPC verifier checks len(list) >= k but only tests pairs u < v, so [v, v, ..., v] passed
+    if len(set(c)) != len(c):
+        raise Invalid("clique contains duplicates")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(c), 2):
+        if (u, v) not in es:
+            raise Invalid(f"no edge between {u} and {v}")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-clique-l6-s4/tests/instance.json b/tasks/construct-nppc-clique-l6-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9847518742ab49cd0c26f8a4b7ddd67e10cf01c8
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s4/tests/instance.json
@@ -0,0 +1 @@
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[95, 98], [96, 98], [97, 98], [97, 99], [98, 99]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l6-s4/tests/run.py b/tasks/construct-nppc-clique-l6-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-clique-l6-s4/tests/test.sh b/tasks/construct-nppc-clique-l6-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-dominating-set-l6-s4/environment/Dockerfile b/tasks/construct-nppc-dominating-set-l6-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l6-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-dominating-set-l6-s4/environment/instance.json b/tasks/construct-nppc-dominating-set-l6-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c365ac170cf7d5c4e64dc497ba3ba8e01f9fd4c3
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l6-s4/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 300, "k": 20, "edges": [[0, 31], [0, 47], [0, 90], [0, 96], [0, 101], [0, 107], [0, 113], [0, 114], [0, 121], [0, 158], [0, 179], [0, 185], [0, 188], [0, 194], [0, 204], [0, 207], [0, 217], [0, 219], [0, 238], [0, 274], [1, 9], [1, 20], [1, 43], [1, 72], [1, 90], [1, 91], [1, 153], [1, 178], [1, 197], [1, 219], [1, 220], [1, 222], [1, 223], [1, 225], [1, 234], [1, 263], [1, 280], [1, 292], [2, 7], [2, 8], [2, 38], [2, 50], [2, 55], [2, 58], [2, 97], [2, 102], [2, 112], [2, 168], [2, 174], [2, 183], [2, 185], [2, 189], [2, 239], [2, 241], [2, 245], [2, 254], [2, 260], [2, 268], [2, 272], [2, 288], [3, 11], [3, 20], [3, 25], [3, 29], [3, 32], [3, 33], [3, 40], [3, 65], [3, 72], [3, 78], [3, 83], [3, 87], [3, 90], [3, 109], [3, 156], [3, 158], [3, 185], [3, 191], [3, 200], [3, 236], [3, 238], [3, 271], [3, 273], [3, 276], [4, 33], [4, 37], [4, 63], [4, 64], [4, 78], [4, 81], [4, 98], [4, 127], [4, 134], [4, 155], [4, 157], [4, 158], [4, 171], [4, 174], [4, 182], [4, 203], 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[257, 299], [258, 266], [258, 284], [259, 272], [259, 281], [259, 294], [260, 261], [260, 266], [260, 284], [261, 274], [261, 283], [262, 291], [263, 267], [263, 277], [263, 285], [263, 288], [263, 290], [264, 282], [264, 293], [266, 269], [266, 274], [266, 282], [267, 287], [267, 298], [268, 282], [268, 289], [270, 280], [270, 282], [272, 274], [272, 285], [272, 288], [273, 279], [274, 276], [275, 289], [275, 292], [276, 280], [278, 286], [279, 291], [279, 297], [280, 283], [280, 289], [280, 294], [280, 296], [281, 287], [281, 294], [282, 297], [283, 287], [283, 289], [287, 290], [288, 290], [291, 299], [292, 297], [294, 299], [295, 296]], "family": "nppc_dominating_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-dominating-set-l6-s4/solution/solve.sh b/tasks/construct-nppc-dominating-set-l6-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..cec50b1774d0d893b512838c8bea9d3953e17230
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l6-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"dominating_set": [8, 18, 54, 69, 76, 77, 83, 91, 101, 107, 137, 156, 161, 164, 181, 243, 245, 257, 274, 282]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-dominating-set-l6-s4/tests/check.py b/tasks/construct-nppc-dominating-set-l6-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0677a7bcbccb02297d022ffa4b5dd15da6371bff
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l6-s4/tests/check.py
@@ -0,0 +1,23 @@
+"""Dominating set of size <= k. Accepts any valid dominating set."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier has no type/range checks (out-of-range labels and floats are silently used)
+    d = int_list(ans.get("dominating_set"), None, 0, n - 1, "dominating_set")
+    if len(set(d)) != len(d):
+        raise Invalid("dominating_set contains duplicates")
+    if not d or len(d) > k:
+        raise Invalid(f"dominating_set must have 1..{k} vertices, got {len(d)}")
+    dom = set(d)
+    s = set(d)
+    for u, v in inst["edges"]:
+        if u in s:
+            dom.add(v)
+        if v in s:
+            dom.add(u)
+    if len(dom) != n:
+        miss = min(set(range(n)) - dom)
+        raise Invalid(f"vertex {miss} is not dominated")
+    return None, {"size": len(d)}
diff --git a/tasks/construct-nppc-dominating-set-l6-s4/tests/instance.json b/tasks/construct-nppc-dominating-set-l6-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c365ac170cf7d5c4e64dc497ba3ba8e01f9fd4c3
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l6-s4/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 300, "k": 20, "edges": [[0, 31], [0, 47], [0, 90], [0, 96], [0, 101], [0, 107], [0, 113], [0, 114], [0, 121], [0, 158], [0, 179], [0, 185], [0, 188], [0, 194], [0, 204], [0, 207], [0, 217], [0, 219], [0, 238], [0, 274], [1, 9], [1, 20], [1, 43], [1, 72], [1, 90], [1, 91], [1, 153], [1, 178], [1, 197], [1, 219], [1, 220], [1, 222], [1, 223], [1, 225], [1, 234], [1, 263], [1, 280], [1, 292], [2, 7], [2, 8], [2, 38], [2, 50], [2, 55], [2, 58], [2, 97], [2, 102], [2, 112], [2, 168], [2, 174], [2, 183], [2, 185], [2, 189], [2, 239], [2, 241], [2, 245], [2, 254], [2, 260], [2, 268], [2, 272], [2, 288], [3, 11], [3, 20], [3, 25], [3, 29], [3, 32], [3, 33], [3, 40], [3, 65], [3, 72], [3, 78], [3, 83], [3, 87], [3, 90], [3, 109], [3, 156], [3, 158], [3, 185], [3, 191], [3, 200], [3, 236], [3, 238], [3, 271], [3, 273], [3, 276], [4, 33], [4, 37], [4, 63], [4, 64], [4, 78], [4, 81], [4, 98], [4, 127], [4, 134], [4, 155], [4, 157], [4, 158], [4, 171], [4, 174], [4, 182], [4, 203], 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[190, 236], [190, 237], [190, 241], [190, 246], [190, 249], [190, 265], [191, 206], [191, 215], [191, 225], [191, 240], [191, 247], [191, 268], [191, 274], [191, 280], [191, 286], [191, 288], [191, 296], [193, 199], [193, 213], [193, 218], [193, 229], [193, 232], [193, 245], [193, 251], [193, 253], [193, 254], [193, 275], [193, 277], [193, 281], [193, 282], [193, 296], [194, 224], [194, 236], [194, 259], [194, 271], [194, 286], [194, 299], [195, 196], [195, 201], [195, 204], [195, 222], [195, 251], [195, 257], [195, 298], [196, 222], [196, 225], [196, 233], [196, 236], [196, 242], [196, 256], [196, 257], [196, 297], [197, 201], [197, 207], [197, 238], [197, 269], [197, 274], [198, 204], [198, 235], [198, 260], [198, 270], [198, 282], [198, 287], [199, 216], [199, 252], [199, 257], [199, 272], [200, 205], [200, 206], [200, 220], [200, 249], [200, 251], [200, 255], [200, 273], [200, 295], [201, 245], [201, 247], [201, 271], [202, 207], [202, 220], [202, 222], [202, 224], [202, 229], [202, 266], [202, 273], [202, 291], [203, 206], [203, 208], [203, 257], [203, 259], [203, 283], [204, 209], [204, 210], [204, 220], [204, 228], [204, 231], [204, 238], [204, 259], [205, 249], [205, 251], [205, 263], [205, 288], [206, 276], [207, 211], [207, 227], [207, 228], [207, 285], [207, 296], [207, 299], [208, 212], [208, 229], [208, 256], [208, 264], [208, 265], [208, 286], [208, 298], [209, 217], [209, 222], [209, 230], [209, 238], [209, 259], [209, 262], [209, 279], [209, 291], [210, 212], [210, 230], [210, 240], [210, 241], [210, 264], [210, 287], [211, 215], [211, 228], [211, 232], [211, 236], [211, 258], [212, 245], [212, 266], [212, 274], [212, 276], [212, 277], [213, 227], [213, 229], [213, 247], [213, 257], [213, 266], [213, 267], [213, 273], [213, 275], [214, 243], [214, 244], [214, 270], [215, 217], [215, 236], [215, 254], [215, 256], [215, 262], [216, 238], [216, 247], [216, 254], [216, 268], [216, 275], [217, 227], [217, 243], [217, 249], [217, 271], [217, 282], [218, 232], [218, 234], [218, 265], [219, 228], [219, 245], [219, 275], [219, 291], [220, 224], [220, 225], [220, 234], [220, 236], [220, 249], [220, 256], [220, 270], [220, 287], [221, 225], [221, 235], [221, 245], [221, 247], [221, 250], [221, 269], [221, 274], [221, 284], [221, 293], [222, 232], [222, 257], [222, 258], [222, 263], [222, 270], [222, 291], [223, 262], [223, 266], [223, 282], [224, 236], [224, 255], [224, 261], [224, 268], [224, 289], [225, 231], [225, 245], [225, 247], [225, 250], [225, 260], [225, 266], [225, 271], [225, 283], [225, 294], [226, 243], [226, 262], [226, 284], [226, 285], [226, 295], [227, 250], [227, 251], [227, 272], [228, 246], [228, 275], [229, 246], [229, 274], [229, 296], [230, 254], [230, 257], [230, 260], [231, 234], [231, 240], [231, 264], [231, 270], [231, 288], [231, 290], [232, 275], [232, 283], [232, 297], [233, 250], [233, 260], [234, 237], [234, 244], [234, 249], [234, 261], [234, 273], [234, 275], [234, 277], [234, 283], [234, 291], [234, 294], [234, 298], [235, 242], [235, 265], [235, 274], [235, 284], [235, 292], [236, 242], [236, 248], [236, 260], [236, 288], [236, 292], [237, 260], [237, 262], [237, 277], [237, 283], [238, 243], [238, 271], [238, 281], [238, 291], [238, 293], [239, 249], [239, 275], [240, 252], [240, 294], [240, 296], [241, 247], [241, 255], [241, 270], [241, 283], [241, 289], [242, 270], [243, 266], [243, 273], [243, 275], [243, 279], [243, 287], [244, 245], [244, 288], [245, 248], [245, 267], [245, 282], [245, 285], [245, 288], [247, 272], [247, 276], [247, 282], [247, 290], [247, 295], [247, 296], [248, 250], [248, 257], [248, 262], [248, 267], [248, 287], [248, 290], [249, 285], [249, 297], [250, 256], [250, 269], [250, 276], [251, 267], [251, 274], [251, 277], [252, 256], [252, 259], [252, 272], [252, 278], [252, 293], [253, 258], [253, 280], [253, 291], [254, 274], [255, 272], [255, 281], [255, 282], [255, 293], [256, 266], [256, 270], [256, 277], [257, 279], [257, 289], [257, 295], [257, 299], [258, 266], [258, 284], [259, 272], [259, 281], [259, 294], [260, 261], [260, 266], [260, 284], [261, 274], [261, 283], [262, 291], [263, 267], [263, 277], [263, 285], [263, 288], [263, 290], [264, 282], [264, 293], [266, 269], [266, 274], [266, 282], [267, 287], [267, 298], [268, 282], [268, 289], [270, 280], [270, 282], [272, 274], [272, 285], [272, 288], [273, 279], [274, 276], [275, 289], [275, 292], [276, 280], [278, 286], [279, 291], [279, 297], [280, 283], [280, 289], [280, 294], [280, 296], [281, 287], [281, 294], [282, 297], [283, 287], [283, 289], [287, 290], [288, 290], [291, 299], [292, 297], [294, 299], [295, 296]], "family": "nppc_dominating_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-dominating-set-l6-s4/tests/run.py b/tasks/construct-nppc-dominating-set-l6-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l6-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-dominating-set-l6-s4/tests/test.sh b/tasks/construct-nppc-dominating-set-l6-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l6-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-independent-set-l3-s5/environment/Dockerfile b/tasks/construct-nppc-independent-set-l3-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-independent-set-l3-s5/environment/instance.json b/tasks/construct-nppc-independent-set-l3-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aefec35f1fe3084f93d82dd07cbaff6f459bb720
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s5/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 7], [0, 11], [0, 12], [0, 16], [0, 17], [0, 18], [1, 3], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 7], [2, 9], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 20], [2, 22], [3, 5], [3, 8], [3, 10], [3, 11], [3, 13], [3, 14], [3, 16], [3, 17], [3, 18], [3, 19], [3, 21], [3, 23], [4, 7], [4, 8], [4, 11], [4, 18], [5, 11], [5, 12], [5, 13], [5, 14], [5, 16], [5, 18], [6, 7], [6, 8], [6, 10], [6, 12], [6, 13], [6, 14], [6, 18], [7, 10], [7, 12], [7, 13], [7, 15], [7, 17], [7, 20], [7, 21], [7, 22], [7, 23], [8, 10], [8, 11], [8, 16], [8, 17], [8, 20], [8, 21], [8, 23], [9, 10], [9, 11], [10, 11], [10, 15], [10, 16], [10, 19], [10, 20], [10, 23], [11, 13], [11, 16], [11, 17], [11, 18], [11, 19], [11, 22], [11, 23], [12, 14], [12, 15], [12, 17], [12, 20], [13, 20], [13, 21], [13, 22], [14, 15], [14, 16], [14, 21], [14, 22], [15, 16], [16, 17], [16, 23], [17, 18], [17, 19], [17, 23], [18, 20], [18, 21], [18, 23]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s5/solution/solve.sh b/tasks/construct-nppc-independent-set-l3-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f69a80079fa0cadfaf2da804a6c73206a1649afa
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [0, 1, 4, 5, 6, 9, 15, 19, 20, 21, 22, 23]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l3-s5/tests/check.py b/tasks/construct-nppc-independent-set-l3-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s5/tests/check.py
@@ -0,0 +1,19 @@
+"""Independent set of size >= k. Accepts any valid independent set."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    s = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    # upstream NPPC verifier checks len(list) >= size but only tests pairs u < v, so [v]*k passed
+    if len(set(s)) != len(s):
+        raise Invalid("independent_set contains duplicates")
+    if len(s) < k:
+        raise Invalid(f"independent_set has {len(s)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(s), 2):
+        if (u, v) in es:
+            raise Invalid(f"edge between {u} and {v}")
+    return None, {"size": len(s)}
diff --git a/tasks/construct-nppc-independent-set-l3-s5/tests/instance.json b/tasks/construct-nppc-independent-set-l3-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aefec35f1fe3084f93d82dd07cbaff6f459bb720
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s5/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 7], [0, 11], [0, 12], [0, 16], [0, 17], [0, 18], [1, 3], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 7], [2, 9], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 20], [2, 22], [3, 5], [3, 8], [3, 10], [3, 11], [3, 13], [3, 14], [3, 16], [3, 17], [3, 18], [3, 19], [3, 21], [3, 23], [4, 7], [4, 8], [4, 11], [4, 18], [5, 11], [5, 12], [5, 13], [5, 14], [5, 16], [5, 18], [6, 7], [6, 8], [6, 10], [6, 12], [6, 13], [6, 14], [6, 18], [7, 10], [7, 12], [7, 13], [7, 15], [7, 17], [7, 20], [7, 21], [7, 22], [7, 23], [8, 10], [8, 11], [8, 16], [8, 17], [8, 20], [8, 21], [8, 23], [9, 10], [9, 11], [10, 11], [10, 15], [10, 16], [10, 19], [10, 20], [10, 23], [11, 13], [11, 16], [11, 17], [11, 18], [11, 19], [11, 22], [11, 23], [12, 14], [12, 15], [12, 17], [12, 20], [13, 20], [13, 21], [13, 22], [14, 15], [14, 16], [14, 21], [14, 22], [15, 16], [16, 17], [16, 23], [17, 18], [17, 19], [17, 23], [18, 20], [18, 21], [18, 23]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s5/tests/run.py b/tasks/construct-nppc-independent-set-l3-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-independent-set-l3-s5/tests/test.sh b/tasks/construct-nppc-independent-set-l3-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quad-diophantine-l1-s1/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l1-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l1-s1/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..60de6920c91826939d82ee522cdee6e6d3947bea
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"a": 35, "b": 28, "c": 4263, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s3/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l2-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s3/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l2-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..33ee0f785406e87d54771476e8b09e9f2b6db824
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s3/environment/instance.json
@@ -0,0 +1 @@
+{"a": 600, "b": 237, "c": 20676252, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s3/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l2-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3d4bdf79ff6311ab690d00c80ca1cfc8d7610530
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 185, "y": 596}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s3/tests/check.py b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/check.py
@@ -0,0 +1,11 @@
+"""a*x^2 + b*y = c in positive integers. Accepts any solution (exact integer arithmetic)."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier only checks x > 0 and y > 0, so non-integer (float) x, y were accepted
+    x = as_int(ans.get("x"), "x", lo=1)
+    y = as_int(ans.get("y"), "y", lo=1)
+    if inst["a"] * x * x + inst["b"] * y != inst["c"]:
+        raise Invalid("a*x^2 + b*y != c")
+    return None, {}
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s3/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..33ee0f785406e87d54771476e8b09e9f2b6db824
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/instance.json
@@ -0,0 +1 @@
+{"a": 600, "b": 237, "c": 20676252, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s3/tests/run.py b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s3/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quad-diophantine-l5-s9/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l5-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l5-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l5-s9/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l5-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a72ed30325ea8d1decb23224001ecd6316453cf9
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l5-s9/environment/instance.json
@@ -0,0 +1 @@
+{"a": 8800349, "b": 6412954, "c": 2190197601323440210, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l5-s9/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l5-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1729b56b625502aaaf3dafb62930de3497b8eeef
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l5-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 498868, "y": 9522821}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l5-s9/tests/check.py b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/check.py
@@ -0,0 +1,11 @@
+"""a*x^2 + b*y = c in positive integers. Accepts any solution (exact integer arithmetic)."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier only checks x > 0 and y > 0, so non-integer (float) x, y were accepted
+    x = as_int(ans.get("x"), "x", lo=1)
+    y = as_int(ans.get("y"), "y", lo=1)
+    if inst["a"] * x * x + inst["b"] * y != inst["c"]:
+        raise Invalid("a*x^2 + b*y != c")
+    return None, {}
diff --git a/tasks/construct-nppc-quad-diophantine-l5-s9/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a72ed30325ea8d1decb23224001ecd6316453cf9
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/instance.json
@@ -0,0 +1 @@
+{"a": 8800349, "b": 6412954, "c": 2190197601323440210, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l5-s9/tests/run.py b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quad-diophantine-l5-s9/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l5-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s2/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s2/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a23ccfd21505cf9b6aec22fbd9e4795079bc1c0
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"a": 1237432915, "b": 1095508825, "c": 67618899370475198423419290835, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s2/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f7508be59a0b7030df269908ddb2da32b7cac80c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 7392191632, "y": 4887119115}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s2/tests/check.py b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/check.py
@@ -0,0 +1,11 @@
+"""a*x^2 + b*y = c in positive integers. Accepts any solution (exact integer arithmetic)."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier only checks x > 0 and y > 0, so non-integer (float) x, y were accepted
+    x = as_int(ans.get("x"), "x", lo=1)
+    y = as_int(ans.get("y"), "y", lo=1)
+    if inst["a"] * x * x + inst["b"] * y != inst["c"]:
+        raise Invalid("a*x^2 + b*y != c")
+    return None, {}
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s2/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a23ccfd21505cf9b6aec22fbd9e4795079bc1c0
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"a": 1237432915, "b": 1095508825, "c": 67618899370475198423419290835, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s2/tests/run.py b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s2/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s5/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l6-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s5/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l6-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..80162ccface06532c4f700b9bd7e3c09ab29e9f3
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s5/environment/instance.json
@@ -0,0 +1 @@
+{"a": 9827784743, "b": 1297521230, "c": 170925871072130354043696519463, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s5/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l6-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..958165f3cf7cef81cabe8fbf035ab59ee0acaf25
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 4170384359, "y": 5716432456}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s5/tests/check.py b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/check.py
@@ -0,0 +1,11 @@
+"""a*x^2 + b*y = c in positive integers. Accepts any solution (exact integer arithmetic)."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier only checks x > 0 and y > 0, so non-integer (float) x, y were accepted
+    x = as_int(ans.get("x"), "x", lo=1)
+    y = as_int(ans.get("y"), "y", lo=1)
+    if inst["a"] * x * x + inst["b"] * y != inst["c"]:
+        raise Invalid("a*x^2 + b*y != c")
+    return None, {}
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s5/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..80162ccface06532c4f700b9bd7e3c09ab29e9f3
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/instance.json
@@ -0,0 +1 @@
+{"a": 9827784743, "b": 1297521230, "c": 170925871072130354043696519463, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s5/tests/run.py b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s5/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quadratic-congruence-l1-s1/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l1-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quadratic-congruence-l1-s1/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bdb4d7f88b2b637df6f7f302aceac575a6c456e7
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"a": 9, "b": 18, "c": 137, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l1-s1/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..472c4be857beb48959bcae20fb2dcd3fe1476b5d
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l1-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 69}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/check.py
@@ -0,0 +1,11 @@
+"""Quadratic congruence: integer x with 1 <= x < c and x^2 = a (mod b). Accepts any such x."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier did int(x) (accepting "12", 12.9 -> 12) and only checked x < c, so negative x
+    # (e.g. -r for any root r) and x = 0 passed and the bound c was meaningless
+    x = as_int(ans.get("x"), "x", lo=1, hi=inst["c"] - 1)
+    if x * x % inst["b"] != inst["a"]:
+        raise Invalid("x^2 mod b != a")
+    return None, {}
diff --git a/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bdb4d7f88b2b637df6f7f302aceac575a6c456e7
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"a": 9, "b": 18, "c": 137, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l1-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s4/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l2-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s4/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l2-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..477b86cc1992819f9a4f8dd5410c557b8e526691
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s4/environment/instance.json
@@ -0,0 +1 @@
+{"a": 0, "b": 147, "c": 13114, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s4/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l2-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..448bc18599658ef691fa83bbb4eab6fc4a2fe940
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 6174}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/check.py
@@ -0,0 +1,11 @@
+"""Quadratic congruence: integer x with 1 <= x < c and x^2 = a (mod b). Accepts any such x."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier did int(x) (accepting "12", 12.9 -> 12) and only checked x < c, so negative x
+    # (e.g. -r for any root r) and x = 0 passed and the bound c was meaningless
+    x = as_int(ans.get("x"), "x", lo=1, hi=inst["c"] - 1)
+    if x * x % inst["b"] != inst["a"]:
+        raise Invalid("x^2 mod b != a")
+    return None, {}
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..477b86cc1992819f9a4f8dd5410c557b8e526691
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/instance.json
@@ -0,0 +1 @@
+{"a": 0, "b": 147, "c": 13114, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quadratic-congruence-l5-s9/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l5-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l5-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quadratic-congruence-l5-s9/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l5-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..45edec22a028d7c6a0e7da9f0661ebe673aa5c3f
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l5-s9/environment/instance.json
@@ -0,0 +1 @@
+{"a": 3958282488698417668, "b": 7575469236806246299, "c": 7102530124532258728, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l5-s9/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l5-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..23c1c2f89fd6685f0d3a294d0b529d1ddbeaf0cd
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l5-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 7097494890560016282}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/check.py
@@ -0,0 +1,11 @@
+"""Quadratic congruence: integer x with 1 <= x < c and x^2 = a (mod b). Accepts any such x."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier did int(x) (accepting "12", 12.9 -> 12) and only checked x < c, so negative x
+    # (e.g. -r for any root r) and x = 0 passed and the bound c was meaningless
+    x = as_int(ans.get("x"), "x", lo=1, hi=inst["c"] - 1)
+    if x * x % inst["b"] != inst["a"]:
+        raise Invalid("x^2 mod b != a")
+    return None, {}
diff --git a/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..45edec22a028d7c6a0e7da9f0661ebe673aa5c3f
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/instance.json
@@ -0,0 +1 @@
+{"a": 3958282488698417668, "b": 7575469236806246299, "c": 7102530124532258728, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l5-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s2/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s2/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fd9434e156744801849490d196938bf3782837d7
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"a": 116757058586784956845388387762449504413262155501, "b": 163682378999643305001128986687253590802264586097, "c": 157691229587311232391096340338894324214503389407, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s2/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f10737aee52d8d21baf1d1b8f4780097c1f2538a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 157684794827699656837768561542320876530022839838}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/check.py
@@ -0,0 +1,11 @@
+"""Quadratic congruence: integer x with 1 <= x < c and x^2 = a (mod b). Accepts any such x."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier did int(x) (accepting "12", 12.9 -> 12) and only checked x < c, so negative x
+    # (e.g. -r for any root r) and x = 0 passed and the bound c was meaningless
+    x = as_int(ans.get("x"), "x", lo=1, hi=inst["c"] - 1)
+    if x * x % inst["b"] != inst["a"]:
+        raise Invalid("x^2 mod b != a")
+    return None, {}
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fd9434e156744801849490d196938bf3782837d7
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"a": 116757058586784956845388387762449504413262155501, "b": 163682378999643305001128986687253590802264586097, "c": 157691229587311232391096340338894324214503389407, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s5/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l6-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s5/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l6-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fee33ce10897616c9fe76202c754c4588b82ae7b
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s5/environment/instance.json
@@ -0,0 +1 @@
+{"a": 80528802366340258782383235369770509707082011454, "b": 157897939657185658163447453336584125604239801029, "c": 99545841375422446286744653121014064371677176364, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s5/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l6-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bc9b58ab6b5f80a1bb655c86ac467e444e460f3e
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 99540853897249993691539252562013622436228496156}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/check.py
@@ -0,0 +1,11 @@
+"""Quadratic congruence: integer x with 1 <= x < c and x^2 = a (mod b). Accepts any such x."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier did int(x) (accepting "12", 12.9 -> 12) and only checked x < c, so negative x
+    # (e.g. -r for any root r) and x = 0 passed and the bound c was meaningless
+    x = as_int(ans.get("x"), "x", lo=1, hi=inst["c"] - 1)
+    if x * x % inst["b"] != inst["a"]:
+        raise Invalid("x^2 mod b != a")
+    return None, {}
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fee33ce10897616c9fe76202c754c4588b82ae7b
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/instance.json
@@ -0,0 +1 @@
+{"a": 80528802366340258782383235369770509707082011454, "b": 157897939657185658163447453336584125604239801029, "c": 99545841375422446286744653121014064371677176364, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-vertex-cover-l4-s0/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-vertex-cover-l4-s0/environment/instance.json b/tasks/construct-nppc-vertex-cover-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6c010529cbed665c2b6e1b459df9d8008e57c27e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 6], [0, 9], [0, 11], [0, 17], [0, 19], [0, 21], [0, 24], [0, 25], [0, 26], [0, 30], [0, 31], [0, 35], [0, 37], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 11], [1, 13], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 31], [1, 32], [1, 34], [1, 35], [1, 36], [1, 37], [1, 38], [2, 11], [2, 12], [2, 13], [2, 17], [2, 24], [2, 25], [2, 26], [2, 38], [3, 6], [3, 7], [3, 11], [3, 17], [3, 19], [3, 25], [3, 30], [3, 37], [3, 39], [4, 7], [4, 12], [4, 13], [4, 21], [4, 23], [4, 26], [4, 30], [4, 39], [5, 6], [5, 7], [5, 9], [5, 12], [5, 19], [5, 23], [5, 24], [5, 25], [5, 26], [5, 30], [5, 37], [5, 39], [6, 7], [6, 8], [6, 9], [6, 10], [6, 12], [6, 13], [6, 15], [6, 17], [6, 18], [6, 20], [6, 21], [6, 22], [6, 23], [6, 24], [6, 25], [6, 28], [6, 29], [6, 33], [6, 35], [6, 37], [6, 38], [6, 39], [7, 8], [7, 9], [7, 11], [7, 12], [7, 13], [7, 16], [7, 17], [7, 21], [7, 22], [7, 23], [7, 24], [7, 27], [7, 28], [7, 29], [7, 34], [7, 35], [7, 38], [7, 39], [8, 13], [8, 17], [8, 19], [8, 24], [8, 30], [8, 31], [8, 35], [8, 37], [9, 11], [9, 12], [9, 13], [9, 15], [9, 17], [9, 18], [9, 19], [9, 21], [9, 23], [9, 24], [9, 25], [9, 29], [9, 30], [9, 32], [9, 33], [9, 36], [9, 39], [10, 11], [10, 13], [10, 17], [10, 21], [10, 24], [10, 26], [10, 30], [10, 35], [10, 37], [10, 38], [11, 12], [11, 16], [11, 17], [11, 19], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 31], [11, 32], [11, 33], [11, 35], [11, 36], [11, 37], [11, 38], [11, 39], [12, 13], [12, 14], [12, 15], [12, 17], [12, 18], [12, 19], [12, 24], [12, 25], [12, 26], [12, 27], [12, 28], [12, 29], [12, 30], [12, 32], [12, 37], [12, 38], [13, 16], [13, 17], [13, 19], [13, 21], [13, 23], [13, 24], [13, 25], [13, 26], [13, 27], [13, 30], [13, 31], [13, 33], [13, 35], [13, 37], [13, 38], [14, 17], [14, 19], [14, 21], [14, 23], [14, 24], [14, 25], [14, 26], [14, 31], [14, 37], [15, 17], [15, 23], [15, 24], [15, 26], [15, 30], [15, 31], [15, 38], [16, 31], [16, 35], [16, 37], [17, 19], [17, 21], [17, 22], [17, 23], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 31], [17, 34], [17, 37], [17, 38], [17, 39], [18, 24], [18, 26], [18, 38], [19, 21], [19, 22], [19, 23], [19, 24], [19, 25], [19, 26], [19, 28], [19, 29], [19, 30], [19, 31], [19, 32], [19, 33], [19, 35], [19, 36], [19, 37], [19, 38], [19, 39], [20, 21], [20, 23], [20, 26], [20, 30], [20, 35], [20, 39], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 32], [21, 33], [21, 35], [21, 39], [22, 25], [22, 26], [22, 30], [22, 31], [22, 35], [22, 38], [23, 26], [23, 27], [23, 29], [23, 30], [23, 31], [23, 33], [23, 34], [23, 35], [23, 37], [23, 38], [23, 39], [24, 25], [24, 26], [24, 28], [24, 29], [24, 32], [24, 34], [24, 35], [24, 37], [24, 38], [24, 39], [25, 26], [25, 29], [25, 30], [25, 32], [25, 34], [25, 36], [25, 38], [26, 28], [26, 29], [26, 31], [26, 32], [26, 34], [26, 35], [26, 37], [26, 38], [27, 30], [27, 31], [27, 38], [27, 39], [28, 30], [28, 31], [28, 37], [28, 38], [29, 30], [29, 31], [29, 38], [30, 31], [30, 34], [30, 35], [30, 36], [30, 37], [30, 38], [30, 39], [31, 33], [31, 34], [31, 35], [31, 37], [31, 38], [32, 35], [32, 38], [33, 35], [33, 38], [34, 35], [34, 38], [34, 39], [35, 36], [35, 37], [35, 38], [35, 39], [36, 37], [36, 38], [37, 38], [37, 39], [38, 39]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s0/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8b9c32ccb2bf8132ffea0284d38e1ca5896aa60d
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [1, 6, 7, 9, 11, 12, 13, 17, 19, 21, 23, 24, 25, 26, 30, 31, 35, 37, 38, 39]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l4-s0/tests/check.py b/tasks/construct-nppc-vertex-cover-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s0/tests/check.py
@@ -0,0 +1,18 @@
+"""Vertex cover of size <= k. Accepts any valid cover."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier converts to a set without type checks (floats/bools slip through and
+    # duplicates are silently merged); here entries must be distinct ints in range
+    c = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(c)) != len(c):
+        raise Invalid("cover contains duplicates")
+    if len(c) > k:
+        raise Invalid(f"cover has {len(c)} > {k} vertices")
+    s = set(c)
+    for u, v in inst["edges"]:
+        if u not in s and v not in s:
+            raise Invalid(f"edge ({u},{v}) not covered")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-vertex-cover-l4-s0/tests/instance.json b/tasks/construct-nppc-vertex-cover-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6c010529cbed665c2b6e1b459df9d8008e57c27e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 6], [0, 9], [0, 11], [0, 17], [0, 19], [0, 21], [0, 24], [0, 25], [0, 26], [0, 30], [0, 31], [0, 35], [0, 37], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 11], [1, 13], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 31], [1, 32], [1, 34], [1, 35], [1, 36], [1, 37], [1, 38], [2, 11], [2, 12], [2, 13], [2, 17], [2, 24], [2, 25], [2, 26], [2, 38], [3, 6], [3, 7], [3, 11], [3, 17], [3, 19], [3, 25], [3, 30], [3, 37], [3, 39], [4, 7], [4, 12], [4, 13], [4, 21], [4, 23], [4, 26], [4, 30], [4, 39], [5, 6], [5, 7], [5, 9], [5, 12], [5, 19], [5, 23], [5, 24], [5, 25], [5, 26], [5, 30], [5, 37], [5, 39], [6, 7], [6, 8], [6, 9], [6, 10], [6, 12], [6, 13], [6, 15], [6, 17], [6, 18], [6, 20], [6, 21], [6, 22], [6, 23], [6, 24], [6, 25], [6, 28], [6, 29], [6, 33], [6, 35], [6, 37], [6, 38], [6, 39], [7, 8], [7, 9], [7, 11], [7, 12], [7, 13], [7, 16], [7, 17], [7, 21], [7, 22], [7, 23], [7, 24], [7, 27], [7, 28], [7, 29], [7, 34], [7, 35], [7, 38], [7, 39], [8, 13], [8, 17], [8, 19], [8, 24], [8, 30], [8, 31], [8, 35], [8, 37], [9, 11], [9, 12], [9, 13], [9, 15], [9, 17], [9, 18], [9, 19], [9, 21], [9, 23], [9, 24], [9, 25], [9, 29], [9, 30], [9, 32], [9, 33], [9, 36], [9, 39], [10, 11], [10, 13], [10, 17], [10, 21], [10, 24], [10, 26], [10, 30], [10, 35], [10, 37], [10, 38], [11, 12], [11, 16], [11, 17], [11, 19], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 31], [11, 32], [11, 33], [11, 35], [11, 36], [11, 37], [11, 38], [11, 39], [12, 13], [12, 14], [12, 15], [12, 17], [12, 18], [12, 19], [12, 24], [12, 25], [12, 26], [12, 27], [12, 28], [12, 29], [12, 30], [12, 32], [12, 37], [12, 38], [13, 16], [13, 17], [13, 19], [13, 21], [13, 23], [13, 24], [13, 25], [13, 26], [13, 27], [13, 30], [13, 31], [13, 33], [13, 35], [13, 37], [13, 38], [14, 17], [14, 19], [14, 21], [14, 23], [14, 24], [14, 25], [14, 26], [14, 31], [14, 37], [15, 17], [15, 23], [15, 24], [15, 26], [15, 30], [15, 31], [15, 38], [16, 31], [16, 35], [16, 37], [17, 19], [17, 21], [17, 22], [17, 23], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 31], [17, 34], [17, 37], [17, 38], [17, 39], [18, 24], [18, 26], [18, 38], [19, 21], [19, 22], [19, 23], [19, 24], [19, 25], [19, 26], [19, 28], [19, 29], [19, 30], [19, 31], [19, 32], [19, 33], [19, 35], [19, 36], [19, 37], [19, 38], [19, 39], [20, 21], [20, 23], [20, 26], [20, 30], [20, 35], [20, 39], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 32], [21, 33], [21, 35], [21, 39], [22, 25], [22, 26], [22, 30], [22, 31], [22, 35], [22, 38], [23, 26], [23, 27], [23, 29], [23, 30], [23, 31], [23, 33], [23, 34], [23, 35], [23, 37], [23, 38], [23, 39], [24, 25], [24, 26], [24, 28], [24, 29], [24, 32], [24, 34], [24, 35], [24, 37], [24, 38], [24, 39], [25, 26], [25, 29], [25, 30], [25, 32], [25, 34], [25, 36], [25, 38], [26, 28], [26, 29], [26, 31], [26, 32], [26, 34], [26, 35], [26, 37], [26, 38], [27, 30], [27, 31], [27, 38], [27, 39], [28, 30], [28, 31], [28, 37], [28, 38], [29, 30], [29, 31], [29, 38], [30, 31], [30, 34], [30, 35], [30, 36], [30, 37], [30, 38], [30, 39], [31, 33], [31, 34], [31, 35], [31, 37], [31, 38], [32, 35], [32, 38], [33, 35], [33, 38], [34, 35], [34, 38], [34, 39], [35, 36], [35, 37], [35, 38], [35, 39], [36, 37], [36, 38], [37, 38], [37, 39], [38, 39]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s0/tests/run.py b/tasks/construct-nppc-vertex-cover-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-vertex-cover-l4-s0/tests/test.sh b/tasks/construct-nppc-vertex-cover-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-vertex-cover-l4-s7/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-vertex-cover-l4-s7/environment/instance.json b/tasks/construct-nppc-vertex-cover-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3751782de94d0be09a49142208814e6d1de67fdd
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [0, 11], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 37], [0, 39], [1, 4], [1, 7], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 24], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 34], [1, 39], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 20], [2, 22], [2, 23], [2, 24], [2, 25], [2, 27], [2, 30], [2, 31], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [3, 6], [3, 7], [3, 10], [3, 13], [3, 23], [3, 29], [3, 30], [3, 37], [4, 5], [4, 7], [4, 10], [4, 11], [4, 12], [4, 15], [4, 19], [4, 22], [4, 23], [4, 26], [4, 28], [4, 29], [4, 30], [4, 31], [4, 33], [5, 8], [5, 10], [5, 13], [5, 24], [5, 27], [5, 30], [5, 33], [5, 39], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 13], [6, 15], [6, 16], [6, 17], [6, 18], [6, 19], [6, 21], [6, 22], [6, 23], [6, 25], [6, 26], [6, 27], [6, 29], [6, 30], [6, 32], [6, 33], [6, 35], [6, 37], [6, 39], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 14], [7, 15], [7, 17], [7, 18], [7, 19], [7, 20], [7, 22], [7, 23], [7, 24], [7, 27], [7, 29], [7, 30], [7, 33], [7, 34], [7, 36], [7, 37], [7, 38], [7, 39], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 20], [8, 21], [8, 23], [8, 24], [8, 26], [8, 27], [8, 28], [8, 29], [8, 30], [8, 31], [8, 32], [8, 33], [8, 34], [8, 35], [8, 36], [8, 38], [8, 39], [9, 10], [9, 11], [9, 17], [9, 19], [9, 23], [9, 27], [9, 29], [9, 33], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 23], [10, 27], [10, 28], [10, 30], [10, 33], [10, 34], [10, 37], [10, 39], [11, 13], [11, 17], [11, 19], [11, 21], [11, 23], [11, 24], [11, 26], [11, 27], [11, 32], [11, 33], [11, 35], [11, 37], [11, 39], [12, 17], [12, 27], [12, 29], [12, 30], [12, 33], [12, 39], [13, 14], [13, 15], [13, 16], [13, 17], [13, 19], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 25], [13, 27], [13, 29], [13, 30], [13, 33], [13, 34], [13, 38], [13, 39], [14, 17], [14, 23], [14, 29], [14, 30], [14, 37], [14, 39], [15, 17], [15, 19], [15, 27], [15, 29], [15, 33], [15, 37], [15, 39], [16, 17], [16, 19], [16, 23], [16, 24], [16, 27], [16, 33], [16, 37], [17, 18], [17, 19], [17, 21], [17, 22], [17, 23], [17, 24], [17, 26], [17, 27], [17, 28], [17, 30], [17, 31], [17, 32], [17, 33], [17, 37], [17, 38], [17, 39], [18, 23], [18, 24], [18, 27], [18, 29], [18, 30], [18, 33], [18, 39], [19, 25], [19, 27], [19, 29], [19, 30], [19, 32], [19, 35], [19, 37], [19, 39], [20, 23], [20, 29], [20, 30], [20, 37], [20, 39], [21, 23], [21, 24], [21, 30], [21, 37], [21, 39], [22, 23], [22, 24], [22, 27], [22, 39], [23, 25], [23, 26], [23, 29], [23, 32], [23, 33], [23, 34], [23, 35], [23, 36], [23, 38], [23, 39], [24, 25], [24, 26], [24, 27], [24, 28], [24, 29], [24, 31], [24, 33], [24, 35], [24, 36], [24, 37], [24, 38], [24, 39], [25, 27], [25, 29], [25, 39], [26, 27], [26, 29], [26, 39], [27, 29], [27, 30], [27, 33], [27, 34], [27, 35], [27, 37], [27, 38], [27, 39], [28, 29], [28, 30], [28, 33], [28, 39], [29, 30], [29, 33], [29, 37], [29, 39], [30, 31], [30, 32], [30, 33], [30, 34], [30, 36], [30, 37], [30, 38], [30, 39], [31, 33], [31, 37], [31, 39], [32, 33], [32, 37], [33, 34], [33, 35], [33, 37], [33, 38], [33, 39], [34, 37], [35, 39], [36, 37], [37, 38], [37, 39]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s7/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..775bb52a7121ba31f2e926e61d3e4529978a1fac
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 1, 2, 4, 6, 7, 8, 10, 11, 13, 17, 19, 23, 24, 27, 29, 30, 33, 37, 39]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l4-s7/tests/check.py b/tasks/construct-nppc-vertex-cover-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s7/tests/check.py
@@ -0,0 +1,18 @@
+"""Vertex cover of size <= k. Accepts any valid cover."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier converts to a set without type checks (floats/bools slip through and
+    # duplicates are silently merged); here entries must be distinct ints in range
+    c = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(c)) != len(c):
+        raise Invalid("cover contains duplicates")
+    if len(c) > k:
+        raise Invalid(f"cover has {len(c)} > {k} vertices")
+    s = set(c)
+    for u, v in inst["edges"]:
+        if u not in s and v not in s:
+            raise Invalid(f"edge ({u},{v}) not covered")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-vertex-cover-l4-s7/tests/instance.json b/tasks/construct-nppc-vertex-cover-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3751782de94d0be09a49142208814e6d1de67fdd
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [0, 11], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 37], [0, 39], [1, 4], [1, 7], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 24], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 34], [1, 39], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 20], [2, 22], [2, 23], [2, 24], [2, 25], [2, 27], [2, 30], [2, 31], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [3, 6], [3, 7], [3, 10], [3, 13], [3, 23], [3, 29], [3, 30], [3, 37], [4, 5], [4, 7], [4, 10], [4, 11], [4, 12], [4, 15], [4, 19], [4, 22], [4, 23], [4, 26], [4, 28], [4, 29], [4, 30], [4, 31], [4, 33], [5, 8], [5, 10], [5, 13], [5, 24], [5, 27], [5, 30], [5, 33], [5, 39], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 13], [6, 15], [6, 16], [6, 17], [6, 18], [6, 19], [6, 21], [6, 22], [6, 23], [6, 25], [6, 26], [6, 27], [6, 29], [6, 30], [6, 32], [6, 33], [6, 35], [6, 37], [6, 39], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 14], [7, 15], [7, 17], [7, 18], [7, 19], [7, 20], [7, 22], [7, 23], [7, 24], [7, 27], [7, 29], [7, 30], [7, 33], [7, 34], [7, 36], [7, 37], [7, 38], [7, 39], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 20], [8, 21], [8, 23], [8, 24], [8, 26], [8, 27], [8, 28], [8, 29], [8, 30], [8, 31], [8, 32], [8, 33], [8, 34], [8, 35], [8, 36], [8, 38], [8, 39], [9, 10], [9, 11], [9, 17], [9, 19], [9, 23], [9, 27], [9, 29], [9, 33], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 23], [10, 27], [10, 28], [10, 30], [10, 33], [10, 34], [10, 37], [10, 39], [11, 13], [11, 17], [11, 19], [11, 21], [11, 23], [11, 24], [11, 26], [11, 27], [11, 32], [11, 33], [11, 35], [11, 37], [11, 39], [12, 17], [12, 27], [12, 29], [12, 30], [12, 33], [12, 39], [13, 14], [13, 15], [13, 16], [13, 17], [13, 19], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 25], [13, 27], [13, 29], [13, 30], [13, 33], [13, 34], [13, 38], [13, 39], [14, 17], [14, 23], [14, 29], [14, 30], [14, 37], [14, 39], [15, 17], [15, 19], [15, 27], [15, 29], [15, 33], [15, 37], [15, 39], [16, 17], [16, 19], [16, 23], [16, 24], [16, 27], [16, 33], [16, 37], [17, 18], [17, 19], [17, 21], [17, 22], [17, 23], [17, 24], [17, 26], [17, 27], [17, 28], [17, 30], [17, 31], [17, 32], [17, 33], [17, 37], [17, 38], [17, 39], [18, 23], [18, 24], [18, 27], [18, 29], [18, 30], [18, 33], [18, 39], [19, 25], [19, 27], [19, 29], [19, 30], [19, 32], [19, 35], [19, 37], [19, 39], [20, 23], [20, 29], [20, 30], [20, 37], [20, 39], [21, 23], [21, 24], [21, 30], [21, 37], [21, 39], [22, 23], [22, 24], [22, 27], [22, 39], [23, 25], [23, 26], [23, 29], [23, 32], [23, 33], [23, 34], [23, 35], [23, 36], [23, 38], [23, 39], [24, 25], [24, 26], [24, 27], [24, 28], [24, 29], [24, 31], [24, 33], [24, 35], [24, 36], [24, 37], [24, 38], [24, 39], [25, 27], [25, 29], [25, 39], [26, 27], [26, 29], [26, 39], [27, 29], [27, 30], [27, 33], [27, 34], [27, 35], [27, 37], [27, 38], [27, 39], [28, 29], [28, 30], [28, 33], [28, 39], [29, 30], [29, 33], [29, 37], [29, 39], [30, 31], [30, 32], [30, 33], [30, 34], [30, 36], [30, 37], [30, 38], [30, 39], [31, 33], [31, 37], [31, 39], [32, 33], [32, 37], [33, 34], [33, 35], [33, 37], [33, 38], [33, 39], [34, 37], [35, 39], [36, 37], [37, 38], [37, 39]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s7/tests/run.py b/tasks/construct-nppc-vertex-cover-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-vertex-cover-l4-s7/tests/test.sh b/tasks/construct-nppc-vertex-cover-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-vertex-cover-l4-s9/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l4-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-vertex-cover-l4-s9/environment/instance.json b/tasks/construct-nppc-vertex-cover-l4-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..85c142ddb045bf33e0d7658749a899bffdd28349
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s9/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 3], [0, 6], [0, 8], [0, 17], [0, 31], [0, 32], [0, 35], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 17], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 25], [1, 27], [1, 28], [1, 29], [1, 30], [1, 32], [1, 33], [1, 35], [1, 36], [1, 37], [1, 38], [1, 39], [2, 4], [2, 7], [2, 8], [2, 9], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 20], [2, 22], [2, 23], [2, 24], [2, 26], [2, 27], [2, 31], [2, 32], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [3, 4], [3, 5], [3, 6], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 17], [3, 18], [3, 20], [3, 21], [3, 22], [3, 23], [3, 24], [3, 28], [3, 30], [3, 32], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [4, 6], [4, 8], [4, 12], [4, 14], [4, 16], [4, 17], [4, 21], [4, 22], [4, 23], [4, 25], [4, 26], [4, 27], [4, 29], [4, 30], [4, 32], [4, 33], [4, 34], [4, 35], [4, 36], [4, 37], [4, 39], [5, 6], [5, 8], [5, 15], [5, 18], [5, 21], [5, 22], [5, 23], [5, 31], [5, 32], [5, 34], [5, 35], [5, 39], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 14], [6, 15], [6, 16], [6, 18], [6, 19], [6, 20], [6, 21], [6, 24], [6, 25], [6, 27], [6, 28], [6, 29], [6, 30], [6, 31], [6, 32], [6, 34], [6, 39], [7, 18], [7, 21], [7, 26], [7, 31], [7, 39], [8, 9], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 20], [8, 21], [8, 22], [8, 23], [8, 26], [8, 27], [8, 28], [8, 30], [8, 31], [8, 32], [8, 33], [8, 36], [8, 37], [8, 38], [8, 39], [9, 15], [9, 22], [9, 25], [9, 27], [9, 31], [9, 32], [9, 35], [10, 15], [10, 21], [10, 22], [10, 23], [10, 26], [10, 35], [10, 39], [11, 22], [11, 23], [11, 27], [11, 32], [11, 39], [12, 17], [12, 18], [12, 22], [12, 23], [12, 26], [12, 27], [12, 35], [12, 39], [13, 15], [13, 21], [13, 22], [13, 25], [13, 32], [13, 35], [13, 39], [14, 22], [14, 23], [14, 31], [14, 32], [14, 35], [14, 39], [15, 16], [15, 17], [15, 18], [15, 19], [15, 21], [15, 22], [15, 23], [15, 26], [15, 27], [15, 29], [15, 31], [15, 32], [15, 33], [15, 34], [15, 35], [15, 36], [15, 38], [16, 22], [16, 23], [16, 25], [16, 32], [16, 34], [17, 18], [17, 19], [17, 20], [17, 21], [17, 22], [17, 23], [17, 24], [17, 27], [17, 29], [17, 30], [17, 31], [17, 34], [17, 35], [17, 37], [17, 39], [18, 23], [18, 24], [18, 26], [18, 27], [18, 28], [18, 31], [18, 32], [18, 34], [18, 35], [18, 36], [18, 39], [19, 21], [19, 22], [19, 23], [19, 25], [19, 26], [19, 32], [19, 34], [19, 35], [19, 39], [20, 21], [20, 22], [20, 23], [20, 26], [20, 27], [20, 31], [20, 32], [20, 35], [20, 39], [21, 22], [21, 25], [21, 27], [21, 31], [21, 32], [21, 33], [21, 35], [21, 36], [21, 38], [21, 39], [22, 23], [22, 25], [22, 26], [22, 27], [22, 28], [22, 31], [22, 33], [22, 34], [22, 35], [22, 36], [22, 38], [22, 39], [23, 24], [23, 34], [23, 35], [23, 37], [23, 38], [23, 39], [24, 27], [24, 32], [24, 35], [24, 39], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 34], [25, 38], [26, 27], [26, 29], [26, 30], [26, 31], [26, 34], [26, 36], [26, 39], [27, 29], [27, 30], [27, 31], [27, 32], [27, 34], [27, 35], [27, 36], [27, 38], [27, 39], [28, 32], [28, 34], [28, 35], [28, 39], [29, 31], [29, 35], [30, 31], [30, 32], [30, 34], [30, 35], [30, 39], [31, 32], [31, 34], [31, 37], [31, 38], [31, 39], [32, 33], [32, 34], [32, 35], [32, 37], [33, 35], [34, 38], [34, 39], [35, 36], [35, 39]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s9/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l4-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2abc793d393497ad3a5fc720ce7536af9e580986
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [1, 2, 3, 4, 6, 8, 15, 17, 18, 21, 22, 23, 25, 26, 27, 31, 32, 34, 35, 39]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l4-s9/tests/check.py b/tasks/construct-nppc-vertex-cover-l4-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s9/tests/check.py
@@ -0,0 +1,18 @@
+"""Vertex cover of size <= k. Accepts any valid cover."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier converts to a set without type checks (floats/bools slip through and
+    # duplicates are silently merged); here entries must be distinct ints in range
+    c = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(c)) != len(c):
+        raise Invalid("cover contains duplicates")
+    if len(c) > k:
+        raise Invalid(f"cover has {len(c)} > {k} vertices")
+    s = set(c)
+    for u, v in inst["edges"]:
+        if u not in s and v not in s:
+            raise Invalid(f"edge ({u},{v}) not covered")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-vertex-cover-l4-s9/tests/instance.json b/tasks/construct-nppc-vertex-cover-l4-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..85c142ddb045bf33e0d7658749a899bffdd28349
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s9/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 3], [0, 6], [0, 8], [0, 17], [0, 31], [0, 32], [0, 35], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 17], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 25], [1, 27], [1, 28], [1, 29], [1, 30], [1, 32], [1, 33], [1, 35], [1, 36], [1, 37], [1, 38], [1, 39], [2, 4], [2, 7], [2, 8], [2, 9], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 20], [2, 22], [2, 23], [2, 24], [2, 26], [2, 27], [2, 31], [2, 32], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [3, 4], [3, 5], [3, 6], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 17], [3, 18], [3, 20], [3, 21], [3, 22], [3, 23], [3, 24], [3, 28], [3, 30], [3, 32], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [4, 6], [4, 8], [4, 12], [4, 14], [4, 16], [4, 17], [4, 21], [4, 22], [4, 23], [4, 25], [4, 26], [4, 27], [4, 29], [4, 30], [4, 32], [4, 33], [4, 34], [4, 35], [4, 36], [4, 37], [4, 39], [5, 6], [5, 8], [5, 15], [5, 18], [5, 21], [5, 22], [5, 23], [5, 31], [5, 32], [5, 34], [5, 35], [5, 39], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 14], [6, 15], [6, 16], [6, 18], [6, 19], [6, 20], [6, 21], [6, 24], [6, 25], [6, 27], [6, 28], [6, 29], [6, 30], [6, 31], [6, 32], [6, 34], [6, 39], [7, 18], [7, 21], [7, 26], [7, 31], [7, 39], [8, 9], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 20], [8, 21], [8, 22], [8, 23], [8, 26], [8, 27], [8, 28], [8, 30], [8, 31], [8, 32], [8, 33], [8, 36], [8, 37], [8, 38], [8, 39], [9, 15], [9, 22], [9, 25], [9, 27], [9, 31], [9, 32], [9, 35], [10, 15], [10, 21], [10, 22], [10, 23], [10, 26], [10, 35], [10, 39], [11, 22], [11, 23], [11, 27], [11, 32], [11, 39], [12, 17], [12, 18], [12, 22], [12, 23], [12, 26], [12, 27], [12, 35], [12, 39], [13, 15], [13, 21], [13, 22], [13, 25], [13, 32], [13, 35], [13, 39], [14, 22], [14, 23], [14, 31], [14, 32], [14, 35], [14, 39], [15, 16], [15, 17], [15, 18], [15, 19], [15, 21], [15, 22], [15, 23], [15, 26], [15, 27], [15, 29], [15, 31], [15, 32], [15, 33], [15, 34], [15, 35], [15, 36], [15, 38], [16, 22], [16, 23], [16, 25], [16, 32], [16, 34], [17, 18], [17, 19], [17, 20], [17, 21], [17, 22], [17, 23], [17, 24], [17, 27], [17, 29], [17, 30], [17, 31], [17, 34], [17, 35], [17, 37], [17, 39], [18, 23], [18, 24], [18, 26], [18, 27], [18, 28], [18, 31], [18, 32], [18, 34], [18, 35], [18, 36], [18, 39], [19, 21], [19, 22], [19, 23], [19, 25], [19, 26], [19, 32], [19, 34], [19, 35], [19, 39], [20, 21], [20, 22], [20, 23], [20, 26], [20, 27], [20, 31], [20, 32], [20, 35], [20, 39], [21, 22], [21, 25], [21, 27], [21, 31], [21, 32], [21, 33], [21, 35], [21, 36], [21, 38], [21, 39], [22, 23], [22, 25], [22, 26], [22, 27], [22, 28], [22, 31], [22, 33], [22, 34], [22, 35], [22, 36], [22, 38], [22, 39], [23, 24], [23, 34], [23, 35], [23, 37], [23, 38], [23, 39], [24, 27], [24, 32], [24, 35], [24, 39], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 34], [25, 38], [26, 27], [26, 29], [26, 30], [26, 31], [26, 34], [26, 36], [26, 39], [27, 29], [27, 30], [27, 31], [27, 32], [27, 34], [27, 35], [27, 36], [27, 38], [27, 39], [28, 32], [28, 34], [28, 35], [28, 39], [29, 31], [29, 35], [30, 31], [30, 32], [30, 34], [30, 35], [30, 39], [31, 32], [31, 34], [31, 37], [31, 38], [31, 39], [32, 33], [32, 34], [32, 35], [32, 37], [33, 35], [34, 38], [34, 39], [35, 36], [35, 39]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s9/tests/run.py b/tasks/construct-nppc-vertex-cover-l4-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-vertex-cover-l4-s9/tests/test.sh b/tasks/construct-nppc-vertex-cover-l4-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-intermediate-integration-l1-s1/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l1-s1/environment/instance.json b/tasks/construct-rg-intermediate-integration-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9262533f9f008af2bfc9a6d3fd9352fd3f35dfd6
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "(x - 6)**3", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l1-s1/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b805ccba025a4201d90ccf2217abe10786d612c1
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "x**4/4 - 6*x**3 + 54*x**2 - 216*x + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l1-s1/tests/check.py b/tasks/construct-rg-intermediate-integration-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s1/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l1-s1/tests/instance.json b/tasks/construct-rg-intermediate-integration-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9262533f9f008af2bfc9a6d3fd9352fd3f35dfd6
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "(x - 6)**3", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l1-s1/tests/run.py b/tasks/construct-rg-intermediate-integration-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l1-s1/tests/test.sh b/tasks/construct-rg-intermediate-integration-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-intermediate-integration-l1-s6/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l1-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l1-s6/environment/instance.json b/tasks/construct-rg-intermediate-integration-l1-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e9296675e92223625a6aa8332f5abad4fbd721e1
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s6/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-3*(6*x - 9)**2", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l1-s6/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l1-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1b10be8691a00dfb5425cf42a15ad10ead609e89
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "-36*x**3 + 162*x**2 - 243*x + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l1-s6/tests/check.py b/tasks/construct-rg-intermediate-integration-l1-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s6/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l1-s6/tests/instance.json b/tasks/construct-rg-intermediate-integration-l1-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e9296675e92223625a6aa8332f5abad4fbd721e1
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s6/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-3*(6*x - 9)**2", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l1-s6/tests/run.py b/tasks/construct-rg-intermediate-integration-l1-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l1-s6/tests/test.sh b/tasks/construct-rg-intermediate-integration-l1-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-intermediate-integration-l1-s8/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l1-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l1-s8/environment/instance.json b/tasks/construct-rg-intermediate-integration-l1-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2c5acd10d82446f152c4c46170659c7a012fc237
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s8/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-3*(8*x - 8)**4", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l1-s8/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l1-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..96b02eaf90ad85af9e12ef02b1a1b593425c273b
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "-12288*x**5/5 + 12288*x**4 - 24576*x**3 + 24576*x**2 - 12288*x + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l1-s8/tests/check.py b/tasks/construct-rg-intermediate-integration-l1-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s8/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l1-s8/tests/instance.json b/tasks/construct-rg-intermediate-integration-l1-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2c5acd10d82446f152c4c46170659c7a012fc237
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s8/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-3*(8*x - 8)**4", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l1-s8/tests/run.py b/tasks/construct-rg-intermediate-integration-l1-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l1-s8/tests/test.sh b/tasks/construct-rg-intermediate-integration-l1-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-intermediate-integration-l5-s7/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l5-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l5-s7/environment/instance.json b/tasks/construct-rg-intermediate-integration-l5-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e49a78796f72792ff247a0b2690d1dde08e09e18
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s7/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "x*sin(x)", "problem_type": "polynomial_exp_trig", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l5-s7/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l5-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bbd195b1e2ae9e07ecff002e03200cbc70db89a4
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "-x*cos(x) + sin(x) + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l5-s7/tests/check.py b/tasks/construct-rg-intermediate-integration-l5-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s7/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l5-s7/tests/instance.json b/tasks/construct-rg-intermediate-integration-l5-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e49a78796f72792ff247a0b2690d1dde08e09e18
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s7/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "x*sin(x)", "problem_type": "polynomial_exp_trig", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l5-s7/tests/run.py b/tasks/construct-rg-intermediate-integration-l5-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l5-s7/tests/test.sh b/tasks/construct-rg-intermediate-integration-l5-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-intermediate-integration-l5-s9/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l5-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l5-s9/environment/instance.json b/tasks/construct-rg-intermediate-integration-l5-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..801175b5c687e819d3c02f0fdb98468c7dd19121
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s9/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l5-s9/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l5-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..54f893b8836f8da253a742b0e0c6a1b913355f1d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "-sin(x)**2/2 + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l5-s9/tests/check.py b/tasks/construct-rg-intermediate-integration-l5-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s9/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l5-s9/tests/instance.json b/tasks/construct-rg-intermediate-integration-l5-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..801175b5c687e819d3c02f0fdb98468c7dd19121
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s9/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l5-s9/tests/run.py b/tasks/construct-rg-intermediate-integration-l5-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l5-s9/tests/test.sh b/tasks/construct-rg-intermediate-integration-l5-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-intermediate-integration-l6-s5/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l6-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l6-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l6-s5/environment/instance.json b/tasks/construct-rg-intermediate-integration-l6-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9a5b371eea128f22405da70a4046148d008e1249
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l6-s5/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l6-s5/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l6-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4be1cd27f7a14d03b05f6827e29474658dceca55
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l6-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l6-s5/tests/check.py b/tasks/construct-rg-intermediate-integration-l6-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l6-s5/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l6-s5/tests/instance.json b/tasks/construct-rg-intermediate-integration-l6-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9a5b371eea128f22405da70a4046148d008e1249
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l6-s5/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l6-s5/tests/run.py b/tasks/construct-rg-intermediate-integration-l6-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l6-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l6-s5/tests/test.sh b/tasks/construct-rg-intermediate-integration-l6-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l6-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-bezout-identity-l3-s8/environment/Dockerfile b/tasks/construct-rlve-bezout-identity-l3-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l3-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-bezout-identity-l3-s8/environment/instance.json b/tasks/construct-rlve-bezout-identity-l3-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f0b39b8ee7c364c063a6718ee3d65c1ad94557d
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l3-s8/environment/instance.json
@@ -0,0 +1 @@
+{"A": [-469, -105, -322, 427, -462, 196], "target": 7, "family": "rlve_bezout_identity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-bezout-identity-l3-s8/solution/solve.sh b/tasks/construct-rlve-bezout-identity-l3-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c89d0497a50d8566966c0ba0cdf1aec25608c9c2
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l3-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"X": [2, -9, 0, 0, 0, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-bezout-identity-l3-s8/tests/check.py b/tasks/construct-rlve-bezout-identity-l3-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b4cb860ed36974a12b71adc9a0fa3f1ad85c814a
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l3-s8/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A = inst["A"]
+    X = int_list(ans.get("X"), len(A), name="X")
+    S = sum(a * x for a, x in zip(A, X))
+    if S != inst["target"]:
+        raise Invalid(f"S = {S}, required {inst['target']}")
+    return None, {}
diff --git a/tasks/construct-rlve-bezout-identity-l3-s8/tests/instance.json b/tasks/construct-rlve-bezout-identity-l3-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f0b39b8ee7c364c063a6718ee3d65c1ad94557d
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l3-s8/tests/instance.json
@@ -0,0 +1 @@
+{"A": [-469, -105, -322, 427, -462, 196], "target": 7, "family": "rlve_bezout_identity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-bezout-identity-l3-s8/tests/run.py b/tasks/construct-rlve-bezout-identity-l3-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l3-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-bezout-identity-l3-s8/tests/test.sh b/tasks/construct-rlve-bezout-identity-l3-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l3-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s2/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s2/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..81e998f9ec11dc73750cec7061a9c081726a37e8
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 77, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s2/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c7d4e06070fb513f3a25df140242727b6582d26a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"L": 8, "R": 21}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/check.py
@@ -0,0 +1,30 @@
+from run import Invalid, as_int
+
+
+def digit_sum_prefix(n):
+    """sum of digit sums of all integers in [0, n] (exact, digit DP)."""
+    if n <= 0:
+        return 0
+    s = str(n)
+    total, prefix_sum = 0, 0
+    k = len(s)
+    for i, ch in enumerate(s):
+        d = int(ch)
+        rest = k - i - 1
+        p = 10 ** rest
+        # numbers with this digit < d, free suffix of `rest` digits
+        total += d * prefix_sum * p + (d * (d - 1) // 2) * p + d * (45 * rest * p // 10 if rest else 0)
+        prefix_sum += d
+    return total + prefix_sum  # include n itself
+
+
+def check(inst, ans):
+    mod = inst["mod"]
+    L = as_int(ans.get("L"), "L", lo=1)
+    R = as_int(ans.get("R"), "R", lo=1, hi=10 * mod)
+    if L > R:
+        raise Invalid("need L <= R")
+    total = digit_sum_prefix(R) - digit_sum_prefix(L - 1)
+    if total % mod:
+        raise Invalid(f"sum of digit sums over [L, R] is {total}, not divisible by {mod}")
+    return None, {}
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..81e998f9ec11dc73750cec7061a9c081726a37e8
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 77, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-construct-hack-interval-l2-s7/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l2-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l2-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-construct-hack-interval-l2-s7/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l2-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a52bf0a81b39d3333f5f69e5ca75a24b4af59a6e
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l2-s7/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 2498, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l2-s7/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l2-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1eac0ccd734aa17145bd8fbf7d8d34197f3093ba
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l2-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"L": 23, "R": 273}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/check.py
@@ -0,0 +1,30 @@
+from run import Invalid, as_int
+
+
+def digit_sum_prefix(n):
+    """sum of digit sums of all integers in [0, n] (exact, digit DP)."""
+    if n <= 0:
+        return 0
+    s = str(n)
+    total, prefix_sum = 0, 0
+    k = len(s)
+    for i, ch in enumerate(s):
+        d = int(ch)
+        rest = k - i - 1
+        p = 10 ** rest
+        # numbers with this digit < d, free suffix of `rest` digits
+        total += d * prefix_sum * p + (d * (d - 1) // 2) * p + d * (45 * rest * p // 10 if rest else 0)
+        prefix_sum += d
+    return total + prefix_sum  # include n itself
+
+
+def check(inst, ans):
+    mod = inst["mod"]
+    L = as_int(ans.get("L"), "L", lo=1)
+    R = as_int(ans.get("R"), "R", lo=1, hi=10 * mod)
+    if L > R:
+        raise Invalid("need L <= R")
+    total = digit_sum_prefix(R) - digit_sum_prefix(L - 1)
+    if total % mod:
+        raise Invalid(f"sum of digit sums over [L, R] is {total}, not divisible by {mod}")
+    return None, {}
diff --git a/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a52bf0a81b39d3333f5f69e5ca75a24b4af59a6e
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 2498, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l2-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s3/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s3/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c8550de09fbfa85a858a0570485833d63671c360
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 806685780153518, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s3/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fef4bda098fa1ad883561c33b537fb6918ff629c
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"L": 153486241228144, "R": 253486241228143}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/check.py
@@ -0,0 +1,30 @@
+from run import Invalid, as_int
+
+
+def digit_sum_prefix(n):
+    """sum of digit sums of all integers in [0, n] (exact, digit DP)."""
+    if n <= 0:
+        return 0
+    s = str(n)
+    total, prefix_sum = 0, 0
+    k = len(s)
+    for i, ch in enumerate(s):
+        d = int(ch)
+        rest = k - i - 1
+        p = 10 ** rest
+        # numbers with this digit < d, free suffix of `rest` digits
+        total += d * prefix_sum * p + (d * (d - 1) // 2) * p + d * (45 * rest * p // 10 if rest else 0)
+        prefix_sum += d
+    return total + prefix_sum  # include n itself
+
+
+def check(inst, ans):
+    mod = inst["mod"]
+    L = as_int(ans.get("L"), "L", lo=1)
+    R = as_int(ans.get("R"), "R", lo=1, hi=10 * mod)
+    if L > R:
+        raise Invalid("need L <= R")
+    total = digit_sum_prefix(R) - digit_sum_prefix(L - 1)
+    if total % mod:
+        raise Invalid(f"sum of digit sums over [L, R] is {total}, not divisible by {mod}")
+    return None, {}
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c8550de09fbfa85a858a0570485833d63671c360
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 806685780153518, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s4/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l5-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s4/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..19a4282ffb0663632d07b23741d0345bc671ee46
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s4/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 418967893858583, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s4/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l5-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1e4c5dc2707781082e60145c95259c4f42003a8d
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"L": 403486301737328, "R": 503486301737327}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/check.py
@@ -0,0 +1,30 @@
+from run import Invalid, as_int
+
+
+def digit_sum_prefix(n):
+    """sum of digit sums of all integers in [0, n] (exact, digit DP)."""
+    if n <= 0:
+        return 0
+    s = str(n)
+    total, prefix_sum = 0, 0
+    k = len(s)
+    for i, ch in enumerate(s):
+        d = int(ch)
+        rest = k - i - 1
+        p = 10 ** rest
+        # numbers with this digit < d, free suffix of `rest` digits
+        total += d * prefix_sum * p + (d * (d - 1) // 2) * p + d * (45 * rest * p // 10 if rest else 0)
+        prefix_sum += d
+    return total + prefix_sum  # include n itself
+
+
+def check(inst, ans):
+    mod = inst["mod"]
+    L = as_int(ans.get("L"), "L", lo=1)
+    R = as_int(ans.get("R"), "R", lo=1, hi=10 * mod)
+    if L > R:
+        raise Invalid("need L <= R")
+    total = digit_sum_prefix(R) - digit_sum_prefix(L - 1)
+    if total % mod:
+        raise Invalid(f"sum of digit sums over [L, R] is {total}, not divisible by {mod}")
+    return None, {}
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..19a4282ffb0663632d07b23741d0345bc671ee46
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 418967893858583, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/environment/Dockerfile b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/environment/instance.json b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2e9420c64a2f89486216041b7a984983c7dc0170
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"A": [7, 0, 6, 2], "family": "rlve_distinct_subset_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/solution/solve.sh b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5eb9de481ba0d1e0c08f42ce2951dfded0be19df
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"B": [0, 2, 7, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/check.py b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..06bbbcf872c2fca05785f40fdfdcf85a5e5a0e7c
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/check.py
@@ -0,0 +1,22 @@
+from collections import Counter
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A = inst["A"]
+    n = len(A)
+    B = int_list(ans.get("B"), n, name="B")
+    if Counter(B) != Counter(A):
+        raise Invalid("B is not a permutation of A")
+    d = [a - b for a, b in zip(A, B)]
+    # count subsets (including empty and full) with sum 0; the empty and full sets always qualify
+    ways = Counter({0: 1})
+    for x in d:
+        nxt = Counter(ways)
+        for s, c in ways.items():
+            nxt[s + x] += c
+        ways = nxt
+    if ways[0] != 2:
+        raise Invalid(f"{ways[0] - 2} non-empty proper subsets have equal sums in A and B")
+    return None, {}
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/instance.json b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2e9420c64a2f89486216041b7a984983c7dc0170
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"A": [7, 0, 6, 2], "family": "rlve_distinct_subset_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/run.py b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/test.sh b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l1-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-even-degree-partition-l4-s5/environment/Dockerfile b/tasks/construct-rlve-even-degree-partition-l4-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l4-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-even-degree-partition-l4-s5/environment/instance.json b/tasks/construct-rlve-even-degree-partition-l4-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bfe83278377f524cb5625d8cd3404f94d551d7e1
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l4-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 18, "edges": [[0, 1], [0, 3], [0, 8], [0, 9], [0, 11], [0, 14], [0, 17], [1, 4], [1, 8], [1, 11], [1, 15], [1, 16], [1, 17], [2, 8], [2, 13], [2, 14], [2, 15], [3, 4], [3, 5], [3, 15], [3, 16], [4, 6], [4, 9], [4, 11], [4, 15], [4, 17], [5, 15], [6, 7], [6, 13], [7, 8], [7, 9], [7, 12], [8, 10], [8, 13], [10, 11], [10, 12], [10, 13], [11, 13], [11, 17], [12, 14], [12, 17], [13, 17], [14, 15], [14, 17], [15, 16], [15, 17], [16, 17]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l4-s5/solution/solve.sh b/tasks/construct-rlve-even-degree-partition-l4-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..eeebe1c8ad8f7846a8da34977ac7a5332c5adf3c
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l4-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"groups": [1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-even-degree-partition-l4-s5/tests/check.py b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c7f0f71ea6d10264ececcc933b97a4a0e6eaf8e
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    g = int_list(ans.get("groups"), n, 1, 2, "groups")
+    deg = [0] * n
+    for u, v in inst["edges"]:
+        if g[u] == g[v]:
+            deg[u] += 1
+            deg[v] += 1
+    for v in range(n):
+        if deg[v] % 2:
+            raise Invalid(f"vertex {v} has {deg[v]} same-group neighbours")
+    return None, {}
diff --git a/tasks/construct-rlve-even-degree-partition-l4-s5/tests/instance.json b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bfe83278377f524cb5625d8cd3404f94d551d7e1
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 18, "edges": [[0, 1], [0, 3], [0, 8], [0, 9], [0, 11], [0, 14], [0, 17], [1, 4], [1, 8], [1, 11], [1, 15], [1, 16], [1, 17], [2, 8], [2, 13], [2, 14], [2, 15], [3, 4], [3, 5], [3, 15], [3, 16], [4, 6], [4, 9], [4, 11], [4, 15], [4, 17], [5, 15], [6, 7], [6, 13], [7, 8], [7, 9], [7, 12], [8, 10], [8, 13], [10, 11], [10, 12], [10, 13], [11, 13], [11, 17], [12, 14], [12, 17], [13, 17], [14, 15], [14, 17], [15, 16], [15, 17], [16, 17]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l4-s5/tests/run.py b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-even-degree-partition-l4-s5/tests/test.sh b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l4-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-graph-isomorphism-l2-s8/environment/Dockerfile b/tasks/construct-rlve-graph-isomorphism-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l2-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-graph-isomorphism-l2-s8/environment/instance.json b/tasks/construct-rlve-graph-isomorphism-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..72e23dc7d8fb22a9fec3cd6ab04b5c80e24dd1cf
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 8, "edges1": [[3, 4], [2, 4], [3, 5], [2, 3], [1, 2], [5, 7], [2, 6], [1, 5], [0, 2], [3, 6], [0, 1], [0, 7], [4, 7], [1, 6], [0, 3], [4, 5], [1, 7], [1, 3]], "edges2": [[4, 7], [3, 4], [2, 4], [1, 5], [4, 5], [0, 2], [3, 6], [5, 6], [1, 2], [1, 4], [2, 6], [0, 7], [6, 7], [4, 6], [0, 1], [3, 5], [5, 7], [0, 5]], "family": "rlve_graph_isomorphism", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-graph-isomorphism-l2-s8/solution/solve.sh b/tasks/construct-rlve-graph-isomorphism-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9bf7b1b2d5340b243a87f2235af2c4956fe10f8e
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l2-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"p": [7, 5, 6, 4, 2, 1, 3, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/check.py b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..64b755f5ab12e7270811ccfc2f02d104715517b7
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/check.py
@@ -0,0 +1,13 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("p"), n, 0, n - 1, "p")
+    if len(set(p)) != n:
+        raise Invalid("p is not a permutation")
+    e2 = {(min(u, v), max(u, v)) for u, v in inst["edges2"]}
+    img = {(min(p[u], p[v]), max(p[u], p[v])) for u, v in inst["edges1"]}
+    if img != e2:
+        raise Invalid(f"{len(img - e2)} edges of G1 are not mapped onto edges of G2")
+    return None, {}
diff --git a/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/instance.json b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..72e23dc7d8fb22a9fec3cd6ab04b5c80e24dd1cf
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 8, "edges1": [[3, 4], [2, 4], [3, 5], [2, 3], [1, 2], [5, 7], [2, 6], [1, 5], [0, 2], [3, 6], [0, 1], [0, 7], [4, 7], [1, 6], [0, 3], [4, 5], [1, 7], [1, 3]], "edges2": [[4, 7], [3, 4], [2, 4], [1, 5], [4, 5], [0, 2], [3, 6], [5, 6], [1, 2], [1, 4], [2, 6], [0, 7], [6, 7], [4, 6], [0, 1], [3, 5], [5, 7], [0, 5]], "family": "rlve_graph_isomorphism", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/run.py b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/test.sh b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l2-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-grid-parity-construction-l6-s0/environment/Dockerfile b/tasks/construct-rlve-grid-parity-construction-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-grid-parity-construction-l6-s0/environment/instance.json b/tasks/construct-rlve-grid-parity-construction-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7e6601df8230c0531e0f60831364602347ba959
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"parity": ["1101010100111000100111", "1100110011001100101101", "0101101010010011101011", "1100100101100100011101", "1101010000110010001111", "0100101110111001001010", "0011100010001110011110", "1101100001111011101000", "1111101110100011001110", "1000110001100100111010", "0100000100010100010011", "1010101100001111110011", "1101011011111110111110", "1011001000110101110110"], "family": "rlve_grid_parity_construction", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-grid-parity-construction-l6-s0/solution/solve.sh b/tasks/construct-rlve-grid-parity-construction-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..45bfdc17600c5bdc715b60d458f26603116d0cd9
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"grid": ["0011001010111100111101", "1001101110100011111110", "0001111101000101101101", "1110111101011100010100", "1001000001101011000110", "1100001111100110110010", "1111111000001010000011", "1000011001110011101000", "1110111111011100100111", "0011101001011011011100", "0011000001111000010111", "0011001111111011111101", "1101011010000110011101", "1111010111001100101010"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/check.py b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..89d5d286593348d0000ac10db74e1c6242be6c97
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/check.py
@@ -0,0 +1,22 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    P = inst["parity"]
+    N, M = len(P), len(P[0])
+    G = ans.get("grid")
+    if not isinstance(G, list) or len(G) != N:
+        raise Invalid(f"grid must be a list of {N} strings")
+    for r in G:
+        if not isinstance(r, str) or len(r) != M or set(r) - {"0", "1"}:
+            raise Invalid(f"each row must be a string of {M} characters '0'/'1'")
+    for i in range(N):
+        for j in range(M):
+            v = int(G[i][j])
+            for di, dj in ((-1, 0), (1, 0), (0, -1), (0, 1)):
+                a, b = i + di, j + dj
+                if 0 <= a < N and 0 <= b < M:
+                    v ^= int(G[a][b])
+            if v != int(P[i][j]):
+                raise Invalid(f"parity mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/instance.json b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7e6601df8230c0531e0f60831364602347ba959
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"parity": ["1101010100111000100111", "1100110011001100101101", "0101101010010011101011", "1100100101100100011101", "1101010000110010001111", "0100101110111001001010", "0011100010001110011110", "1101100001111011101000", "1111101110100011001110", "1000110001100100111010", "0100000100010100010011", "1010101100001111110011", "1101011011111110111110", "1011001000110101110110"], "family": "rlve_grid_parity_construction", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/run.py b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/test.sh b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-imp-party-l3-s5/tests/run.py b/tasks/construct-rlve-imp-party-l3-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l3-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-imp-party-l4-s1/environment/Dockerfile b/tasks/construct-rlve-imp-party-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-imp-party-l4-s1/environment/instance.json b/tasks/construct-rlve-imp-party-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..48994e27400fafb5b0c0795ee7b050d4ef64dff2
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 32], [0, 33], [0, 34], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 32], [1, 33], [1, 35], [2, 4], [2, 15], [2, 16], [2, 18], [2, 23], [2, 25], [2, 26], [2, 27], [2, 28], [2, 30], [2, 33], [3, 4], [3, 8], [3, 11], [3, 14], [3, 15], [3, 17], [3, 18], [3, 20], [3, 21], [3, 23], [3, 24], [3, 25], [3, 27], [3, 29], [3, 32], [4, 7], [4, 8], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 20], [4, 21], [4, 23], [4, 24], [4, 25], [4, 26], [4, 27], [4, 28], [4, 29], [4, 30], [4, 31], [4, 32], [4, 33], [4, 34], [5, 8], [5, 14], [5, 15], [5, 16], [5, 17], [5, 24], [5, 26], [5, 27], [5, 28], [5, 29], [5, 30], [6, 8], [6, 11], [6, 14], [6, 16], [6, 21], [6, 27], [6, 28], [6, 32], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 20], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 26], [7, 27], [7, 28], [7, 29], [7, 30], [7, 31], [7, 32], [7, 33], [7, 34], [7, 35], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [8, 22], [8, 23], [8, 24], [8, 25], [8, 26], [8, 27], [8, 28], [8, 29], [8, 30], [8, 31], [8, 32], [8, 33], [8, 35], [9, 11], [9, 14], [9, 16], [9, 17], [9, 20], [9, 25], [9, 33], [10, 14], [10, 16], [10, 18], [10, 20], [10, 24], [10, 29], [10, 32], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 23], [11, 24], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 30], [11, 32], [11, 33], [12, 14], [12, 17], [12, 21], [12, 23], [12, 27], [12, 29], [12, 33], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 25], [13, 26], [13, 27], [13, 28], [13, 29], [13, 30], [13, 32], [13, 33], [13, 34], [14, 15], [14, 16], [14, 17], [14, 18], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 25], [14, 26], [14, 27], [14, 28], [14, 29], [14, 30], [14, 31], [14, 32], [14, 33], [14, 35], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [15, 23], [15, 24], [15, 25], [15, 26], [15, 27], [15, 28], [15, 29], [15, 30], [15, 32], [15, 33], [15, 34], [15, 35], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [16, 22], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 28], [16, 29], [16, 30], [16, 31], [16, 32], [16, 33], [16, 35], [17, 18], [17, 19], [17, 20], [17, 21], [17, 22], [17, 23], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 30], [17, 32], [17, 33], [17, 35], [18, 19], [18, 20], [18, 21], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [18, 28], [18, 29], [18, 30], [18, 31], [18, 32], [18, 33], [18, 34], [18, 35], [19, 21], [19, 23], [19, 24], [19, 32], [20, 21], [20, 23], [20, 24], [20, 25], [20, 26], [20, 27], [20, 28], [20, 29], [20, 30], [20, 31], [20, 32], [20, 33], [20, 34], [20, 35], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 32], [21, 33], [21, 34], [22, 24], [22, 30], [22, 33], [23, 24], [23, 25], [23, 26], [23, 27], [23, 28], [23, 29], [23, 30], [23, 31], [23, 32], [23, 33], [23, 34], [23, 35], [24, 25], [24, 26], [24, 27], [24, 28], [24, 29], [24, 30], [24, 31], [24, 32], [24, 33], [24, 34], [24, 35], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 33], [25, 34], [26, 27], [26, 28], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 34], [26, 35], [27, 28], [27, 29], [27, 30], [27, 31], [27, 32], [27, 33], [28, 29], [28, 30], [28, 31], [28, 32], [28, 33], [28, 34], [29, 30], [29, 32], [29, 33], [29, 34], [30, 32], [30, 33], [31, 32], [31, 33], [32, 33], [32, 34]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s1/solution/solve.sh b/tasks/construct-rlve-imp-party-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..eb8b41584920297541410898eb9eff685f6b24b7
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 4, 7, 8, 17, 20, 21, 24, 26, 27, 28, 29]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-imp-party-l4-s1/tests/check.py b/tasks/construct-rlve-imp-party-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..97b5a037a2ba8bf4495cf87cc074d1c60b11311c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s1/tests/check.py
@@ -0,0 +1,14 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    c = int_list(ans.get("clique"), n, 0, 3 * n - 1, "clique")
+    if len(set(c)) != n:
+        raise Invalid("vertices must be distinct")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(n):
+        for j in range(i + 1, n):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-imp-party-l4-s1/tests/instance.json b/tasks/construct-rlve-imp-party-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..48994e27400fafb5b0c0795ee7b050d4ef64dff2
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 32], [0, 33], [0, 34], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 32], [1, 33], [1, 35], [2, 4], [2, 15], [2, 16], [2, 18], [2, 23], [2, 25], [2, 26], [2, 27], [2, 28], [2, 30], [2, 33], [3, 4], [3, 8], [3, 11], [3, 14], [3, 15], [3, 17], [3, 18], [3, 20], [3, 21], [3, 23], [3, 24], [3, 25], [3, 27], [3, 29], [3, 32], [4, 7], [4, 8], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 20], [4, 21], [4, 23], [4, 24], [4, 25], [4, 26], [4, 27], [4, 28], [4, 29], [4, 30], [4, 31], [4, 32], [4, 33], [4, 34], [5, 8], [5, 14], [5, 15], [5, 16], [5, 17], [5, 24], [5, 26], [5, 27], [5, 28], [5, 29], [5, 30], [6, 8], [6, 11], [6, 14], [6, 16], [6, 21], [6, 27], [6, 28], [6, 32], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 20], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 26], [7, 27], [7, 28], [7, 29], [7, 30], [7, 31], [7, 32], [7, 33], [7, 34], [7, 35], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [8, 22], [8, 23], [8, 24], [8, 25], [8, 26], [8, 27], [8, 28], [8, 29], [8, 30], [8, 31], [8, 32], [8, 33], [8, 35], [9, 11], [9, 14], [9, 16], [9, 17], [9, 20], [9, 25], [9, 33], [10, 14], [10, 16], [10, 18], [10, 20], [10, 24], [10, 29], [10, 32], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 23], [11, 24], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 30], [11, 32], [11, 33], [12, 14], [12, 17], [12, 21], [12, 23], [12, 27], [12, 29], [12, 33], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 25], [13, 26], [13, 27], [13, 28], [13, 29], [13, 30], [13, 32], [13, 33], [13, 34], [14, 15], [14, 16], [14, 17], [14, 18], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 25], [14, 26], [14, 27], [14, 28], [14, 29], [14, 30], [14, 31], [14, 32], [14, 33], [14, 35], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [15, 23], [15, 24], [15, 25], [15, 26], [15, 27], [15, 28], [15, 29], [15, 30], [15, 32], [15, 33], [15, 34], [15, 35], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [16, 22], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 28], [16, 29], [16, 30], [16, 31], [16, 32], [16, 33], [16, 35], [17, 18], [17, 19], [17, 20], [17, 21], [17, 22], [17, 23], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 30], [17, 32], [17, 33], [17, 35], [18, 19], [18, 20], [18, 21], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [18, 28], [18, 29], [18, 30], [18, 31], [18, 32], [18, 33], [18, 34], [18, 35], [19, 21], [19, 23], [19, 24], [19, 32], [20, 21], [20, 23], [20, 24], [20, 25], [20, 26], [20, 27], [20, 28], [20, 29], [20, 30], [20, 31], [20, 32], [20, 33], [20, 34], [20, 35], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 32], [21, 33], [21, 34], [22, 24], [22, 30], [22, 33], [23, 24], [23, 25], [23, 26], [23, 27], [23, 28], [23, 29], [23, 30], [23, 31], [23, 32], [23, 33], [23, 34], [23, 35], [24, 25], [24, 26], [24, 27], [24, 28], [24, 29], [24, 30], [24, 31], [24, 32], [24, 33], [24, 34], [24, 35], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 33], [25, 34], [26, 27], [26, 28], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 34], [26, 35], [27, 28], [27, 29], [27, 30], [27, 31], [27, 32], [27, 33], [28, 29], [28, 30], [28, 31], [28, 32], [28, 33], [28, 34], [29, 30], [29, 32], [29, 33], [29, 34], [30, 32], [30, 33], [31, 32], [31, 33], [32, 33], [32, 34]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s1/tests/run.py b/tasks/construct-rlve-imp-party-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-imp-party-l4-s1/tests/test.sh b/tasks/construct-rlve-imp-party-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-imp-party-l4-s6/environment/Dockerfile b/tasks/construct-rlve-imp-party-l4-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-imp-party-l4-s6/environment/instance.json b/tasks/construct-rlve-imp-party-l4-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e02af37db848e8dc6b56bea58c8b24a65c66ed5
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 35], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 35], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 23], [2, 24], [2, 25], [2, 26], [2, 27], [2, 28], [2, 30], [2, 33], [2, 34], [2, 35], [3, 4], [3, 5], [3, 6], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 19], [3, 20], [3, 21], [3, 22], [3, 23], [3, 24], [3, 25], [3, 26], [3, 27], [3, 28], [3, 30], [3, 33], [3, 34], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 20], [4, 21], [4, 22], [4, 23], [4, 24], [4, 25], [4, 26], [4, 27], [4, 28], [4, 30], [4, 31], [4, 33], [4, 35], [5, 6], [5, 9], [5, 11], [5, 15], [5, 16], [5, 18], [5, 20], [5, 21], [5, 23], [5, 24], [5, 25], [5, 28], [5, 30], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 17], [6, 18], [6, 19], [6, 20], [6, 21], [6, 23], [6, 24], [6, 25], [6, 26], [6, 27], [6, 28], [6, 29], [6, 30], [6, 31], [6, 32], [6, 33], [6, 34], [7, 9], [7, 10], [7, 12], [7, 14], [7, 15], [7, 16], [7, 18], [7, 21], [7, 23], [7, 24], [7, 25], [7, 27], [7, 28], [7, 33], [8, 9], [8, 10], [8, 11], [8, 12], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 20], [8, 21], [8, 23], [8, 24], [8, 27], [8, 30], [8, 33], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 17], [9, 18], [9, 20], [9, 21], [9, 22], [9, 23], [9, 24], [9, 25], [9, 26], [9, 27], [9, 28], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 35], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 22], [10, 23], [10, 24], [10, 25], [10, 27], [10, 28], [10, 29], [10, 30], [10, 31], [10, 33], [10, 35], [11, 12], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 22], [11, 23], [11, 24], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 30], [11, 31], [11, 33], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [12, 22], [12, 23], [12, 24], [12, 25], [12, 26], [12, 27], [12, 28], [12, 29], [12, 30], [12, 32], [12, 33], [12, 34], [12, 35], [13, 14], [13, 16], [13, 17], [13, 18], [13, 20], [13, 21], [13, 23], [13, 24], [13, 25], [13, 27], [13, 28], [14, 15], [14, 16], [14, 17], [14, 18], [14, 19], [14, 20], [14, 21], [14, 23], [14, 24], [14, 25], [14, 26], [14, 27], [14, 28], [14, 29], [14, 30], [14, 31], [14, 33], [14, 35], [15, 16], [15, 17], [15, 18], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 25], [15, 27], [15, 28], [15, 29], [15, 30], [15, 32], [15, 33], [15, 35], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 28], [16, 29], [16, 30], [16, 31], [16, 32], [16, 33], [16, 34], [16, 35], [17, 18], [17, 20], [17, 21], [17, 23], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 30], [17, 31], [17, 33], [17, 34], [17, 35], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [18, 28], [18, 29], [18, 30], [18, 33], [18, 34], [19, 20], [19, 21], [19, 25], [19, 28], [19, 33], [20, 21], [20, 23], [20, 24], [20, 25], [20, 27], [20, 28], [20, 29], [20, 30], [20, 33], [20, 34], [20, 35], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 30], [21, 33], [21, 34], [21, 35], [22, 23], [22, 27], [22, 30], [23, 24], [23, 25], [23, 26], [23, 27], [23, 28], [23, 29], [23, 30], [23, 31], [23, 33], [23, 34], [24, 25], [24, 26], [24, 27], [24, 28], [24, 30], [24, 32], [24, 33], [24, 34], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 33], [25, 34], [25, 35], [26, 27], [26, 28], [26, 30], [26, 33], [27, 28], [27, 29], [27, 30], [27, 31], [27, 33], [27, 34], [27, 35], [28, 29], [28, 30], [28, 31], [28, 32], [28, 33], [28, 34], [28, 35], [29, 30], [29, 33], [30, 31], [30, 32], [30, 33], [30, 34], [31, 33], [32, 33], [33, 34]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s6/solution/solve.sh b/tasks/construct-rlve-imp-party-l4-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b358e77245c8745e544429fa8eba13842a465412
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [1, 2, 3, 9, 11, 12, 14, 18, 20, 25, 27, 30]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-imp-party-l4-s6/tests/check.py b/tasks/construct-rlve-imp-party-l4-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..97b5a037a2ba8bf4495cf87cc074d1c60b11311c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s6/tests/check.py
@@ -0,0 +1,14 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    c = int_list(ans.get("clique"), n, 0, 3 * n - 1, "clique")
+    if len(set(c)) != n:
+        raise Invalid("vertices must be distinct")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(n):
+        for j in range(i + 1, n):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-imp-party-l4-s6/tests/instance.json b/tasks/construct-rlve-imp-party-l4-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e02af37db848e8dc6b56bea58c8b24a65c66ed5
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 35], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 35], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 23], [2, 24], [2, 25], [2, 26], [2, 27], [2, 28], [2, 30], [2, 33], [2, 34], [2, 35], [3, 4], [3, 5], [3, 6], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 19], [3, 20], [3, 21], [3, 22], [3, 23], [3, 24], [3, 25], [3, 26], [3, 27], [3, 28], [3, 30], [3, 33], [3, 34], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 20], [4, 21], [4, 22], [4, 23], [4, 24], [4, 25], [4, 26], [4, 27], [4, 28], [4, 30], [4, 31], [4, 33], [4, 35], [5, 6], [5, 9], [5, 11], [5, 15], [5, 16], [5, 18], [5, 20], [5, 21], [5, 23], [5, 24], [5, 25], [5, 28], [5, 30], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 17], [6, 18], [6, 19], [6, 20], [6, 21], [6, 23], [6, 24], [6, 25], [6, 26], [6, 27], [6, 28], [6, 29], [6, 30], [6, 31], [6, 32], [6, 33], [6, 34], [7, 9], [7, 10], [7, 12], [7, 14], [7, 15], [7, 16], [7, 18], [7, 21], [7, 23], [7, 24], [7, 25], [7, 27], [7, 28], [7, 33], [8, 9], [8, 10], [8, 11], [8, 12], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 20], [8, 21], [8, 23], [8, 24], [8, 27], [8, 30], [8, 33], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 17], [9, 18], [9, 20], [9, 21], [9, 22], [9, 23], [9, 24], [9, 25], [9, 26], [9, 27], [9, 28], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 35], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 22], [10, 23], [10, 24], [10, 25], [10, 27], [10, 28], [10, 29], [10, 30], [10, 31], [10, 33], [10, 35], [11, 12], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 22], [11, 23], [11, 24], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 30], [11, 31], [11, 33], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [12, 22], [12, 23], [12, 24], [12, 25], [12, 26], [12, 27], [12, 28], [12, 29], [12, 30], [12, 32], [12, 33], [12, 34], [12, 35], [13, 14], [13, 16], [13, 17], [13, 18], [13, 20], [13, 21], [13, 23], [13, 24], [13, 25], [13, 27], [13, 28], [14, 15], [14, 16], [14, 17], [14, 18], [14, 19], [14, 20], [14, 21], [14, 23], [14, 24], [14, 25], [14, 26], [14, 27], [14, 28], [14, 29], [14, 30], [14, 31], [14, 33], [14, 35], [15, 16], [15, 17], [15, 18], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 25], [15, 27], [15, 28], [15, 29], [15, 30], [15, 32], [15, 33], [15, 35], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 28], [16, 29], [16, 30], [16, 31], [16, 32], [16, 33], [16, 34], [16, 35], [17, 18], [17, 20], [17, 21], [17, 23], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 30], [17, 31], [17, 33], [17, 34], [17, 35], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [18, 28], [18, 29], [18, 30], [18, 33], [18, 34], [19, 20], [19, 21], [19, 25], [19, 28], [19, 33], [20, 21], [20, 23], [20, 24], [20, 25], [20, 27], [20, 28], [20, 29], [20, 30], [20, 33], [20, 34], [20, 35], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 30], [21, 33], [21, 34], [21, 35], [22, 23], [22, 27], [22, 30], [23, 24], [23, 25], [23, 26], [23, 27], [23, 28], [23, 29], [23, 30], [23, 31], [23, 33], [23, 34], [24, 25], [24, 26], [24, 27], [24, 28], [24, 30], [24, 32], [24, 33], [24, 34], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 33], [25, 34], [25, 35], [26, 27], [26, 28], [26, 30], [26, 33], [27, 28], [27, 29], [27, 30], [27, 31], [27, 33], [27, 34], [27, 35], [28, 29], [28, 30], [28, 31], [28, 32], [28, 33], [28, 34], [28, 35], [29, 30], [29, 33], [30, 31], [30, 32], [30, 33], [30, 34], [31, 33], [32, 33], [33, 34]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s6/tests/run.py b/tasks/construct-rlve-imp-party-l4-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-imp-party-l4-s6/tests/test.sh b/tasks/construct-rlve-imp-party-l4-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-imp-party-l4-s8/environment/Dockerfile b/tasks/construct-rlve-imp-party-l4-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-imp-party-l4-s8/environment/instance.json b/tasks/construct-rlve-imp-party-l4-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..30378f4272524e4ed6b592d7bef5e1390c9b9ad3
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 5], [0, 7], [0, 8], [0, 9], [0, 11], [0, 13], [0, 14], [0, 16], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 34], [1, 35], [2, 5], [2, 7], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 16], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 23], [2, 24], [2, 25], [2, 26], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [3, 13], [3, 14], [3, 16], [3, 19], [3, 20], [3, 21], [3, 22], [3, 23], [3, 25], [3, 26], [3, 28], [3, 29], [3, 30], [3, 31], [3, 32], [3, 33], [4, 7], [4, 9], [4, 11], [4, 13], [4, 14], [4, 16], [4, 18], [4, 19], [4, 20], [4, 21], [4, 22], [4, 23], [4, 24], [4, 25], [4, 26], [4, 28], [4, 29], [4, 30], [4, 31], [4, 32], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [5, 21], [5, 22], [5, 23], [5, 24], [5, 25], [5, 26], [5, 27], [5, 28], [5, 29], [5, 30], [5, 31], [5, 32], [5, 33], [5, 34], [5, 35], [6, 7], [6, 8], [6, 9], [6, 11], [6, 13], [6, 14], [6, 16], [6, 18], [6, 19], [6, 21], [6, 22], [6, 23], [6, 24], [6, 25], [6, 26], [6, 28], [6, 29], [6, 30], [6, 31], [6, 32], [6, 33], [7, 8], [7, 9], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 18], [7, 19], [7, 20], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 26], [7, 27], [7, 28], [7, 29], [7, 30], [7, 31], [7, 32], [7, 33], [7, 34], [8, 9], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 18], [8, 19], [8, 20], [8, 21], [8, 22], [8, 23], [8, 24], [8, 25], [8, 26], [8, 27], [8, 28], [8, 29], [8, 30], [8, 31], [8, 32], [8, 33], [8, 34], [8, 35], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 18], [9, 19], [9, 20], [9, 21], [9, 22], [9, 23], [9, 24], [9, 25], [9, 26], [9, 28], [9, 29], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 35], [10, 11], [10, 13], [10, 14], [10, 16], [10, 18], [10, 19], [10, 20], [10, 21], [10, 22], [10, 23], [10, 24], [10, 26], [10, 28], [10, 29], [10, 30], [10, 31], [10, 32], [10, 33], [11, 12], [11, 13], [11, 14], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [11, 22], [11, 23], [11, 24], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 30], [11, 31], [11, 32], [11, 33], [11, 35], [12, 13], [12, 14], [12, 18], [12, 20], [12, 21], [12, 22], [12, 23], [12, 24], [12, 25], [12, 26], [12, 28], [12, 29], [12, 30], [12, 31], [12, 33], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 25], [13, 26], [13, 27], [13, 28], [13, 29], [13, 30], [13, 31], [13, 32], [13, 33], [13, 35], [14, 15], [14, 16], [14, 18], [14, 19], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 25], [14, 26], [14, 27], [14, 28], [14, 29], [14, 30], [14, 31], [14, 32], [14, 33], [14, 34], [14, 35], [15, 16], [15, 18], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 25], [15, 26], [15, 29], [15, 30], [15, 31], [15, 32], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [16, 22], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 28], [16, 29], [16, 30], [16, 31], [16, 32], [16, 33], [16, 34], [17, 18], [17, 19], [17, 20], [17, 21], [17, 22], [17, 23], [17, 24], [17, 25], [17, 26], [17, 28], [17, 29], [17, 30], [17, 31], [17, 32], [17, 33], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [18, 28], [18, 29], [18, 30], [18, 31], [18, 32], [18, 33], [18, 34], [18, 35], [19, 20], [19, 21], [19, 22], [19, 23], [19, 24], [19, 25], [19, 26], [19, 27], [19, 28], [19, 29], [19, 30], [19, 31], [19, 32], [19, 33], [19, 35], [20, 21], [20, 22], [20, 23], [20, 24], [20, 25], [20, 26], [20, 27], [20, 28], [20, 29], [20, 30], [20, 31], [20, 32], [20, 33], [20, 34], [20, 35], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 32], [21, 33], [21, 34], [21, 35], [22, 23], [22, 24], [22, 25], [22, 26], [22, 27], [22, 28], [22, 29], [22, 30], [22, 31], [22, 32], [22, 33], [22, 34], [22, 35], [23, 24], [23, 25], [23, 26], [23, 27], [23, 28], [23, 29], [23, 30], [23, 31], [23, 32], [23, 33], [23, 35], [24, 25], [24, 26], [24, 27], [24, 28], [24, 29], [24, 30], [24, 31], [24, 32], [24, 33], [24, 34], [24, 35], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 33], [25, 34], [26, 27], [26, 28], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 35], [27, 28], [27, 29], [27, 30], [27, 31], [27, 32], [27, 33], [28, 29], [28, 30], [28, 31], [28, 32], [28, 33], [28, 34], [28, 35], [29, 30], [29, 31], [29, 32], [29, 33], [29, 35], [30, 31], [30, 32], [30, 33], [30, 34], [30, 35], [31, 32], [31, 33], [31, 34], [31, 35], [32, 33], [32, 34], [32, 35], [33, 34], [33, 35]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s8/solution/solve.sh b/tasks/construct-rlve-imp-party-l4-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..09a2cd1af30f589b49a3fe4fee430d670f897347
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [1, 5, 8, 9, 21, 22, 24, 26, 28, 30, 31, 32]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-imp-party-l4-s8/tests/check.py b/tasks/construct-rlve-imp-party-l4-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..97b5a037a2ba8bf4495cf87cc074d1c60b11311c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s8/tests/check.py
@@ -0,0 +1,14 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    c = int_list(ans.get("clique"), n, 0, 3 * n - 1, "clique")
+    if len(set(c)) != n:
+        raise Invalid("vertices must be distinct")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(n):
+        for j in range(i + 1, n):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-imp-party-l4-s8/tests/instance.json b/tasks/construct-rlve-imp-party-l4-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..30378f4272524e4ed6b592d7bef5e1390c9b9ad3
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 5], [0, 7], [0, 8], [0, 9], [0, 11], [0, 13], [0, 14], [0, 16], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 34], [1, 35], [2, 5], [2, 7], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 16], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 23], [2, 24], [2, 25], [2, 26], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [3, 13], [3, 14], [3, 16], [3, 19], [3, 20], [3, 21], [3, 22], [3, 23], [3, 25], [3, 26], [3, 28], [3, 29], [3, 30], [3, 31], [3, 32], [3, 33], [4, 7], [4, 9], [4, 11], [4, 13], [4, 14], [4, 16], [4, 18], [4, 19], [4, 20], [4, 21], [4, 22], [4, 23], [4, 24], [4, 25], [4, 26], [4, 28], [4, 29], [4, 30], [4, 31], [4, 32], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [5, 21], [5, 22], [5, 23], [5, 24], [5, 25], [5, 26], [5, 27], [5, 28], [5, 29], [5, 30], [5, 31], [5, 32], [5, 33], [5, 34], [5, 35], [6, 7], [6, 8], [6, 9], [6, 11], [6, 13], [6, 14], [6, 16], [6, 18], [6, 19], [6, 21], [6, 22], [6, 23], [6, 24], [6, 25], [6, 26], [6, 28], [6, 29], [6, 30], [6, 31], [6, 32], [6, 33], [7, 8], [7, 9], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 18], [7, 19], [7, 20], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 26], [7, 27], [7, 28], [7, 29], [7, 30], [7, 31], [7, 32], [7, 33], [7, 34], [8, 9], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 18], [8, 19], [8, 20], [8, 21], [8, 22], [8, 23], [8, 24], [8, 25], [8, 26], [8, 27], [8, 28], [8, 29], [8, 30], [8, 31], [8, 32], [8, 33], [8, 34], [8, 35], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 18], [9, 19], [9, 20], [9, 21], [9, 22], [9, 23], [9, 24], [9, 25], [9, 26], [9, 28], [9, 29], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 35], [10, 11], [10, 13], [10, 14], [10, 16], [10, 18], [10, 19], [10, 20], [10, 21], [10, 22], [10, 23], [10, 24], [10, 26], [10, 28], [10, 29], [10, 30], [10, 31], [10, 32], [10, 33], [11, 12], [11, 13], [11, 14], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [11, 22], [11, 23], [11, 24], [11, 25], [11, 26], [11, 27], [11, 28], [11, 29], [11, 30], [11, 31], [11, 32], [11, 33], [11, 35], [12, 13], [12, 14], [12, 18], [12, 20], [12, 21], [12, 22], [12, 23], [12, 24], [12, 25], [12, 26], [12, 28], [12, 29], [12, 30], [12, 31], [12, 33], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 25], [13, 26], [13, 27], [13, 28], [13, 29], [13, 30], [13, 31], [13, 32], [13, 33], [13, 35], [14, 15], [14, 16], [14, 18], [14, 19], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 25], [14, 26], [14, 27], [14, 28], [14, 29], [14, 30], [14, 31], [14, 32], [14, 33], [14, 34], [14, 35], [15, 16], [15, 18], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 25], [15, 26], [15, 29], [15, 30], [15, 31], [15, 32], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [16, 22], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 28], [16, 29], [16, 30], [16, 31], [16, 32], [16, 33], [16, 34], [17, 18], [17, 19], [17, 20], [17, 21], [17, 22], [17, 23], [17, 24], [17, 25], [17, 26], [17, 28], [17, 29], [17, 30], [17, 31], [17, 32], [17, 33], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [18, 28], [18, 29], [18, 30], [18, 31], [18, 32], [18, 33], [18, 34], [18, 35], [19, 20], [19, 21], [19, 22], [19, 23], [19, 24], [19, 25], [19, 26], [19, 27], [19, 28], [19, 29], [19, 30], [19, 31], [19, 32], [19, 33], [19, 35], [20, 21], [20, 22], [20, 23], [20, 24], [20, 25], [20, 26], [20, 27], [20, 28], [20, 29], [20, 30], [20, 31], [20, 32], [20, 33], [20, 34], [20, 35], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 30], [21, 31], [21, 32], [21, 33], [21, 34], [21, 35], [22, 23], [22, 24], [22, 25], [22, 26], [22, 27], [22, 28], [22, 29], [22, 30], [22, 31], [22, 32], [22, 33], [22, 34], [22, 35], [23, 24], [23, 25], [23, 26], [23, 27], [23, 28], [23, 29], [23, 30], [23, 31], [23, 32], [23, 33], [23, 35], [24, 25], [24, 26], [24, 27], [24, 28], [24, 29], [24, 30], [24, 31], [24, 32], [24, 33], [24, 34], [24, 35], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 33], [25, 34], [26, 27], [26, 28], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 35], [27, 28], [27, 29], [27, 30], [27, 31], [27, 32], [27, 33], [28, 29], [28, 30], [28, 31], [28, 32], [28, 33], [28, 34], [28, 35], [29, 30], [29, 31], [29, 32], [29, 33], [29, 35], [30, 31], [30, 32], [30, 33], [30, 34], [30, 35], [31, 32], [31, 33], [31, 34], [31, 35], [32, 33], [32, 34], [32, 35], [33, 34], [33, 35]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s8/tests/run.py b/tasks/construct-rlve-imp-party-l4-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-imp-party-l4-s8/tests/test.sh b/tasks/construct-rlve-imp-party-l4-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s1/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l3-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s1/environment/instance.json b/tasks/construct-rlve-integer-linear-system-l3-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..89e84217ffafd9957dac7ade4d59a18ce874050f
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s1/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[1, 0, 1, 0, 1, 0, 0, 1], [0, 1, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 0, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 1, 1, 0, 1, 1, 0]], "rhs": [14, 24, 15, 13, 15, 24, 4, 13, 12, 4, 20, 16, 1, 5, 9, 24], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s1/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l3-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f32f4a191c2b3f2d110e1f872c968928268248bc
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [4, 6, 8, 3, 1, 5, 4, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s1/tests/check.py b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = len(inst["coeffs"][0])
+    x = int_list(ans.get("x"), n, name="x")
+    for k, (e, r) in enumerate(zip(inst["coeffs"], inst["rhs"])):
+        if sum(c * v for c, v in zip(e, x)) != r:
+            raise Invalid(f"equation {k} is violated")
+    return None, {}
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s1/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..89e84217ffafd9957dac7ade4d59a18ce874050f
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[1, 0, 1, 0, 1, 0, 0, 1], [0, 1, 1, 0, 0, 1, 1, 1], [0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 0, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 1, 0, 0, 1], [1, 0, 1, 1, 0, 1, 1, 0]], "rhs": [14, 24, 15, 13, 15, 24, 4, 13, 12, 4, 20, 16, 1, 5, 9, 24], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s1/tests/run.py b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s1/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s6/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l3-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s6/environment/instance.json b/tasks/construct-rlve-integer-linear-system-l3-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..becf83615786cc4a2a1ace97d690fe8d7fe50599
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s6/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[0, 1, 1, 1, 0, 1, 1, 0], [0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 1, 1, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1], [1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0], [1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0]], "rhs": [19, 10, 31, 37, 25, 20, 12, 19, 15, 15, 20, 23, 21, 15, 23, 18, 14, 16, 5, 17, 19, 17, 24, 6], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s6/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l3-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fb2b4419928029f21562c0c24c25acb0ec5c745f
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [4, 4, 1, 4, 6, 2, 8, 8]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s6/tests/check.py b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = len(inst["coeffs"][0])
+    x = int_list(ans.get("x"), n, name="x")
+    for k, (e, r) in enumerate(zip(inst["coeffs"], inst["rhs"])):
+        if sum(c * v for c, v in zip(e, x)) != r:
+            raise Invalid(f"equation {k} is violated")
+    return None, {}
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s6/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..becf83615786cc4a2a1ace97d690fe8d7fe50599
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[0, 1, 1, 1, 0, 1, 1, 0], [0, 0, 0, 0, 0, 1, 0, 1], [1, 1, 1, 1, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0, 1], [1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0, 1, 0], [1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0]], "rhs": [19, 10, 31, 37, 25, 20, 12, 19, 15, 15, 20, 23, 21, 15, 23, 18, 14, 16, 5, 17, 19, 17, 24, 6], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s6/tests/run.py b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s6/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s8/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l3-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s8/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l3-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a059f72c840638bd6b2397fd65def580305a5e18
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [2, 5, 3, 6, 4, 1, 1, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s8/tests/check.py b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = len(inst["coeffs"][0])
+    x = int_list(ans.get("x"), n, name="x")
+    for k, (e, r) in enumerate(zip(inst["coeffs"], inst["rhs"])):
+        if sum(c * v for c, v in zip(e, x)) != r:
+            raise Invalid(f"equation {k} is violated")
+    return None, {}
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s8/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..da6295c64a8594312ee5521af5d943d9f3bd8bf9
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[1, 1, 1, 0, 0, 0, 1, 0], [1, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0], [1, 0, 1, 0, 1, 1, 1, 0], [1, 0, 1, 1, 0, 1, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 1], [0, 1, 0, 1, 0, 0, 1, 1], [0, 1, 1, 1, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 1, 1, 1, 1], [1, 1, 0, 0, 0, 0, 1, 1], [1, 1, 1, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, 1]], "rhs": [11, 20, 16, 11, 19, 4, 6, 6, 12, 18, 7, 14, 18, 20, 12, 23, 14, 20, 12], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s8/tests/run.py b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s8/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-integer-linear-system-l4-s5/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l4-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l4-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-integer-linear-system-l4-s5/environment/instance.json b/tasks/construct-rlve-integer-linear-system-l4-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8dd5aba7383a5ee775f105c36a4422dd5eb6eb03
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l4-s5/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2], [0, 2, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1], [0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 2], [0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 1], [2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 1, 1], [2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0], [0, 1, 1, 2, 2, 2, 1, 2, 0, 0, 2, 0], [1, 2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2], [1, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2], [0, 2, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0], [0, 2, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 0], [2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1], [1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 2, 1], [2, 0, 0, 1, 1, 2, 1, 0, 2, 1, 0, 0], [1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1], [1, 1, 2, 2, 1, 0, 0, 1, 0, 0, 0, 0], [2, 2, 1, 0, 0, 0, 1, 1, 0, 2, 1, 0], [1, 2, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0], [0, 2, 0, 0, 2, 1, 0, 1, 0, 2, 0, 0], [1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0], [0, 0, 0, 2, 0, 1, 1, 0, 0, 2, 2, 0], [2, 0, 0, 2, 0, 2, 2, 1, 2, 1, 2, 2], [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]], "rhs": [42, 84, 56, 38, 100, 61, 13, 31, 94, 71, 65, 50, 71, 54, 44, 73, 80, 36, 91, 57, 73, 63, 34, 63, 46, 40, 110, 51], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l4-s5/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l4-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7dde519c70146862654e99a2ad8235a9c22f26a6
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l4-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [9, 11, 5, 5, 8, 10, 12, 9, 7, 3, 1, 5]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l4-s5/tests/check.py b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = len(inst["coeffs"][0])
+    x = int_list(ans.get("x"), n, name="x")
+    for k, (e, r) in enumerate(zip(inst["coeffs"], inst["rhs"])):
+        if sum(c * v for c, v in zip(e, x)) != r:
+            raise Invalid(f"equation {k} is violated")
+    return None, {}
diff --git a/tasks/construct-rlve-integer-linear-system-l4-s5/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8dd5aba7383a5ee775f105c36a4422dd5eb6eb03
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2], [0, 2, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1], [0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 2], [0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 1], [2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 1, 1], [2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0], [0, 1, 1, 2, 2, 2, 1, 2, 0, 0, 2, 0], [1, 2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2], [1, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2], [0, 2, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0], [0, 2, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 0], [2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1], [1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 2, 1], [2, 0, 0, 1, 1, 2, 1, 0, 2, 1, 0, 0], [1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1], [1, 1, 2, 2, 1, 0, 0, 1, 0, 0, 0, 0], [2, 2, 1, 0, 0, 0, 1, 1, 0, 2, 1, 0], [1, 2, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0], [0, 2, 0, 0, 2, 1, 0, 1, 0, 2, 0, 0], [1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0], [0, 0, 0, 2, 0, 1, 1, 0, 0, 2, 2, 0], [2, 0, 0, 2, 0, 2, 2, 1, 2, 1, 2, 2], [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]], "rhs": [42, 84, 56, 38, 100, 61, 13, 31, 94, 71, 65, 50, 71, 54, 44, 73, 80, 36, 91, 57, 73, 63, 34, 63, 46, 40, 110, 51], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l4-s5/tests/run.py b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-integer-linear-system-l4-s5/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l4-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-largest-convex-polygon-l4-s0/environment/Dockerfile b/tasks/construct-rlve-largest-convex-polygon-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l4-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-largest-convex-polygon-l4-s0/environment/instance.json b/tasks/construct-rlve-largest-convex-polygon-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e9f57fb2e96f0d118777641678f71d79d8ffe8d
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[2, 14], [16, 16], [7, 7], [14, 17], [1, 11], [12, 16], [3, 7], [1, 15], [18, 10], [17, 3], [13, 0], [18, 12], [15, 3], [8, 2], [7, 5], [0, 14], [14, 15], [13, 11]], "k": 11, "family": "rlve_largest_convex_polygon", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-convex-polygon-l4-s0/solution/solve.sh b/tasks/construct-rlve-largest-convex-polygon-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..76fca25b3ba3039a32b03d8870e7e06a7b9c3c86
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l4-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"indices": [15, 7, 5, 16, 11, 8, 9, 12, 14, 6, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/check.py b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a09cc858f41ce5745e4e491188cd42360c65dae
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/check.py
@@ -0,0 +1,27 @@
+from run import Invalid, int_list
+
+
+def _cross(o, a, b):
+    return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])
+
+
+def check(inst, ans):
+    P, k = inst["points"], inst["k"]
+    idx = int_list(ans.get("indices"), None, 0, len(P) - 1, "indices")
+    if len(set(idx)) != len(idx):
+        raise Invalid("indices must be distinct")
+    if len(idx) < k:
+        raise Invalid(f"{len(idx)} points given, need {k}")
+    pts = sorted(tuple(P[i]) for i in idx)
+    lower, upper = [], []
+    for p in pts:  # monotone chain, strict (collinear points dropped)
+        while len(lower) >= 2 and _cross(lower[-2], lower[-1], p) <= 0:
+            lower.pop()
+        lower.append(p)
+    for p in reversed(pts):
+        while len(upper) >= 2 and _cross(upper[-2], upper[-1], p) <= 0:
+            upper.pop()
+        upper.append(p)
+    if len(lower) + len(upper) - 2 != len(pts):
+        raise Invalid("the chosen points are not in convex position")
+    return None, {}
diff --git a/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/instance.json b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e9f57fb2e96f0d118777641678f71d79d8ffe8d
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[2, 14], [16, 16], [7, 7], [14, 17], [1, 11], [12, 16], [3, 7], [1, 15], [18, 10], [17, 3], [13, 0], [18, 12], [15, 3], [8, 2], [7, 5], [0, 14], [14, 15], [13, 11]], "k": 11, "family": "rlve_largest_convex_polygon", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/run.py b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/test.sh b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l4-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-largest-rectangle-l6-s0/environment/Dockerfile b/tasks/construct-rlve-largest-rectangle-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-largest-rectangle-l6-s0/environment/instance.json b/tasks/construct-rlve-largest-rectangle-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d56078cd0993303aaa5869fb15c063e93231e03
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[59, -11], [-51, -43], [33, -40], [21, 60], [5, -54], [-32, 24], [20, 34], [-44, 1], [57, -16], [-35, -16], [-41, 42], [52, 29], [-38, -36], [10, 18], [35, -60], [32, -16], [38, 27], [-50, 17], [-39, 15], [14, -18], [56, -32], [24, -26], [2, 43], [52, -47], [-12, 56], [16, -46], [-22, -34], [-54, 46], [-30, 10], [-6, -21], [-18, 49], [-50, -49], [-40, -8], [-58, -6], [18, 4], [-13, 11], [-19, 57], [36, 27], [-8, -36], [30, -2], [53, -55], [56, -51], [-21, 24], [-35, -42], [44, -33], [60, 42], [26, -6], [-17, -47], [41, 31], [22, -16], [13, -15], [18, 25], [30, -50], [-27, 36], [-3, 44], [-48, -58], [38, 24], [22, -8], [27, 58], [30, 15]], "area": 164, "family": "rlve_largest_rectangle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-rectangle-l6-s0/solution/solve.sh b/tasks/construct-rlve-largest-rectangle-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0cd0e8d2617051f4ef0cec1cffbb9171e21eeb68
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"indices": [15, 21, 19, 57]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-largest-rectangle-l6-s0/tests/check.py b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2251b2af23a481e598fa1e48d0a8249f70b6cc44
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    P = inst["points"]
+    idx = int_list(ans.get("indices"), 4, 0, len(P) - 1, "indices")
+    if len(set(idx)) != 4:
+        raise Invalid("indices must be distinct")
+    A, *rest = [tuple(P[i]) for i in idx]
+    if len(set([A] + rest)) != 4:
+        raise Invalid("points must be distinct")
+    # the vertex farthest from A is opposite; the other two are A's neighbours
+    rest.sort(key=lambda X: (X[0] - A[0]) ** 2 + (X[1] - A[1]) ** 2)
+    B, D, C = rest
+    u = (B[0] - A[0], B[1] - A[1])
+    v = (D[0] - A[0], D[1] - A[1])
+    if u[0] * v[0] + u[1] * v[1] != 0:
+        raise Invalid("not a rectangle (no right angle at the first vertex)")
+    if (B[0] + D[0] - A[0], B[1] + D[1] - A[1]) != C:
+        raise Invalid("not a rectangle")
+    area = abs(u[0] * v[1] - u[1] * v[0])
+    if area < inst["area"]:
+        raise Invalid(f"area {area} < {inst['area']}")
+    return None, {"area": area}
diff --git a/tasks/construct-rlve-largest-rectangle-l6-s0/tests/instance.json b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d56078cd0993303aaa5869fb15c063e93231e03
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[59, -11], [-51, -43], [33, -40], [21, 60], [5, -54], [-32, 24], [20, 34], [-44, 1], [57, -16], [-35, -16], [-41, 42], [52, 29], [-38, -36], [10, 18], [35, -60], [32, -16], [38, 27], [-50, 17], [-39, 15], [14, -18], [56, -32], [24, -26], [2, 43], [52, -47], [-12, 56], [16, -46], [-22, -34], [-54, 46], [-30, 10], [-6, -21], [-18, 49], [-50, -49], [-40, -8], [-58, -6], [18, 4], [-13, 11], [-19, 57], [36, 27], [-8, -36], [30, -2], [53, -55], [56, -51], [-21, 24], [-35, -42], [44, -33], [60, 42], [26, -6], [-17, -47], [41, 31], [22, -16], [13, -15], [18, 25], [30, -50], [-27, 36], [-3, 44], [-48, -58], [38, 24], [22, -8], [27, 58], [30, 15]], "area": 164, "family": "rlve_largest_rectangle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-rectangle-l6-s0/tests/run.py b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-largest-rectangle-l6-s0/tests/test.sh b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a72cd0ecf3421b0f882ab824d869e2c118d5ab7c
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["01", "01"], "B": ["01", "01"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1c0659332884117a306926de80fc5e441a50a280
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"a": [0, 1], "b": [0, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A, B = inst["A"], inst["B"]
+    N, M = len(A), len(A[0])
+    a = int_list(ans.get("a"), N, 0, N - 1, "a")
+    b = int_list(ans.get("b"), M, 0, M - 1, "b")
+    if len(set(a)) != N or len(set(b)) != M:
+        raise Invalid("a and b must be permutations")
+    for i in range(N):
+        for j in range(M):
+            if A[a[i]][b[j]] != B[i][j]:
+                raise Invalid(f"mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a72cd0ecf3421b0f882ab824d869e2c118d5ab7c
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["01", "01"], "B": ["01", "01"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..47a5c86273a36143bf7ee79cbe11bfeea159b15c
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["101", "110", "011"], "B": ["101", "011", "110"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..88c5702f8d97ebb99d3d42f7b48c07e706cad43e
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"a": [0, 2, 1], "b": [0, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A, B = inst["A"], inst["B"]
+    N, M = len(A), len(A[0])
+    a = int_list(ans.get("a"), N, 0, N - 1, "a")
+    b = int_list(ans.get("b"), M, 0, M - 1, "b")
+    if len(set(a)) != N or len(set(b)) != M:
+        raise Invalid("a and b must be permutations")
+    for i in range(N):
+        for j in range(M):
+            if A[a[i]][b[j]] != B[i][j]:
+                raise Invalid(f"mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..47a5c86273a36143bf7ee79cbe11bfeea159b15c
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["101", "110", "011"], "B": ["101", "011", "110"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l2-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..021a00875c5e7cb2819227c1ccfdcfb42feefa96
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["0000000000011", "0000000000000", "0010000000000", "0100000000011", "0000000000000", "0011100100000", "0000000000000", "0000100000000", "0000000011000", "0001000001000", "0000000000000", "1100000001100", "0000000000000", "0000000000010", "0010010000000", "0100100000001", "1010000000000"], "B": ["0000101000001", "0000000001000", "0000010001000", "0000000000011", "0000100000000", "0000000000010", "0000000000000", "0000000100100", "0000000000000", "0000000000000", "0000001000011", "1010001100000", "0000000000000", "0000000000000", "0001000100000", "0010000001000", "0101100001000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7f61a587dd14ee5453c04ec2937a7edd72796fac
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"a": [15, 2, 14, 0, 7, 13, 4, 8, 6, 10, 3, 11, 1, 12, 9, 16, 5], "b": [10, 7, 0, 3, 4, 5, 1, 9, 6, 2, 8, 11, 12]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A, B = inst["A"], inst["B"]
+    N, M = len(A), len(A[0])
+    a = int_list(ans.get("a"), N, 0, N - 1, "a")
+    b = int_list(ans.get("b"), M, 0, M - 1, "b")
+    if len(set(a)) != N or len(set(b)) != M:
+        raise Invalid("a and b must be permutations")
+    for i in range(N):
+        for j in range(M):
+            if A[a[i]][b[j]] != B[i][j]:
+                raise Invalid(f"mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..021a00875c5e7cb2819227c1ccfdcfb42feefa96
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["0000000000011", "0000000000000", "0010000000000", "0100000000011", "0000000000000", "0011100100000", "0000000000000", "0000100000000", "0000000011000", "0001000001000", "0000000000000", "1100000001100", "0000000000000", "0000000000010", "0010010000000", "0100100000001", "1010000000000"], "B": ["0000101000001", "0000000001000", "0000010001000", "0000000000011", "0000100000000", "0000000000010", "0000000000000", "0000000100100", "0000000000000", "0000000000000", "0000001000011", "1010001100000", "0000000000000", "0000000000000", "0001000100000", "0010000001000", "0101100001000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3bc205a68c5338c8940330405dbf6dbe48fb8953
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["00011000000001", "10111011110001", "00010101001100", "00000010000011", "11000010000011", "00011100001011", "00111000000100", "00010000111001", "01001011101001", "11110000100001"], "B": ["11100000100001", "11000011000101", "00000011000001", "00001111111011", "00011101000100", "00010101001011", "10011011101000", "10000001011001", "00001001000100", "00100010000011"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c95ef8f7c34ca3d054092dfa808dc4565b10d0b6
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"a": [2, 5, 0, 1, 4, 9, 8, 7, 3, 6], "b": [10, 5, 11, 1, 6, 0, 4, 13, 7, 9, 8, 12, 2, 3]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A, B = inst["A"], inst["B"]
+    N, M = len(A), len(A[0])
+    a = int_list(ans.get("a"), N, 0, N - 1, "a")
+    b = int_list(ans.get("b"), M, 0, M - 1, "b")
+    if len(set(a)) != N or len(set(b)) != M:
+        raise Invalid("a and b must be permutations")
+    for i in range(N):
+        for j in range(M):
+            if A[a[i]][b[j]] != B[i][j]:
+                raise Invalid(f"mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3bc205a68c5338c8940330405dbf6dbe48fb8953
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["00011000000001", "10111011110001", "00010101001100", "00000010000011", "11000010000011", "00011100001011", "00111000000100", "00010000111001", "01001011101001", "11110000100001"], "B": ["11100000100001", "11000011000101", "00000011000001", "00001111111011", "00011101000100", "00010101001011", "10011011101000", "10000001011001", "00001001000100", "00100010000011"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l4-s1/environment/Dockerfile b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l4-s1/environment/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc7b35122e4d68124e952df265fc9d3eb600dda4
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "k": 7, "edges": [[0, 1], [0, 3], [0, 5], [0, 6], [0, 11], [1, 3], [1, 5], [1, 9], [1, 10], [1, 11], [2, 3], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [4, 5], [4, 6], [4, 7], [4, 9], [4, 11], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [6, 8], [6, 9], [6, 10], [6, 11], [7, 8], [7, 10], [9, 11], [10, 11]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l4-s1/solution/solve.sh b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..643aea9c3a6fefdfd73505a075d19433c4a6d60e
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 1, 0, 2, 0, 2, 3, 4, 1, 4, 5, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/check.py b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..bb676a518264e5db4fb0964e27ccffccf6980807
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    if len(set(c)) != k:
+        raise Invalid(f"uses {len(set(c))} colours, need all {k}")
+    pairs = set()
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"edge ({u},{v}) is monochromatic")
+        pairs.add((min(c[u], c[v]), max(c[u], c[v])))
+    if len(pairs) != k * (k - 1) // 2:
+        raise Invalid("some pair of colours is not joined by an edge")
+    return None, {}
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc7b35122e4d68124e952df265fc9d3eb600dda4
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "k": 7, "edges": [[0, 1], [0, 3], [0, 5], [0, 6], [0, 11], [1, 3], [1, 5], [1, 9], [1, 10], [1, 11], [2, 3], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [4, 5], [4, 6], [4, 7], [4, 9], [4, 11], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [6, 8], [6, 9], [6, 10], [6, 11], [7, 8], [7, 10], [9, 11], [10, 11]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/run.py b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/test.sh b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l4-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-maximum-clique-l1-s6/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l1-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l1-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-maximum-clique-l1-s6/environment/instance.json b/tasks/construct-rlve-maximum-clique-l1-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4bbb22ffbbbfed03a19b1d9e55eb4f7ce24c44a3
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l1-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 8, "k": 3, "edges": [[0, 2], [1, 2], [1, 5], [1, 6], [1, 7], [2, 4], [2, 5], [3, 5], [3, 7]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l1-s6/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l1-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..30182a7169a3903b7777a8e75a1c2666744b02b5
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l1-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [1, 2, 5]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l1-s6/tests/check.py b/tasks/construct-rlve-maximum-clique-l1-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l1-s6/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(c)) != len(c):
+        raise Invalid("vertices must be distinct")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} vertices, need {k}")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(len(c)):
+        for j in range(i + 1, len(c)):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-maximum-clique-l1-s6/tests/instance.json b/tasks/construct-rlve-maximum-clique-l1-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4bbb22ffbbbfed03a19b1d9e55eb4f7ce24c44a3
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l1-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 8, "k": 3, "edges": [[0, 2], [1, 2], [1, 5], [1, 6], [1, 7], [2, 4], [2, 5], [3, 5], [3, 7]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l1-s6/tests/run.py b/tasks/construct-rlve-maximum-clique-l1-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l1-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-maximum-clique-l1-s6/tests/test.sh b/tasks/construct-rlve-maximum-clique-l1-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l1-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-maximum-clique-l2-s4/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l2-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-maximum-clique-l2-s4/environment/instance.json b/tasks/construct-rlve-maximum-clique-l2-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..759a7f9e9ea02d761fa6cfdd036aa7768a293a7c
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 6, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 10], [0, 11], [0, 13], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 13], [3, 4], [3, 5], [3, 8], [3, 9], [3, 10], [3, 11], [4, 6], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 8], [5, 9], [5, 11], [5, 13], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 13], [7, 8], [7, 9], [7, 10], [7, 12], [7, 13], [8, 12], [8, 13], [9, 12], [10, 11], [10, 12], [10, 13], [11, 12], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s4/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l2-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4e76fdf68dfda6fbeb3aada7f5914bea96e559d9
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 1, 3, 4, 10, 11]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l2-s4/tests/check.py b/tasks/construct-rlve-maximum-clique-l2-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s4/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(c)) != len(c):
+        raise Invalid("vertices must be distinct")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} vertices, need {k}")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(len(c)):
+        for j in range(i + 1, len(c)):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-maximum-clique-l2-s4/tests/instance.json b/tasks/construct-rlve-maximum-clique-l2-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..759a7f9e9ea02d761fa6cfdd036aa7768a293a7c
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s4/tests/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 6, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 10], [0, 11], [0, 13], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 13], [3, 4], [3, 5], [3, 8], [3, 9], [3, 10], [3, 11], [4, 6], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 8], [5, 9], [5, 11], [5, 13], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 13], [7, 8], [7, 9], [7, 10], [7, 12], [7, 13], [8, 12], [8, 13], [9, 12], [10, 11], [10, 12], [10, 13], [11, 12], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s4/tests/run.py b/tasks/construct-rlve-maximum-clique-l2-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-maximum-clique-l2-s4/tests/test.sh b/tasks/construct-rlve-maximum-clique-l2-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-maximum-clique-l6-s2/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-maximum-clique-l6-s2/environment/instance.json b/tasks/construct-rlve-maximum-clique-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..18b3800c6b7a5c00f7c9ac994dfa2fa99d8d7c30
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 10, "edges": [[0, 1], [0, 4], [0, 5], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 26], [0, 30], [0, 31], [0, 32], [0, 34], [0, 35], [0, 36], [0, 38], [0, 39], [0, 40], [0, 42], [0, 43], [0, 45], [0, 46], [0, 47], [0, 50], [0, 51], [0, 52], [0, 53], [0, 54], [1, 3], [1, 5], [1, 6], [1, 9], [1, 10], [1, 11], [1, 12], [1, 16], [1, 17], [1, 20], [1, 21], [1, 24], [1, 26], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 35], [1, 36], [1, 37], [1, 38], [1, 39], [1, 41], [1, 42], [1, 43], [1, 44], [1, 46], [1, 47], [1, 48], [1, 50], [1, 51], [1, 53], [1, 54], [1, 55], [2, 3], [2, 5], [2, 6], [2, 8], [2, 9], [2, 13], [2, 14], [2, 16], [2, 19], [2, 20], [2, 24], [2, 25], [2, 28], [2, 30], [2, 31], [2, 33], [2, 36], [2, 37], [2, 39], [2, 41], [2, 42], [2, 44], [2, 45], [2, 47], [2, 48], [2, 49], [2, 53], [2, 54], [2, 55], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [3, 12], [3, 15], [3, 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"subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l6-s2/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..acd4faf29ba845e7d967c3617e7bb80541080ee5
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [1, 10, 16, 26, 29, 38, 41, 48, 51, 55]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l6-s2/tests/check.py b/tasks/construct-rlve-maximum-clique-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s2/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(c)) != len(c):
+        raise Invalid("vertices must be distinct")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} vertices, need {k}")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(len(c)):
+        for j in range(i + 1, len(c)):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-maximum-clique-l6-s2/tests/instance.json b/tasks/construct-rlve-maximum-clique-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..18b3800c6b7a5c00f7c9ac994dfa2fa99d8d7c30
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 10, "edges": [[0, 1], [0, 4], [0, 5], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 26], [0, 30], [0, 31], [0, 32], [0, 34], [0, 35], [0, 36], [0, 38], [0, 39], [0, 40], [0, 42], [0, 43], [0, 45], [0, 46], [0, 47], [0, 50], [0, 51], [0, 52], [0, 53], [0, 54], [1, 3], [1, 5], [1, 6], [1, 9], [1, 10], [1, 11], [1, 12], [1, 16], [1, 17], [1, 20], [1, 21], [1, 24], [1, 26], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 35], [1, 36], [1, 37], [1, 38], [1, 39], [1, 41], [1, 42], [1, 43], [1, 44], [1, 46], [1, 47], [1, 48], [1, 50], [1, 51], [1, 53], [1, 54], [1, 55], [2, 3], [2, 5], [2, 6], [2, 8], [2, 9], [2, 13], [2, 14], [2, 16], [2, 19], [2, 20], [2, 24], [2, 25], [2, 28], [2, 30], [2, 31], [2, 33], [2, 36], [2, 37], [2, 39], [2, 41], [2, 42], [2, 44], [2, 45], [2, 47], [2, 48], [2, 49], [2, 53], [2, 54], [2, 55], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [3, 12], [3, 15], [3, 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"subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l6-s2/tests/run.py b/tasks/construct-rlve-maximum-clique-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-maximum-clique-l6-s2/tests/test.sh b/tasks/construct-rlve-maximum-clique-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-maximum-clique-l6-s5/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l6-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-maximum-clique-l6-s5/environment/instance.json b/tasks/construct-rlve-maximum-clique-l6-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..65594b44f01843ebc4caba8f366fc3625acaca73
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 12, "edges": [[0, 1], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 28], [0, 29], [0, 31], [0, 32], [0, 34], [0, 36], [0, 38], [0, 39], [0, 40], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 49], [0, 50], [0, 52], [0, 53], [0, 54], [0, 55], [1, 3], [1, 5], [1, 6], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 16], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 29], [1, 31], [1, 32], [1, 35], [1, 36], [1, 37], [1, 40], [1, 43], [1, 44], [1, 45], [1, 47], [1, 48], [1, 49], [1, 50], [1, 51], [1, 53], [1, 54], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 17], [2, 18], [2, 20], [2, 21], [2, 23], [2, 25], [2, 26], [2, 27], [2, 29], [2, 30], [2, 32], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 42], [2, 44], [2, 45], [2, 46], [2, 49], [2, 50], [2, 52], [2, 54], [2, 55], [3, 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\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l6-s5/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l6-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1f6d8776d66c022d04a08a05a936d3c463f9818b
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 7, 10, 13, 16, 20, 22, 38, 40, 49, 52, 53]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l6-s5/tests/check.py b/tasks/construct-rlve-maximum-clique-l6-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s5/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(c)) != len(c):
+        raise Invalid("vertices must be distinct")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} vertices, need {k}")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(len(c)):
+        for j in range(i + 1, len(c)):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-maximum-clique-l6-s5/tests/instance.json b/tasks/construct-rlve-maximum-clique-l6-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..65594b44f01843ebc4caba8f366fc3625acaca73
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 12, "edges": [[0, 1], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 28], [0, 29], [0, 31], [0, 32], [0, 34], [0, 36], [0, 38], [0, 39], [0, 40], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 49], [0, 50], [0, 52], [0, 53], [0, 54], [0, 55], [1, 3], [1, 5], [1, 6], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 16], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 29], [1, 31], [1, 32], [1, 35], [1, 36], [1, 37], [1, 40], [1, 43], [1, 44], [1, 45], [1, 47], [1, 48], [1, 49], [1, 50], [1, 51], [1, 53], [1, 54], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 17], [2, 18], [2, 20], [2, 21], [2, 23], [2, 25], [2, 26], [2, 27], [2, 29], [2, 30], [2, 32], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 42], [2, 44], [2, 45], [2, 46], [2, 49], [2, 50], [2, 52], [2, 54], [2, 55], [3, 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[28, 53], [28, 55], [29, 30], [29, 31], [29, 32], [29, 34], [29, 37], [29, 39], [29, 42], [29, 43], [29, 45], [29, 46], [29, 47], [29, 49], [29, 50], [29, 51], [29, 52], [29, 53], [29, 54], [29, 55], [30, 31], [30, 32], [30, 33], [30, 34], [30, 35], [30, 39], [30, 40], [30, 41], [30, 42], [30, 43], [30, 45], [30, 47], [30, 48], [30, 49], [30, 51], [30, 52], [30, 53], [30, 54], [31, 32], [31, 33], [31, 38], [31, 40], [31, 41], [31, 42], [31, 43], [31, 44], [31, 46], [31, 47], [31, 48], [31, 50], [31, 52], [31, 53], [31, 54], [31, 55], [32, 33], [32, 36], [32, 38], [32, 39], [32, 40], [32, 41], [32, 42], [32, 43], [32, 46], [32, 49], [32, 50], [32, 52], [32, 53], [32, 54], [33, 36], [33, 38], [33, 39], [33, 41], [33, 42], [33, 43], [33, 44], [33, 45], [33, 46], [33, 50], [33, 52], [33, 54], [33, 55], [34, 37], [34, 38], [34, 39], [34, 40], [34, 41], [34, 42], [34, 43], [34, 44], [34, 47], [34, 49], [34, 50], [34, 51], [34, 52], [34, 53], [34, 55], [35, 36], [35, 37], [35, 39], [35, 41], [35, 43], [35, 44], [35, 45], [35, 46], [35, 47], [35, 48], [35, 51], [35, 52], [35, 53], [35, 54], [36, 37], [36, 38], [36, 39], [36, 41], [36, 43], [36, 44], [36, 45], [36, 46], [36, 47], [36, 48], [36, 49], [36, 51], [36, 52], [36, 53], [36, 55], [37, 38], [37, 39], [37, 40], [37, 41], [37, 42], [37, 43], [37, 48], [37, 49], [37, 50], [37, 51], [37, 52], [37, 53], [37, 54], [37, 55], [38, 40], [38, 41], [38, 42], [38, 43], [38, 45], [38, 47], [38, 48], [38, 49], [38, 52], [38, 53], [38, 54], [38, 55], [39, 40], [39, 41], [39, 42], [39, 43], [39, 44], [39, 45], [39, 47], [39, 48], [39, 50], [39, 52], [39, 53], [39, 54], [39, 55], [40, 41], [40, 42], [40, 43], [40, 45], [40, 48], [40, 49], [40, 51], [40, 52], [40, 53], [40, 55], [41, 42], [41, 43], [41, 44], [41, 45], [41, 47], [41, 49], [41, 50], [41, 53], [41, 54], [41, 55], [42, 43], [42, 45], [42, 46], [42, 48], [42, 52], [42, 54], [42, 55], [43, 44], [43, 45], [43, 47], [43, 48], [43, 49], [43, 50], [43, 51], [43, 53], [43, 54], [44, 47], [44, 48], [44, 49], [44, 52], [44, 53], [44, 54], [44, 55], [45, 46], [45, 47], [45, 48], [45, 49], [45, 51], [45, 53], [46, 49], [46, 50], [46, 52], [46, 53], [46, 54], [46, 55], [47, 49], [47, 50], [47, 51], [47, 52], [48, 50], [48, 51], [48, 53], [48, 54], [48, 55], [49, 50], [49, 52], [49, 53], [49, 54], [50, 51], [50, 52], [50, 53], [50, 54], [50, 55], [51, 55], [52, 53], [52, 55], [53, 54], [53, 55], [54, 55]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l6-s5/tests/run.py b/tasks/construct-rlve-maximum-clique-l6-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-maximum-clique-l6-s5/tests/test.sh b/tasks/construct-rlve-maximum-clique-l6-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-min-chromatic-number-l1-s7/environment/Dockerfile b/tasks/construct-rlve-min-chromatic-number-l1-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l1-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-min-chromatic-number-l1-s7/environment/instance.json b/tasks/construct-rlve-min-chromatic-number-l1-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf72afdbd7bb397946605eb0703606de74c68b41
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l1-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 6, "k": 3, "edges": [[0, 2], [0, 5], [2, 5]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l1-s7/solution/solve.sh b/tasks/construct-rlve-min-chromatic-number-l1-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b70425146a1f57d8f0818aa5b5ca6b7d754cffec
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l1-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 0, 1, 0, 0, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/check.py b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2b77793fb15e0d97174b3c28e69a86e2a26996f
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"edge ({u},{v}) is monochromatic")
+    return None, {}
diff --git a/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/instance.json b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf72afdbd7bb397946605eb0703606de74c68b41
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 6, "k": 3, "edges": [[0, 2], [0, 5], [2, 5]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/run.py b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/test.sh b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l1-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-min-chromatic-number-l5-s8/environment/Dockerfile b/tasks/construct-rlve-min-chromatic-number-l5-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l5-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-min-chromatic-number-l5-s8/environment/instance.json b/tasks/construct-rlve-min-chromatic-number-l5-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..769e6ad01b4572808bda221f32b6ccadf4a3262b
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l5-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 24, "k": 5, "edges": [[0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 12], [0, 14], [0, 17], [0, 18], [0, 19], [1, 6], [1, 7], [1, 13], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 6], [2, 13], [2, 21], [3, 8], [3, 10], [3, 11], [3, 15], [3, 16], [3, 18], [3, 21], [3, 23], [4, 5], [4, 6], [4, 8], [4, 11], [4, 15], [4, 16], [4, 17], [4, 23], [5, 8], [5, 13], [5, 16], [5, 17], [6, 7], [6, 8], [6, 9], [6, 13], [6, 18], [7, 9], [7, 21], [8, 9], [8, 10], [8, 14], [8, 16], [8, 17], [8, 19], [9, 10], [9, 12], [9, 13], [9, 19], [9, 20], [10, 17], [10, 18], [10, 20], [10, 21], [10, 22], [10, 23], [11, 13], [11, 15], [11, 19], [11, 20], [11, 23], [12, 13], [12, 16], [12, 17], [12, 21], [12, 22], [12, 23], [13, 16], [13, 18], [13, 20], [13, 23], [14, 16], [14, 17], [14, 22], [15, 16], [15, 18], [15, 19], [15, 20], [16, 18], [16, 20], [16, 22], [17, 18], [17, 20], [18, 21], [18, 22], [19, 20], [19, 23]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l5-s8/solution/solve.sh b/tasks/construct-rlve-min-chromatic-number-l5-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7443a281530a66a5c0b86292d70dac3bee606c96
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l5-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 0, 0, 1, 1, 2, 2, 1, 0, 3, 2, 0, 2, 1, 1, 2, 3, 3, 4, 1, 4, 3, 0, 3]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/check.py b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2b77793fb15e0d97174b3c28e69a86e2a26996f
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"edge ({u},{v}) is monochromatic")
+    return None, {}
diff --git a/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/instance.json b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..769e6ad01b4572808bda221f32b6ccadf4a3262b
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 24, "k": 5, "edges": [[0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 12], [0, 14], [0, 17], [0, 18], [0, 19], [1, 6], [1, 7], [1, 13], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 6], [2, 13], [2, 21], [3, 8], [3, 10], [3, 11], [3, 15], [3, 16], [3, 18], [3, 21], [3, 23], [4, 5], [4, 6], [4, 8], [4, 11], [4, 15], [4, 16], [4, 17], [4, 23], [5, 8], [5, 13], [5, 16], [5, 17], [6, 7], [6, 8], [6, 9], [6, 13], [6, 18], [7, 9], [7, 21], [8, 9], [8, 10], [8, 14], [8, 16], [8, 17], [8, 19], [9, 10], [9, 12], [9, 13], [9, 19], [9, 20], [10, 17], [10, 18], [10, 20], [10, 21], [10, 22], [10, 23], [11, 13], [11, 15], [11, 19], [11, 20], [11, 23], [12, 13], [12, 16], [12, 17], [12, 21], [12, 22], [12, 23], [13, 16], [13, 18], [13, 20], [13, 23], [14, 16], [14, 17], [14, 22], [15, 16], [15, 18], [15, 19], [15, 20], [16, 18], [16, 20], [16, 22], [17, 18], [17, 20], [18, 21], [18, 22], [19, 20], [19, 23]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/run.py b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/test.sh b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l5-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l5-s2/environment/Dockerfile b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l5-s2/environment/instance.json b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..06a0b83a005235d6799c6d58c7ba586d8138ffdb
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 15, "k": 9, "edges": [[0, 2], [0, 7], [0, 12], [1, 5], [1, 9], [2, 4], [2, 5], [2, 7], [2, 9], [3, 4], [3, 6], [3, 12], [4, 9], [4, 11], [5, 7], [5, 8], [5, 13], [6, 9], [6, 10], [6, 14], [7, 11], [7, 13], [10, 11], [10, 13], [12, 13], [12, 14]], "family": "rlve_min_harmonious_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l5-s2/solution/solve.sh b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8cc51866d6edd51b08597de173a70321860c3229
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 0, 1, 2, 3, 2, 4, 5, 6, 7, 6, 8, 8, 7, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l5-s2/tests/test.sh b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l5-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-pan-solar-panels-l2-s8/environment/Dockerfile b/tasks/construct-rlve-pan-solar-panels-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l2-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-pan-solar-panels-l2-s8/environment/instance.json b/tasks/construct-rlve-pan-solar-panels-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e87bbe26c8b1cbf220f806ad543cfee93016311c
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"A": 814, "B": 904, "C": 1, "D": 201, "target": 180, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l2-s8/solution/solve.sh b/tasks/construct-rlve-pan-solar-panels-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..90262d39356c986766de52bdbe2311d5d6fe20d3
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l2-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"X": 900, "Y": 180}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/check.py b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bb2e7cc0b0280ab877755cc5d97b510680f7aa3
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/check.py
@@ -0,0 +1,12 @@
+import math
+
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    X = as_int(ans.get("X"), "X", lo=inst["A"], hi=inst["B"])
+    Y = as_int(ans.get("Y"), "Y", lo=inst["C"], hi=inst["D"])
+    g = math.gcd(X, Y)
+    if g < inst["target"]:
+        raise Invalid(f"gcd(X, Y) = {g} < {inst['target']}")
+    return None, {"gcd": g}
diff --git a/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/instance.json b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e87bbe26c8b1cbf220f806ad543cfee93016311c
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"A": 814, "B": 904, "C": 1, "D": 201, "target": 180, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/run.py b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/test.sh b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l2-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-pan-solar-panels-l6-s7/environment/Dockerfile b/tasks/construct-rlve-pan-solar-panels-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l6-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-pan-solar-panels-l6-s7/environment/instance.json b/tasks/construct-rlve-pan-solar-panels-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..77e1b03d61cb0b6f44c30002feb94e287b37361e
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"A": 18558601965, "B": 34495217625, "C": 72377195950, "D": 76079473950, "target": 25359824650, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l6-s7/solution/solve.sh b/tasks/construct-rlve-pan-solar-panels-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..03f73979fd0898d6f47b437c37b624215f8c2dc9
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l6-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"X": 25359824650, "Y": 76079473950}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/check.py b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bb2e7cc0b0280ab877755cc5d97b510680f7aa3
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/check.py
@@ -0,0 +1,12 @@
+import math
+
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    X = as_int(ans.get("X"), "X", lo=inst["A"], hi=inst["B"])
+    Y = as_int(ans.get("Y"), "Y", lo=inst["C"], hi=inst["D"])
+    g = math.gcd(X, Y)
+    if g < inst["target"]:
+        raise Invalid(f"gcd(X, Y) = {g} < {inst['target']}")
+    return None, {"gcd": g}
diff --git a/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/instance.json b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..77e1b03d61cb0b6f44c30002feb94e287b37361e
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"A": 18558601965, "B": 34495217625, "C": 72377195950, "D": 76079473950, "target": 25359824650, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/run.py b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/test.sh b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l6-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l3-s2/environment/Dockerfile b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l3-s2/environment/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7fc5d7eab6b838b5fcd8de6fe8e8666e2f441171
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [4, 16, 32, 40, 32, 12, 2], "fmin": "0.587391075289587500801061587752950893718624289", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l3-s2/solution/solve.sh b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..123677bb39b706b9db9f71c614d9247f09c5ebcc
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x0": -0.5996387644174705}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/check.py b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3be068f4391ad0838c29a4f7d521b8072cf39991
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/check.py
@@ -0,0 +1,19 @@
+from fractions import Fraction
+
+from run import Invalid, num
+
+
+def check(inst, ans):
+    x0 = Fraction(num(ans.get("x0"), "x0"))
+    if abs(x0) > 10 ** 6:
+        raise Invalid("x0 out of range")
+    v = Fraction(0)
+    for a in reversed(inst["coeffs"]):
+        v = v * x0 + a
+    fmin = Fraction(inst["fmin"])
+    tol = Fraction(1, 10 ** 9) * max(Fraction(1), abs(fmin))
+    if v > fmin + tol:
+        raise Invalid(f"f(x0) = {float(v)} is above the global minimum {float(fmin)}")
+    if v < fmin - tol:  # cannot happen for a correct f_min; guards against a bad instance
+        raise Invalid("internal: f(x0) below recorded minimum")
+    return None, {"f_x0": float(v)}
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7fc5d7eab6b838b5fcd8de6fe8e8666e2f441171
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [4, 16, 32, 40, 32, 12, 2], "fmin": "0.587391075289587500801061587752950893718624289", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/run.py b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/test.sh b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l3-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l4-s7/environment/Dockerfile b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l4-s7/environment/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa4d919168223794f1317e36ac4b2c6e4b037b96
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [-3870720000, -1778688000, 628339200, 272110720, -31070816, -15547528, 364316, 401010, 9711, -4426, -220, 16, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l4-s7/solution/solve.sh b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fd3f0491548e0e476464d9d1dd07bab0acde2b36
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"roots": [-12, -10, -8, -7, -6, -5, -2, 4, 5, 5, 8, 12]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/check.py b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d30553cb884c5e03c8afe73ef652efc483ab791
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    c = inst["coeffs"]  # c[i] = coefficient of x^i, monic of degree len(c) - 1
+    n = len(c) - 1
+    r = int_list(ans.get("roots"), n, name="roots")
+    bound = 1 + max(abs(v) for v in c)  # Cauchy bound on roots
+    if any(abs(a) > bound for a in r):  # any integer root divides the constant term / is bounded by max|c_i|
+        raise Invalid("root out of range")
+    prod = [1]
+    for a in r:  # multiply by (x - a)
+        nxt = [0] * (len(prod) + 1)
+        for i, v in enumerate(prod):
+            nxt[i + 1] += v
+            nxt[i] -= a * v
+        prod = nxt
+    if prod != c:
+        raise Invalid("the product does not expand to P(x)")
+    return None, {}
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa4d919168223794f1317e36ac4b2c6e4b037b96
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [-3870720000, -1778688000, 628339200, 272110720, -31070816, -15547528, 364316, 401010, 9711, -4426, -220, 16, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/run.py b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/test.sh b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l4-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-polynomial-interpolation-l3-s9/environment/Dockerfile b/tasks/construct-rlve-polynomial-interpolation-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l3-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-polynomial-interpolation-l3-s9/environment/instance.json b/tasks/construct-rlve-polynomial-interpolation-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..073cce2383f7156a66222601c6570524c3a93c88
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"X": [-1, 0, 6, 5, -5, -6, -4], "Y": [-5, -3, 249195, 83827, 66067, 204255, 16345], "family": "rlve_polynomial_interpolation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-interpolation-l3-s9/solution/solve.sh b/tasks/construct-rlve-polynomial-interpolation-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..deb7d5869d3130688449d2e298321a9cbf63ad72
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l3-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"coeffs": [-3, 1, -2, -4, -5, 3, 5]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/check.py b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..f05264e3fd4584db7cb3768800e4a2497564b4f5
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/check.py
@@ -0,0 +1,13 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    X, Y = inst["X"], inst["Y"]
+    c = int_list(ans.get("coeffs"), len(X), name="coeffs")
+    for x, y in zip(X, Y):
+        v = 0
+        for a in reversed(c):
+            v = v * x + a
+        if v != y:
+            raise Invalid(f"f({x}) = {v}, need {y}")
+    return None, {}
diff --git a/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/instance.json b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..073cce2383f7156a66222601c6570524c3a93c88
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"X": [-1, 0, 6, 5, -5, -6, -4], "Y": [-5, -3, 249195, 83827, 66067, 204255, 16345], "family": "rlve_polynomial_interpolation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/run.py b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/test.sh b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l3-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s3/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s3/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f340fe35159484780d259388f6404faab607315
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 98, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s3/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..cffc9aae34a4638161ad69067894db7540b658d1
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"perm": [98, 1, 96, 3, 94, 5, 92, 7, 90, 9, 88, 11, 86, 13, 84, 15, 82, 17, 80, 19, 78, 21, 76, 23, 74, 25, 72, 27, 70, 29, 68, 31, 66, 33, 64, 35, 62, 37, 60, 39, 58, 41, 56, 43, 54, 45, 52, 47, 50, 49, 48, 51, 46, 53, 44, 55, 42, 57, 40, 59, 38, 61, 36, 63, 34, 65, 32, 67, 30, 69, 28, 71, 26, 73, 24, 75, 22, 77, 20, 79, 18, 81, 16, 83, 14, 85, 12, 87, 10, 89, 8, 91, 6, 93, 4, 95, 2, 97]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("perm"), n, 1, n, "perm")
+    if len(set(p)) != n:
+        raise Invalid("not a permutation")
+    seen, acc = set(), 0
+    for v in p:
+        acc = (acc + v) % n
+        if acc in seen:
+            raise Invalid(f"prefix sum residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f340fe35159484780d259388f6404faab607315
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 98, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s4/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s4/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3c17ae982c263345dc8e7b00708f486523f95e82
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 42, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s4/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..853f893d46e36ea8d6030facfbcef92dfeb49cc6
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"perm": [42, 1, 40, 3, 38, 5, 36, 7, 34, 9, 32, 11, 30, 13, 28, 15, 26, 17, 24, 19, 22, 21, 20, 23, 18, 25, 16, 27, 14, 29, 12, 31, 10, 33, 8, 35, 6, 37, 4, 39, 2, 41]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("perm"), n, 1, n, "perm")
+    if len(set(p)) != n:
+        raise Invalid("not a permutation")
+    seen, acc = set(), 0
+    for v in p:
+        acc = (acc + v) % n
+        if acc in seen:
+            raise Invalid(f"prefix sum residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3c17ae982c263345dc8e7b00708f486523f95e82
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/instance.json
@@ -0,0 +1 @@
+{"n": 42, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l5-s7/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l5-s7/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad49d2f10790c03ee40aff0f3ce5fd5b5f4beadf
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 3282, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l5-s7/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..31ef6f3c7e5b597a6c7e49998bdd6d09862261ed
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"perm": [3282, 1, 3280, 3, 3278, 5, 3276, 7, 3274, 9, 3272, 11, 3270, 13, 3268, 15, 3266, 17, 3264, 19, 3262, 21, 3260, 23, 3258, 25, 3256, 27, 3254, 29, 3252, 31, 3250, 33, 3248, 35, 3246, 37, 3244, 39, 3242, 41, 3240, 43, 3238, 45, 3236, 47, 3234, 49, 3232, 51, 3230, 53, 3228, 55, 3226, 57, 3224, 59, 3222, 61, 3220, 63, 3218, 65, 3216, 67, 3214, 69, 3212, 71, 3210, 73, 3208, 75, 3206, 77, 3204, 79, 3202, 81, 3200, 83, 3198, 85, 3196, 87, 3194, 89, 3192, 91, 3190, 93, 3188, 95, 3186, 97, 3184, 99, 3182, 101, 3180, 103, 3178, 105, 3176, 107, 3174, 109, 3172, 111, 3170, 113, 3168, 115, 3166, 117, 3164, 119, 3162, 121, 3160, 123, 3158, 125, 3156, 127, 3154, 129, 3152, 131, 3150, 133, 3148, 135, 3146, 137, 3144, 139, 3142, 141, 3140, 143, 3138, 145, 3136, 147, 3134, 149, 3132, 151, 3130, 153, 3128, 155, 3126, 157, 3124, 159, 3122, 161, 3120, 163, 3118, 165, 3116, 167, 3114, 169, 3112, 171, 3110, 173, 3108, 175, 3106, 177, 3104, 179, 3102, 181, 3100, 183, 3098, 185, 3096, 187, 3094, 189, 3092, 191, 3090, 193, 3088, 195, 3086, 197, 3084, 199, 3082, 201, 3080, 203, 3078, 205, 3076, 207, 3074, 209, 3072, 211, 3070, 213, 3068, 215, 3066, 217, 3064, 219, 3062, 221, 3060, 223, 3058, 225, 3056, 227, 3054, 229, 3052, 231, 3050, 233, 3048, 235, 3046, 237, 3044, 239, 3042, 241, 3040, 243, 3038, 245, 3036, 247, 3034, 249, 3032, 251, 3030, 253, 3028, 255, 3026, 257, 3024, 259, 3022, 261, 3020, 263, 3018, 265, 3016, 267, 3014, 269, 3012, 271, 3010, 273, 3008, 275, 3006, 277, 3004, 279, 3002, 281, 3000, 283, 2998, 285, 2996, 287, 2994, 289, 2992, 291, 2990, 293, 2988, 295, 2986, 297, 2984, 299, 2982, 301, 2980, 303, 2978, 305, 2976, 307, 2974, 309, 2972, 311, 2970, 313, 2968, 315, 2966, 317, 2964, 319, 2962, 321, 2960, 323, 2958, 325, 2956, 327, 2954, 329, 2952, 331, 2950, 333, 2948, 335, 2946, 337, 2944, 339, 2942, 341, 2940, 343, 2938, 345, 2936, 347, 2934, 349, 2932, 351, 2930, 353, 2928, 355, 2926, 357, 2924, 359, 2922, 361, 2920, 363, 2918, 365, 2916, 367, 2914, 369, 2912, 371, 2910, 373, 2908, 375, 2906, 377, 2904, 379, 2902, 381, 2900, 383, 2898, 385, 2896, 387, 2894, 389, 2892, 391, 2890, 393, 2888, 395, 2886, 397, 2884, 399, 2882, 401, 2880, 403, 2878, 405, 2876, 407, 2874, 409, 2872, 411, 2870, 413, 2868, 415, 2866, 417, 2864, 419, 2862, 421, 2860, 423, 2858, 425, 2856, 427, 2854, 429, 2852, 431, 2850, 433, 2848, 435, 2846, 437, 2844, 439, 2842, 441, 2840, 443, 2838, 445, 2836, 447, 2834, 449, 2832, 451, 2830, 453, 2828, 455, 2826, 457, 2824, 459, 2822, 461, 2820, 463, 2818, 465, 2816, 467, 2814, 469, 2812, 471, 2810, 473, 2808, 475, 2806, 477, 2804, 479, 2802, 481, 2800, 483, 2798, 485, 2796, 487, 2794, 489, 2792, 491, 2790, 493, 2788, 495, 2786, 497, 2784, 499, 2782, 501, 2780, 503, 2778, 505, 2776, 507, 2774, 509, 2772, 511, 2770, 513, 2768, 515, 2766, 517, 2764, 519, 2762, 521, 2760, 523, 2758, 525, 2756, 527, 2754, 529, 2752, 531, 2750, 533, 2748, 535, 2746, 537, 2744, 539, 2742, 541, 2740, 543, 2738, 545, 2736, 547, 2734, 549, 2732, 551, 2730, 553, 2728, 555, 2726, 557, 2724, 559, 2722, 561, 2720, 563, 2718, 565, 2716, 567, 2714, 569, 2712, 571, 2710, 573, 2708, 575, 2706, 577, 2704, 579, 2702, 581, 2700, 583, 2698, 585, 2696, 587, 2694, 589, 2692, 591, 2690, 593, 2688, 595, 2686, 597, 2684, 599, 2682, 601, 2680, 603, 2678, 605, 2676, 607, 2674, 609, 2672, 611, 2670, 613, 2668, 615, 2666, 617, 2664, 619, 2662, 621, 2660, 623, 2658, 625, 2656, 627, 2654, 629, 2652, 631, 2650, 633, 2648, 635, 2646, 637, 2644, 639, 2642, 641, 2640, 643, 2638, 645, 2636, 647, 2634, 649, 2632, 651, 2630, 653, 2628, 655, 2626, 657, 2624, 659, 2622, 661, 2620, 663, 2618, 665, 2616, 667, 2614, 669, 2612, 671, 2610, 673, 2608, 675, 2606, 677, 2604, 679, 2602, 681, 2600, 683, 2598, 685, 2596, 687, 2594, 689, 2592, 691, 2590, 693, 2588, 695, 2586, 697, 2584, 699, 2582, 701, 2580, 703, 2578, 705, 2576, 707, 2574, 709, 2572, 711, 2570, 713, 2568, 715, 2566, 717, 2564, 719, 2562, 721, 2560, 723, 2558, 725, 2556, 727, 2554, 729, 2552, 731, 2550, 733, 2548, 735, 2546, 737, 2544, 739, 2542, 741, 2540, 743, 2538, 745, 2536, 747, 2534, 749, 2532, 751, 2530, 753, 2528, 755, 2526, 757, 2524, 759, 2522, 761, 2520, 763, 2518, 765, 2516, 767, 2514, 769, 2512, 771, 2510, 773, 2508, 775, 2506, 777, 2504, 779, 2502, 781, 2500, 783, 2498, 785, 2496, 787, 2494, 789, 2492, 791, 2490, 793, 2488, 795, 2486, 797, 2484, 799, 2482, 801, 2480, 803, 2478, 805, 2476, 807, 2474, 809, 2472, 811, 2470, 813, 2468, 815, 2466, 817, 2464, 819, 2462, 821, 2460, 823, 2458, 825, 2456, 827, 2454, 829, 2452, 831, 2450, 833, 2448, 835, 2446, 837, 2444, 839, 2442, 841, 2440, 843, 2438, 845, 2436, 847, 2434, 849, 2432, 851, 2430, 853, 2428, 855, 2426, 857, 2424, 859, 2422, 861, 2420, 863, 2418, 865, 2416, 867, 2414, 869, 2412, 871, 2410, 873, 2408, 875, 2406, 877, 2404, 879, 2402, 881, 2400, 883, 2398, 885, 2396, 887, 2394, 889, 2392, 891, 2390, 893, 2388, 895, 2386, 897, 2384, 899, 2382, 901, 2380, 903, 2378, 905, 2376, 907, 2374, 909, 2372, 911, 2370, 913, 2368, 915, 2366, 917, 2364, 919, 2362, 921, 2360, 923, 2358, 925, 2356, 927, 2354, 929, 2352, 931, 2350, 933, 2348, 935, 2346, 937, 2344, 939, 2342, 941, 2340, 943, 2338, 945, 2336, 947, 2334, 949, 2332, 951, 2330, 953, 2328, 955, 2326, 957, 2324, 959, 2322, 961, 2320, 963, 2318, 965, 2316, 967, 2314, 969, 2312, 971, 2310, 973, 2308, 975, 2306, 977, 2304, 979, 2302, 981, 2300, 983, 2298, 985, 2296, 987, 2294, 989, 2292, 991, 2290, 993, 2288, 995, 2286, 997, 2284, 999, 2282, 1001, 2280, 1003, 2278, 1005, 2276, 1007, 2274, 1009, 2272, 1011, 2270, 1013, 2268, 1015, 2266, 1017, 2264, 1019, 2262, 1021, 2260, 1023, 2258, 1025, 2256, 1027, 2254, 1029, 2252, 1031, 2250, 1033, 2248, 1035, 2246, 1037, 2244, 1039, 2242, 1041, 2240, 1043, 2238, 1045, 2236, 1047, 2234, 1049, 2232, 1051, 2230, 1053, 2228, 1055, 2226, 1057, 2224, 1059, 2222, 1061, 2220, 1063, 2218, 1065, 2216, 1067, 2214, 1069, 2212, 1071, 2210, 1073, 2208, 1075, 2206, 1077, 2204, 1079, 2202, 1081, 2200, 1083, 2198, 1085, 2196, 1087, 2194, 1089, 2192, 1091, 2190, 1093, 2188, 1095, 2186, 1097, 2184, 1099, 2182, 1101, 2180, 1103, 2178, 1105, 2176, 1107, 2174, 1109, 2172, 1111, 2170, 1113, 2168, 1115, 2166, 1117, 2164, 1119, 2162, 1121, 2160, 1123, 2158, 1125, 2156, 1127, 2154, 1129, 2152, 1131, 2150, 1133, 2148, 1135, 2146, 1137, 2144, 1139, 2142, 1141, 2140, 1143, 2138, 1145, 2136, 1147, 2134, 1149, 2132, 1151, 2130, 1153, 2128, 1155, 2126, 1157, 2124, 1159, 2122, 1161, 2120, 1163, 2118, 1165, 2116, 1167, 2114, 1169, 2112, 1171, 2110, 1173, 2108, 1175, 2106, 1177, 2104, 1179, 2102, 1181, 2100, 1183, 2098, 1185, 2096, 1187, 2094, 1189, 2092, 1191, 2090, 1193, 2088, 1195, 2086, 1197, 2084, 1199, 2082, 1201, 2080, 1203, 2078, 1205, 2076, 1207, 2074, 1209, 2072, 1211, 2070, 1213, 2068, 1215, 2066, 1217, 2064, 1219, 2062, 1221, 2060, 1223, 2058, 1225, 2056, 1227, 2054, 1229, 2052, 1231, 2050, 1233, 2048, 1235, 2046, 1237, 2044, 1239, 2042, 1241, 2040, 1243, 2038, 1245, 2036, 1247, 2034, 1249, 2032, 1251, 2030, 1253, 2028, 1255, 2026, 1257, 2024, 1259, 2022, 1261, 2020, 1263, 2018, 1265, 2016, 1267, 2014, 1269, 2012, 1271, 2010, 1273, 2008, 1275, 2006, 1277, 2004, 1279, 2002, 1281, 2000, 1283, 1998, 1285, 1996, 1287, 1994, 1289, 1992, 1291, 1990, 1293, 1988, 1295, 1986, 1297, 1984, 1299, 1982, 1301, 1980, 1303, 1978, 1305, 1976, 1307, 1974, 1309, 1972, 1311, 1970, 1313, 1968, 1315, 1966, 1317, 1964, 1319, 1962, 1321, 1960, 1323, 1958, 1325, 1956, 1327, 1954, 1329, 1952, 1331, 1950, 1333, 1948, 1335, 1946, 1337, 1944, 1339, 1942, 1341, 1940, 1343, 1938, 1345, 1936, 1347, 1934, 1349, 1932, 1351, 1930, 1353, 1928, 1355, 1926, 1357, 1924, 1359, 1922, 1361, 1920, 1363, 1918, 1365, 1916, 1367, 1914, 1369, 1912, 1371, 1910, 1373, 1908, 1375, 1906, 1377, 1904, 1379, 1902, 1381, 1900, 1383, 1898, 1385, 1896, 1387, 1894, 1389, 1892, 1391, 1890, 1393, 1888, 1395, 1886, 1397, 1884, 1399, 1882, 1401, 1880, 1403, 1878, 1405, 1876, 1407, 1874, 1409, 1872, 1411, 1870, 1413, 1868, 1415, 1866, 1417, 1864, 1419, 1862, 1421, 1860, 1423, 1858, 1425, 1856, 1427, 1854, 1429, 1852, 1431, 1850, 1433, 1848, 1435, 1846, 1437, 1844, 1439, 1842, 1441, 1840, 1443, 1838, 1445, 1836, 1447, 1834, 1449, 1832, 1451, 1830, 1453, 1828, 1455, 1826, 1457, 1824, 1459, 1822, 1461, 1820, 1463, 1818, 1465, 1816, 1467, 1814, 1469, 1812, 1471, 1810, 1473, 1808, 1475, 1806, 1477, 1804, 1479, 1802, 1481, 1800, 1483, 1798, 1485, 1796, 1487, 1794, 1489, 1792, 1491, 1790, 1493, 1788, 1495, 1786, 1497, 1784, 1499, 1782, 1501, 1780, 1503, 1778, 1505, 1776, 1507, 1774, 1509, 1772, 1511, 1770, 1513, 1768, 1515, 1766, 1517, 1764, 1519, 1762, 1521, 1760, 1523, 1758, 1525, 1756, 1527, 1754, 1529, 1752, 1531, 1750, 1533, 1748, 1535, 1746, 1537, 1744, 1539, 1742, 1541, 1740, 1543, 1738, 1545, 1736, 1547, 1734, 1549, 1732, 1551, 1730, 1553, 1728, 1555, 1726, 1557, 1724, 1559, 1722, 1561, 1720, 1563, 1718, 1565, 1716, 1567, 1714, 1569, 1712, 1571, 1710, 1573, 1708, 1575, 1706, 1577, 1704, 1579, 1702, 1581, 1700, 1583, 1698, 1585, 1696, 1587, 1694, 1589, 1692, 1591, 1690, 1593, 1688, 1595, 1686, 1597, 1684, 1599, 1682, 1601, 1680, 1603, 1678, 1605, 1676, 1607, 1674, 1609, 1672, 1611, 1670, 1613, 1668, 1615, 1666, 1617, 1664, 1619, 1662, 1621, 1660, 1623, 1658, 1625, 1656, 1627, 1654, 1629, 1652, 1631, 1650, 1633, 1648, 1635, 1646, 1637, 1644, 1639, 1642, 1641, 1640, 1643, 1638, 1645, 1636, 1647, 1634, 1649, 1632, 1651, 1630, 1653, 1628, 1655, 1626, 1657, 1624, 1659, 1622, 1661, 1620, 1663, 1618, 1665, 1616, 1667, 1614, 1669, 1612, 1671, 1610, 1673, 1608, 1675, 1606, 1677, 1604, 1679, 1602, 1681, 1600, 1683, 1598, 1685, 1596, 1687, 1594, 1689, 1592, 1691, 1590, 1693, 1588, 1695, 1586, 1697, 1584, 1699, 1582, 1701, 1580, 1703, 1578, 1705, 1576, 1707, 1574, 1709, 1572, 1711, 1570, 1713, 1568, 1715, 1566, 1717, 1564, 1719, 1562, 1721, 1560, 1723, 1558, 1725, 1556, 1727, 1554, 1729, 1552, 1731, 1550, 1733, 1548, 1735, 1546, 1737, 1544, 1739, 1542, 1741, 1540, 1743, 1538, 1745, 1536, 1747, 1534, 1749, 1532, 1751, 1530, 1753, 1528, 1755, 1526, 1757, 1524, 1759, 1522, 1761, 1520, 1763, 1518, 1765, 1516, 1767, 1514, 1769, 1512, 1771, 1510, 1773, 1508, 1775, 1506, 1777, 1504, 1779, 1502, 1781, 1500, 1783, 1498, 1785, 1496, 1787, 1494, 1789, 1492, 1791, 1490, 1793, 1488, 1795, 1486, 1797, 1484, 1799, 1482, 1801, 1480, 1803, 1478, 1805, 1476, 1807, 1474, 1809, 1472, 1811, 1470, 1813, 1468, 1815, 1466, 1817, 1464, 1819, 1462, 1821, 1460, 1823, 1458, 1825, 1456, 1827, 1454, 1829, 1452, 1831, 1450, 1833, 1448, 1835, 1446, 1837, 1444, 1839, 1442, 1841, 1440, 1843, 1438, 1845, 1436, 1847, 1434, 1849, 1432, 1851, 1430, 1853, 1428, 1855, 1426, 1857, 1424, 1859, 1422, 1861, 1420, 1863, 1418, 1865, 1416, 1867, 1414, 1869, 1412, 1871, 1410, 1873, 1408, 1875, 1406, 1877, 1404, 1879, 1402, 1881, 1400, 1883, 1398, 1885, 1396, 1887, 1394, 1889, 1392, 1891, 1390, 1893, 1388, 1895, 1386, 1897, 1384, 1899, 1382, 1901, 1380, 1903, 1378, 1905, 1376, 1907, 1374, 1909, 1372, 1911, 1370, 1913, 1368, 1915, 1366, 1917, 1364, 1919, 1362, 1921, 1360, 1923, 1358, 1925, 1356, 1927, 1354, 1929, 1352, 1931, 1350, 1933, 1348, 1935, 1346, 1937, 1344, 1939, 1342, 1941, 1340, 1943, 1338, 1945, 1336, 1947, 1334, 1949, 1332, 1951, 1330, 1953, 1328, 1955, 1326, 1957, 1324, 1959, 1322, 1961, 1320, 1963, 1318, 1965, 1316, 1967, 1314, 1969, 1312, 1971, 1310, 1973, 1308, 1975, 1306, 1977, 1304, 1979, 1302, 1981, 1300, 1983, 1298, 1985, 1296, 1987, 1294, 1989, 1292, 1991, 1290, 1993, 1288, 1995, 1286, 1997, 1284, 1999, 1282, 2001, 1280, 2003, 1278, 2005, 1276, 2007, 1274, 2009, 1272, 2011, 1270, 2013, 1268, 2015, 1266, 2017, 1264, 2019, 1262, 2021, 1260, 2023, 1258, 2025, 1256, 2027, 1254, 2029, 1252, 2031, 1250, 2033, 1248, 2035, 1246, 2037, 1244, 2039, 1242, 2041, 1240, 2043, 1238, 2045, 1236, 2047, 1234, 2049, 1232, 2051, 1230, 2053, 1228, 2055, 1226, 2057, 1224, 2059, 1222, 2061, 1220, 2063, 1218, 2065, 1216, 2067, 1214, 2069, 1212, 2071, 1210, 2073, 1208, 2075, 1206, 2077, 1204, 2079, 1202, 2081, 1200, 2083, 1198, 2085, 1196, 2087, 1194, 2089, 1192, 2091, 1190, 2093, 1188, 2095, 1186, 2097, 1184, 2099, 1182, 2101, 1180, 2103, 1178, 2105, 1176, 2107, 1174, 2109, 1172, 2111, 1170, 2113, 1168, 2115, 1166, 2117, 1164, 2119, 1162, 2121, 1160, 2123, 1158, 2125, 1156, 2127, 1154, 2129, 1152, 2131, 1150, 2133, 1148, 2135, 1146, 2137, 1144, 2139, 1142, 2141, 1140, 2143, 1138, 2145, 1136, 2147, 1134, 2149, 1132, 2151, 1130, 2153, 1128, 2155, 1126, 2157, 1124, 2159, 1122, 2161, 1120, 2163, 1118, 2165, 1116, 2167, 1114, 2169, 1112, 2171, 1110, 2173, 1108, 2175, 1106, 2177, 1104, 2179, 1102, 2181, 1100, 2183, 1098, 2185, 1096, 2187, 1094, 2189, 1092, 2191, 1090, 2193, 1088, 2195, 1086, 2197, 1084, 2199, 1082, 2201, 1080, 2203, 1078, 2205, 1076, 2207, 1074, 2209, 1072, 2211, 1070, 2213, 1068, 2215, 1066, 2217, 1064, 2219, 1062, 2221, 1060, 2223, 1058, 2225, 1056, 2227, 1054, 2229, 1052, 2231, 1050, 2233, 1048, 2235, 1046, 2237, 1044, 2239, 1042, 2241, 1040, 2243, 1038, 2245, 1036, 2247, 1034, 2249, 1032, 2251, 1030, 2253, 1028, 2255, 1026, 2257, 1024, 2259, 1022, 2261, 1020, 2263, 1018, 2265, 1016, 2267, 1014, 2269, 1012, 2271, 1010, 2273, 1008, 2275, 1006, 2277, 1004, 2279, 1002, 2281, 1000, 2283, 998, 2285, 996, 2287, 994, 2289, 992, 2291, 990, 2293, 988, 2295, 986, 2297, 984, 2299, 982, 2301, 980, 2303, 978, 2305, 976, 2307, 974, 2309, 972, 2311, 970, 2313, 968, 2315, 966, 2317, 964, 2319, 962, 2321, 960, 2323, 958, 2325, 956, 2327, 954, 2329, 952, 2331, 950, 2333, 948, 2335, 946, 2337, 944, 2339, 942, 2341, 940, 2343, 938, 2345, 936, 2347, 934, 2349, 932, 2351, 930, 2353, 928, 2355, 926, 2357, 924, 2359, 922, 2361, 920, 2363, 918, 2365, 916, 2367, 914, 2369, 912, 2371, 910, 2373, 908, 2375, 906, 2377, 904, 2379, 902, 2381, 900, 2383, 898, 2385, 896, 2387, 894, 2389, 892, 2391, 890, 2393, 888, 2395, 886, 2397, 884, 2399, 882, 2401, 880, 2403, 878, 2405, 876, 2407, 874, 2409, 872, 2411, 870, 2413, 868, 2415, 866, 2417, 864, 2419, 862, 2421, 860, 2423, 858, 2425, 856, 2427, 854, 2429, 852, 2431, 850, 2433, 848, 2435, 846, 2437, 844, 2439, 842, 2441, 840, 2443, 838, 2445, 836, 2447, 834, 2449, 832, 2451, 830, 2453, 828, 2455, 826, 2457, 824, 2459, 822, 2461, 820, 2463, 818, 2465, 816, 2467, 814, 2469, 812, 2471, 810, 2473, 808, 2475, 806, 2477, 804, 2479, 802, 2481, 800, 2483, 798, 2485, 796, 2487, 794, 2489, 792, 2491, 790, 2493, 788, 2495, 786, 2497, 784, 2499, 782, 2501, 780, 2503, 778, 2505, 776, 2507, 774, 2509, 772, 2511, 770, 2513, 768, 2515, 766, 2517, 764, 2519, 762, 2521, 760, 2523, 758, 2525, 756, 2527, 754, 2529, 752, 2531, 750, 2533, 748, 2535, 746, 2537, 744, 2539, 742, 2541, 740, 2543, 738, 2545, 736, 2547, 734, 2549, 732, 2551, 730, 2553, 728, 2555, 726, 2557, 724, 2559, 722, 2561, 720, 2563, 718, 2565, 716, 2567, 714, 2569, 712, 2571, 710, 2573, 708, 2575, 706, 2577, 704, 2579, 702, 2581, 700, 2583, 698, 2585, 696, 2587, 694, 2589, 692, 2591, 690, 2593, 688, 2595, 686, 2597, 684, 2599, 682, 2601, 680, 2603, 678, 2605, 676, 2607, 674, 2609, 672, 2611, 670, 2613, 668, 2615, 666, 2617, 664, 2619, 662, 2621, 660, 2623, 658, 2625, 656, 2627, 654, 2629, 652, 2631, 650, 2633, 648, 2635, 646, 2637, 644, 2639, 642, 2641, 640, 2643, 638, 2645, 636, 2647, 634, 2649, 632, 2651, 630, 2653, 628, 2655, 626, 2657, 624, 2659, 622, 2661, 620, 2663, 618, 2665, 616, 2667, 614, 2669, 612, 2671, 610, 2673, 608, 2675, 606, 2677, 604, 2679, 602, 2681, 600, 2683, 598, 2685, 596, 2687, 594, 2689, 592, 2691, 590, 2693, 588, 2695, 586, 2697, 584, 2699, 582, 2701, 580, 2703, 578, 2705, 576, 2707, 574, 2709, 572, 2711, 570, 2713, 568, 2715, 566, 2717, 564, 2719, 562, 2721, 560, 2723, 558, 2725, 556, 2727, 554, 2729, 552, 2731, 550, 2733, 548, 2735, 546, 2737, 544, 2739, 542, 2741, 540, 2743, 538, 2745, 536, 2747, 534, 2749, 532, 2751, 530, 2753, 528, 2755, 526, 2757, 524, 2759, 522, 2761, 520, 2763, 518, 2765, 516, 2767, 514, 2769, 512, 2771, 510, 2773, 508, 2775, 506, 2777, 504, 2779, 502, 2781, 500, 2783, 498, 2785, 496, 2787, 494, 2789, 492, 2791, 490, 2793, 488, 2795, 486, 2797, 484, 2799, 482, 2801, 480, 2803, 478, 2805, 476, 2807, 474, 2809, 472, 2811, 470, 2813, 468, 2815, 466, 2817, 464, 2819, 462, 2821, 460, 2823, 458, 2825, 456, 2827, 454, 2829, 452, 2831, 450, 2833, 448, 2835, 446, 2837, 444, 2839, 442, 2841, 440, 2843, 438, 2845, 436, 2847, 434, 2849, 432, 2851, 430, 2853, 428, 2855, 426, 2857, 424, 2859, 422, 2861, 420, 2863, 418, 2865, 416, 2867, 414, 2869, 412, 2871, 410, 2873, 408, 2875, 406, 2877, 404, 2879, 402, 2881, 400, 2883, 398, 2885, 396, 2887, 394, 2889, 392, 2891, 390, 2893, 388, 2895, 386, 2897, 384, 2899, 382, 2901, 380, 2903, 378, 2905, 376, 2907, 374, 2909, 372, 2911, 370, 2913, 368, 2915, 366, 2917, 364, 2919, 362, 2921, 360, 2923, 358, 2925, 356, 2927, 354, 2929, 352, 2931, 350, 2933, 348, 2935, 346, 2937, 344, 2939, 342, 2941, 340, 2943, 338, 2945, 336, 2947, 334, 2949, 332, 2951, 330, 2953, 328, 2955, 326, 2957, 324, 2959, 322, 2961, 320, 2963, 318, 2965, 316, 2967, 314, 2969, 312, 2971, 310, 2973, 308, 2975, 306, 2977, 304, 2979, 302, 2981, 300, 2983, 298, 2985, 296, 2987, 294, 2989, 292, 2991, 290, 2993, 288, 2995, 286, 2997, 284, 2999, 282, 3001, 280, 3003, 278, 3005, 276, 3007, 274, 3009, 272, 3011, 270, 3013, 268, 3015, 266, 3017, 264, 3019, 262, 3021, 260, 3023, 258, 3025, 256, 3027, 254, 3029, 252, 3031, 250, 3033, 248, 3035, 246, 3037, 244, 3039, 242, 3041, 240, 3043, 238, 3045, 236, 3047, 234, 3049, 232, 3051, 230, 3053, 228, 3055, 226, 3057, 224, 3059, 222, 3061, 220, 3063, 218, 3065, 216, 3067, 214, 3069, 212, 3071, 210, 3073, 208, 3075, 206, 3077, 204, 3079, 202, 3081, 200, 3083, 198, 3085, 196, 3087, 194, 3089, 192, 3091, 190, 3093, 188, 3095, 186, 3097, 184, 3099, 182, 3101, 180, 3103, 178, 3105, 176, 3107, 174, 3109, 172, 3111, 170, 3113, 168, 3115, 166, 3117, 164, 3119, 162, 3121, 160, 3123, 158, 3125, 156, 3127, 154, 3129, 152, 3131, 150, 3133, 148, 3135, 146, 3137, 144, 3139, 142, 3141, 140, 3143, 138, 3145, 136, 3147, 134, 3149, 132, 3151, 130, 3153, 128, 3155, 126, 3157, 124, 3159, 122, 3161, 120, 3163, 118, 3165, 116, 3167, 114, 3169, 112, 3171, 110, 3173, 108, 3175, 106, 3177, 104, 3179, 102, 3181, 100, 3183, 98, 3185, 96, 3187, 94, 3189, 92, 3191, 90, 3193, 88, 3195, 86, 3197, 84, 3199, 82, 3201, 80, 3203, 78, 3205, 76, 3207, 74, 3209, 72, 3211, 70, 3213, 68, 3215, 66, 3217, 64, 3219, 62, 3221, 60, 3223, 58, 3225, 56, 3227, 54, 3229, 52, 3231, 50, 3233, 48, 3235, 46, 3237, 44, 3239, 42, 3241, 40, 3243, 38, 3245, 36, 3247, 34, 3249, 32, 3251, 30, 3253, 28, 3255, 26, 3257, 24, 3259, 22, 3261, 20, 3263, 18, 3265, 16, 3267, 14, 3269, 12, 3271, 10, 3273, 8, 3275, 6, 3277, 4, 3279, 2, 3281]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("perm"), n, 1, n, "perm")
+    if len(set(p)) != n:
+        raise Invalid("not a permutation")
+    seen, acc = set(), 0
+    for v in p:
+        acc = (acc + v) % n
+        if acc in seen:
+            raise Invalid(f"prefix sum residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad49d2f10790c03ee40aff0f3ce5fd5b5f4beadf
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 3282, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l5-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s2/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s2/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a31e29541b92f116d4dc85878e0e38bc96eb83c
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 27942, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s2/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1f1027bc02a03d6fb459d16c834605f55ecc5ebb
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"perm": [27942, 1, 27940, 3, 27938, 5, 27936, 7, 27934, 9, 27932, 11, 27930, 13, 27928, 15, 27926, 17, 27924, 19, 27922, 21, 27920, 23, 27918, 25, 27916, 27, 27914, 29, 27912, 31, 27910, 33, 27908, 35, 27906, 37, 27904, 39, 27902, 41, 27900, 43, 27898, 45, 27896, 47, 27894, 49, 27892, 51, 27890, 53, 27888, 55, 27886, 57, 27884, 59, 27882, 61, 27880, 63, 27878, 65, 27876, 67, 27874, 69, 27872, 71, 27870, 73, 27868, 75, 27866, 77, 27864, 79, 27862, 81, 27860, 83, 27858, 85, 27856, 87, 27854, 89, 27852, 91, 27850, 93, 27848, 95, 27846, 97, 27844, 99, 27842, 101, 27840, 103, 27838, 105, 27836, 107, 27834, 109, 27832, 111, 27830, 113, 27828, 115, 27826, 117, 27824, 119, 27822, 121, 27820, 123, 27818, 125, 27816, 127, 27814, 129, 27812, 131, 27810, 133, 27808, 135, 27806, 137, 27804, 139, 27802, 141, 27800, 143, 27798, 145, 27796, 147, 27794, 149, 27792, 151, 27790, 153, 27788, 155, 27786, 157, 27784, 159, 27782, 161, 27780, 163, 27778, 165, 27776, 167, 27774, 169, 27772, 171, 27770, 173, 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2140, 25803, 2138, 25805, 2136, 25807, 2134, 25809, 2132, 25811, 2130, 25813, 2128, 25815, 2126, 25817, 2124, 25819, 2122, 25821, 2120, 25823, 2118, 25825, 2116, 25827, 2114, 25829, 2112, 25831, 2110, 25833, 2108, 25835, 2106, 25837, 2104, 25839, 2102, 25841, 2100, 25843, 2098, 25845, 2096, 25847, 2094, 25849, 2092, 25851, 2090, 25853, 2088, 25855, 2086, 25857, 2084, 25859, 2082, 25861, 2080, 25863, 2078, 25865, 2076, 25867, 2074, 25869, 2072, 25871, 2070, 25873, 2068, 25875, 2066, 25877, 2064, 25879, 2062, 25881, 2060, 25883, 2058, 25885, 2056, 25887, 2054, 25889, 2052, 25891, 2050, 25893, 2048, 25895, 2046, 25897, 2044, 25899, 2042, 25901, 2040, 25903, 2038, 25905, 2036, 25907, 2034, 25909, 2032, 25911, 2030, 25913, 2028, 25915, 2026, 25917, 2024, 25919, 2022, 25921, 2020, 25923, 2018, 25925, 2016, 25927, 2014, 25929, 2012, 25931, 2010, 25933, 2008, 25935, 2006, 25937, 2004, 25939, 2002, 25941, 2000, 25943, 1998, 25945, 1996, 25947, 1994, 25949, 1992, 25951, 1990, 25953, 1988, 25955, 1986, 25957, 1984, 25959, 1982, 25961, 1980, 25963, 1978, 25965, 1976, 25967, 1974, 25969, 1972, 25971, 1970, 25973, 1968, 25975, 1966, 25977, 1964, 25979, 1962, 25981, 1960, 25983, 1958, 25985, 1956, 25987, 1954, 25989, 1952, 25991, 1950, 25993, 1948, 25995, 1946, 25997, 1944, 25999, 1942, 26001, 1940, 26003, 1938, 26005, 1936, 26007, 1934, 26009, 1932, 26011, 1930, 26013, 1928, 26015, 1926, 26017, 1924, 26019, 1922, 26021, 1920, 26023, 1918, 26025, 1916, 26027, 1914, 26029, 1912, 26031, 1910, 26033, 1908, 26035, 1906, 26037, 1904, 26039, 1902, 26041, 1900, 26043, 1898, 26045, 1896, 26047, 1894, 26049, 1892, 26051, 1890, 26053, 1888, 26055, 1886, 26057, 1884, 26059, 1882, 26061, 1880, 26063, 1878, 26065, 1876, 26067, 1874, 26069, 1872, 26071, 1870, 26073, 1868, 26075, 1866, 26077, 1864, 26079, 1862, 26081, 1860, 26083, 1858, 26085, 1856, 26087, 1854, 26089, 1852, 26091, 1850, 26093, 1848, 26095, 1846, 26097, 1844, 26099, 1842, 26101, 1840, 26103, 1838, 26105, 1836, 26107, 1834, 26109, 1832, 26111, 1830, 26113, 1828, 26115, 1826, 26117, 1824, 26119, 1822, 26121, 1820, 26123, 1818, 26125, 1816, 26127, 1814, 26129, 1812, 26131, 1810, 26133, 1808, 26135, 1806, 26137, 1804, 26139, 1802, 26141, 1800, 26143, 1798, 26145, 1796, 26147, 1794, 26149, 1792, 26151, 1790, 26153, 1788, 26155, 1786, 26157, 1784, 26159, 1782, 26161, 1780, 26163, 1778, 26165, 1776, 26167, 1774, 26169, 1772, 26171, 1770, 26173, 1768, 26175, 1766, 26177, 1764, 26179, 1762, 26181, 1760, 26183, 1758, 26185, 1756, 26187, 1754, 26189, 1752, 26191, 1750, 26193, 1748, 26195, 1746, 26197, 1744, 26199, 1742, 26201, 1740, 26203, 1738, 26205, 1736, 26207, 1734, 26209, 1732, 26211, 1730, 26213, 1728, 26215, 1726, 26217, 1724, 26219, 1722, 26221, 1720, 26223, 1718, 26225, 1716, 26227, 1714, 26229, 1712, 26231, 1710, 26233, 1708, 26235, 1706, 26237, 1704, 26239, 1702, 26241, 1700, 26243, 1698, 26245, 1696, 26247, 1694, 26249, 1692, 26251, 1690, 26253, 1688, 26255, 1686, 26257, 1684, 26259, 1682, 26261, 1680, 26263, 1678, 26265, 1676, 26267, 1674, 26269, 1672, 26271, 1670, 26273, 1668, 26275, 1666, 26277, 1664, 26279, 1662, 26281, 1660, 26283, 1658, 26285, 1656, 26287, 1654, 26289, 1652, 26291, 1650, 26293, 1648, 26295, 1646, 26297, 1644, 26299, 1642, 26301, 1640, 26303, 1638, 26305, 1636, 26307, 1634, 26309, 1632, 26311, 1630, 26313, 1628, 26315, 1626, 26317, 1624, 26319, 1622, 26321, 1620, 26323, 1618, 26325, 1616, 26327, 1614, 26329, 1612, 26331, 1610, 26333, 1608, 26335, 1606, 26337, 1604, 26339, 1602, 26341, 1600, 26343, 1598, 26345, 1596, 26347, 1594, 26349, 1592, 26351, 1590, 26353, 1588, 26355, 1586, 26357, 1584, 26359, 1582, 26361, 1580, 26363, 1578, 26365, 1576, 26367, 1574, 26369, 1572, 26371, 1570, 26373, 1568, 26375, 1566, 26377, 1564, 26379, 1562, 26381, 1560, 26383, 1558, 26385, 1556, 26387, 1554, 26389, 1552, 26391, 1550, 26393, 1548, 26395, 1546, 26397, 1544, 26399, 1542, 26401, 1540, 26403, 1538, 26405, 1536, 26407, 1534, 26409, 1532, 26411, 1530, 26413, 1528, 26415, 1526, 26417, 1524, 26419, 1522, 26421, 1520, 26423, 1518, 26425, 1516, 26427, 1514, 26429, 1512, 26431, 1510, 26433, 1508, 26435, 1506, 26437, 1504, 26439, 1502, 26441, 1500, 26443, 1498, 26445, 1496, 26447, 1494, 26449, 1492, 26451, 1490, 26453, 1488, 26455, 1486, 26457, 1484, 26459, 1482, 26461, 1480, 26463, 1478, 26465, 1476, 26467, 1474, 26469, 1472, 26471, 1470, 26473, 1468, 26475, 1466, 26477, 1464, 26479, 1462, 26481, 1460, 26483, 1458, 26485, 1456, 26487, 1454, 26489, 1452, 26491, 1450, 26493, 1448, 26495, 1446, 26497, 1444, 26499, 1442, 26501, 1440, 26503, 1438, 26505, 1436, 26507, 1434, 26509, 1432, 26511, 1430, 26513, 1428, 26515, 1426, 26517, 1424, 26519, 1422, 26521, 1420, 26523, 1418, 26525, 1416, 26527, 1414, 26529, 1412, 26531, 1410, 26533, 1408, 26535, 1406, 26537, 1404, 26539, 1402, 26541, 1400, 26543, 1398, 26545, 1396, 26547, 1394, 26549, 1392, 26551, 1390, 26553, 1388, 26555, 1386, 26557, 1384, 26559, 1382, 26561, 1380, 26563, 1378, 26565, 1376, 26567, 1374, 26569, 1372, 26571, 1370, 26573, 1368, 26575, 1366, 26577, 1364, 26579, 1362, 26581, 1360, 26583, 1358, 26585, 1356, 26587, 1354, 26589, 1352, 26591, 1350, 26593, 1348, 26595, 1346, 26597, 1344, 26599, 1342, 26601, 1340, 26603, 1338, 26605, 1336, 26607, 1334, 26609, 1332, 26611, 1330, 26613, 1328, 26615, 1326, 26617, 1324, 26619, 1322, 26621, 1320, 26623, 1318, 26625, 1316, 26627, 1314, 26629, 1312, 26631, 1310, 26633, 1308, 26635, 1306, 26637, 1304, 26639, 1302, 26641, 1300, 26643, 1298, 26645, 1296, 26647, 1294, 26649, 1292, 26651, 1290, 26653, 1288, 26655, 1286, 26657, 1284, 26659, 1282, 26661, 1280, 26663, 1278, 26665, 1276, 26667, 1274, 26669, 1272, 26671, 1270, 26673, 1268, 26675, 1266, 26677, 1264, 26679, 1262, 26681, 1260, 26683, 1258, 26685, 1256, 26687, 1254, 26689, 1252, 26691, 1250, 26693, 1248, 26695, 1246, 26697, 1244, 26699, 1242, 26701, 1240, 26703, 1238, 26705, 1236, 26707, 1234, 26709, 1232, 26711, 1230, 26713, 1228, 26715, 1226, 26717, 1224, 26719, 1222, 26721, 1220, 26723, 1218, 26725, 1216, 26727, 1214, 26729, 1212, 26731, 1210, 26733, 1208, 26735, 1206, 26737, 1204, 26739, 1202, 26741, 1200, 26743, 1198, 26745, 1196, 26747, 1194, 26749, 1192, 26751, 1190, 26753, 1188, 26755, 1186, 26757, 1184, 26759, 1182, 26761, 1180, 26763, 1178, 26765, 1176, 26767, 1174, 26769, 1172, 26771, 1170, 26773, 1168, 26775, 1166, 26777, 1164, 26779, 1162, 26781, 1160, 26783, 1158, 26785, 1156, 26787, 1154, 26789, 1152, 26791, 1150, 26793, 1148, 26795, 1146, 26797, 1144, 26799, 1142, 26801, 1140, 26803, 1138, 26805, 1136, 26807, 1134, 26809, 1132, 26811, 1130, 26813, 1128, 26815, 1126, 26817, 1124, 26819, 1122, 26821, 1120, 26823, 1118, 26825, 1116, 26827, 1114, 26829, 1112, 26831, 1110, 26833, 1108, 26835, 1106, 26837, 1104, 26839, 1102, 26841, 1100, 26843, 1098, 26845, 1096, 26847, 1094, 26849, 1092, 26851, 1090, 26853, 1088, 26855, 1086, 26857, 1084, 26859, 1082, 26861, 1080, 26863, 1078, 26865, 1076, 26867, 1074, 26869, 1072, 26871, 1070, 26873, 1068, 26875, 1066, 26877, 1064, 26879, 1062, 26881, 1060, 26883, 1058, 26885, 1056, 26887, 1054, 26889, 1052, 26891, 1050, 26893, 1048, 26895, 1046, 26897, 1044, 26899, 1042, 26901, 1040, 26903, 1038, 26905, 1036, 26907, 1034, 26909, 1032, 26911, 1030, 26913, 1028, 26915, 1026, 26917, 1024, 26919, 1022, 26921, 1020, 26923, 1018, 26925, 1016, 26927, 1014, 26929, 1012, 26931, 1010, 26933, 1008, 26935, 1006, 26937, 1004, 26939, 1002, 26941, 1000, 26943, 998, 26945, 996, 26947, 994, 26949, 992, 26951, 990, 26953, 988, 26955, 986, 26957, 984, 26959, 982, 26961, 980, 26963, 978, 26965, 976, 26967, 974, 26969, 972, 26971, 970, 26973, 968, 26975, 966, 26977, 964, 26979, 962, 26981, 960, 26983, 958, 26985, 956, 26987, 954, 26989, 952, 26991, 950, 26993, 948, 26995, 946, 26997, 944, 26999, 942, 27001, 940, 27003, 938, 27005, 936, 27007, 934, 27009, 932, 27011, 930, 27013, 928, 27015, 926, 27017, 924, 27019, 922, 27021, 920, 27023, 918, 27025, 916, 27027, 914, 27029, 912, 27031, 910, 27033, 908, 27035, 906, 27037, 904, 27039, 902, 27041, 900, 27043, 898, 27045, 896, 27047, 894, 27049, 892, 27051, 890, 27053, 888, 27055, 886, 27057, 884, 27059, 882, 27061, 880, 27063, 878, 27065, 876, 27067, 874, 27069, 872, 27071, 870, 27073, 868, 27075, 866, 27077, 864, 27079, 862, 27081, 860, 27083, 858, 27085, 856, 27087, 854, 27089, 852, 27091, 850, 27093, 848, 27095, 846, 27097, 844, 27099, 842, 27101, 840, 27103, 838, 27105, 836, 27107, 834, 27109, 832, 27111, 830, 27113, 828, 27115, 826, 27117, 824, 27119, 822, 27121, 820, 27123, 818, 27125, 816, 27127, 814, 27129, 812, 27131, 810, 27133, 808, 27135, 806, 27137, 804, 27139, 802, 27141, 800, 27143, 798, 27145, 796, 27147, 794, 27149, 792, 27151, 790, 27153, 788, 27155, 786, 27157, 784, 27159, 782, 27161, 780, 27163, 778, 27165, 776, 27167, 774, 27169, 772, 27171, 770, 27173, 768, 27175, 766, 27177, 764, 27179, 762, 27181, 760, 27183, 758, 27185, 756, 27187, 754, 27189, 752, 27191, 750, 27193, 748, 27195, 746, 27197, 744, 27199, 742, 27201, 740, 27203, 738, 27205, 736, 27207, 734, 27209, 732, 27211, 730, 27213, 728, 27215, 726, 27217, 724, 27219, 722, 27221, 720, 27223, 718, 27225, 716, 27227, 714, 27229, 712, 27231, 710, 27233, 708, 27235, 706, 27237, 704, 27239, 702, 27241, 700, 27243, 698, 27245, 696, 27247, 694, 27249, 692, 27251, 690, 27253, 688, 27255, 686, 27257, 684, 27259, 682, 27261, 680, 27263, 678, 27265, 676, 27267, 674, 27269, 672, 27271, 670, 27273, 668, 27275, 666, 27277, 664, 27279, 662, 27281, 660, 27283, 658, 27285, 656, 27287, 654, 27289, 652, 27291, 650, 27293, 648, 27295, 646, 27297, 644, 27299, 642, 27301, 640, 27303, 638, 27305, 636, 27307, 634, 27309, 632, 27311, 630, 27313, 628, 27315, 626, 27317, 624, 27319, 622, 27321, 620, 27323, 618, 27325, 616, 27327, 614, 27329, 612, 27331, 610, 27333, 608, 27335, 606, 27337, 604, 27339, 602, 27341, 600, 27343, 598, 27345, 596, 27347, 594, 27349, 592, 27351, 590, 27353, 588, 27355, 586, 27357, 584, 27359, 582, 27361, 580, 27363, 578, 27365, 576, 27367, 574, 27369, 572, 27371, 570, 27373, 568, 27375, 566, 27377, 564, 27379, 562, 27381, 560, 27383, 558, 27385, 556, 27387, 554, 27389, 552, 27391, 550, 27393, 548, 27395, 546, 27397, 544, 27399, 542, 27401, 540, 27403, 538, 27405, 536, 27407, 534, 27409, 532, 27411, 530, 27413, 528, 27415, 526, 27417, 524, 27419, 522, 27421, 520, 27423, 518, 27425, 516, 27427, 514, 27429, 512, 27431, 510, 27433, 508, 27435, 506, 27437, 504, 27439, 502, 27441, 500, 27443, 498, 27445, 496, 27447, 494, 27449, 492, 27451, 490, 27453, 488, 27455, 486, 27457, 484, 27459, 482, 27461, 480, 27463, 478, 27465, 476, 27467, 474, 27469, 472, 27471, 470, 27473, 468, 27475, 466, 27477, 464, 27479, 462, 27481, 460, 27483, 458, 27485, 456, 27487, 454, 27489, 452, 27491, 450, 27493, 448, 27495, 446, 27497, 444, 27499, 442, 27501, 440, 27503, 438, 27505, 436, 27507, 434, 27509, 432, 27511, 430, 27513, 428, 27515, 426, 27517, 424, 27519, 422, 27521, 420, 27523, 418, 27525, 416, 27527, 414, 27529, 412, 27531, 410, 27533, 408, 27535, 406, 27537, 404, 27539, 402, 27541, 400, 27543, 398, 27545, 396, 27547, 394, 27549, 392, 27551, 390, 27553, 388, 27555, 386, 27557, 384, 27559, 382, 27561, 380, 27563, 378, 27565, 376, 27567, 374, 27569, 372, 27571, 370, 27573, 368, 27575, 366, 27577, 364, 27579, 362, 27581, 360, 27583, 358, 27585, 356, 27587, 354, 27589, 352, 27591, 350, 27593, 348, 27595, 346, 27597, 344, 27599, 342, 27601, 340, 27603, 338, 27605, 336, 27607, 334, 27609, 332, 27611, 330, 27613, 328, 27615, 326, 27617, 324, 27619, 322, 27621, 320, 27623, 318, 27625, 316, 27627, 314, 27629, 312, 27631, 310, 27633, 308, 27635, 306, 27637, 304, 27639, 302, 27641, 300, 27643, 298, 27645, 296, 27647, 294, 27649, 292, 27651, 290, 27653, 288, 27655, 286, 27657, 284, 27659, 282, 27661, 280, 27663, 278, 27665, 276, 27667, 274, 27669, 272, 27671, 270, 27673, 268, 27675, 266, 27677, 264, 27679, 262, 27681, 260, 27683, 258, 27685, 256, 27687, 254, 27689, 252, 27691, 250, 27693, 248, 27695, 246, 27697, 244, 27699, 242, 27701, 240, 27703, 238, 27705, 236, 27707, 234, 27709, 232, 27711, 230, 27713, 228, 27715, 226, 27717, 224, 27719, 222, 27721, 220, 27723, 218, 27725, 216, 27727, 214, 27729, 212, 27731, 210, 27733, 208, 27735, 206, 27737, 204, 27739, 202, 27741, 200, 27743, 198, 27745, 196, 27747, 194, 27749, 192, 27751, 190, 27753, 188, 27755, 186, 27757, 184, 27759, 182, 27761, 180, 27763, 178, 27765, 176, 27767, 174, 27769, 172, 27771, 170, 27773, 168, 27775, 166, 27777, 164, 27779, 162, 27781, 160, 27783, 158, 27785, 156, 27787, 154, 27789, 152, 27791, 150, 27793, 148, 27795, 146, 27797, 144, 27799, 142, 27801, 140, 27803, 138, 27805, 136, 27807, 134, 27809, 132, 27811, 130, 27813, 128, 27815, 126, 27817, 124, 27819, 122, 27821, 120, 27823, 118, 27825, 116, 27827, 114, 27829, 112, 27831, 110, 27833, 108, 27835, 106, 27837, 104, 27839, 102, 27841, 100, 27843, 98, 27845, 96, 27847, 94, 27849, 92, 27851, 90, 27853, 88, 27855, 86, 27857, 84, 27859, 82, 27861, 80, 27863, 78, 27865, 76, 27867, 74, 27869, 72, 27871, 70, 27873, 68, 27875, 66, 27877, 64, 27879, 62, 27881, 60, 27883, 58, 27885, 56, 27887, 54, 27889, 52, 27891, 50, 27893, 48, 27895, 46, 27897, 44, 27899, 42, 27901, 40, 27903, 38, 27905, 36, 27907, 34, 27909, 32, 27911, 30, 27913, 28, 27915, 26, 27917, 24, 27919, 22, 27921, 20, 27923, 18, 27925, 16, 27927, 14, 27929, 12, 27931, 10, 27933, 8, 27935, 6, 27937, 4, 27939, 2, 27941]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("perm"), n, 1, n, "perm")
+    if len(set(p)) != n:
+        raise Invalid("not a permutation")
+    seen, acc = set(), 0
+    for v in p:
+        acc = (acc + v) % n
+        if acc in seen:
+            raise Invalid(f"prefix sum residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a31e29541b92f116d4dc85878e0e38bc96eb83c
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 27942, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s2/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l3-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s2/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c8a826dbf179d27708cce8d8ab04bf09340e3a24
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 82, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s2/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0157b32ae81e8eb1cc5b8d9d70a928cad30fa55d
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    sieve = [True] * (n + 1)
+    sieve[0] = False
+    if n >= 1:
+        sieve[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if sieve[i]:
+            for j in range(i * i, n + 1, i):
+                sieve[j] = False
+    for p in range(2, n):
+        if sieve[p]:
+            for u in range(n - p):
+                if c[u] == c[u + p]:
+                    raise Invalid(f"vertices {u + 1} and {u + p + 1} (difference {p}) share a colour")
+    return None, {}
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c8a826dbf179d27708cce8d8ab04bf09340e3a24
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 82, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s5/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l3-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s5/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7f093a3dd84237cf2f5e064320747248f3f7ad77
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 46, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s5/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ff474dd218e8857a984c0d41dde3dd12f4a24e71
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    sieve = [True] * (n + 1)
+    sieve[0] = False
+    if n >= 1:
+        sieve[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if sieve[i]:
+            for j in range(i * i, n + 1, i):
+                sieve[j] = False
+    for p in range(2, n):
+        if sieve[p]:
+            for u in range(n - p):
+                if c[u] == c[u + p]:
+                    raise Invalid(f"vertices {u + 1} and {u + p + 1} (difference {p}) share a colour")
+    return None, {}
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7f093a3dd84237cf2f5e064320747248f3f7ad77
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 46, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l1-s6/environment/Dockerfile b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l1-s6/environment/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a38f13a03ecffbe9a2117f71505879b5ac12dab9
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/environment/instance.json
@@ -0,0 +1 @@
+{"F0": 122, "A": 12, "B": 13480, "S": 30474520, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l1-s6/solution/solve.sh b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d442d77cdb9612131b01acbcbc1413e038c3b798
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"indices": [1, 2, 3, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/check.py b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..feda076c3f95e5e12198151dee30e1b8223924bc
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/check.py
@@ -0,0 +1,29 @@
+from run import Invalid, int_list
+
+
+def F(inst, n):
+    F0, A, B = inst["F0"], inst["A"], inst["B"]
+    if A == 1:
+        return F0 + n * B
+    An = A ** n
+    return An * F0 + B * (An - 1) // (A - 1)
+
+
+def check(inst, ans):
+    S = inst["S"]
+    idx = int_list(ans.get("indices"), None, 1, None, "indices")
+    if not idx:
+        raise Invalid("need at least one index")
+    if len(set(idx)) != len(idx):
+        raise Invalid("indices must be distinct")
+    total = 0
+    for n in idx:
+        # F is strictly increasing with F(n) >= n and, when A >= 2, F(n) >= 2^(n-1); bail out before big powers
+        if n > S or (inst["A"] >= 2 and n - 1 > S.bit_length()):
+            raise Invalid(f"F({n}) exceeds S")
+        total += F(inst, n)
+        if total > S:
+            raise Invalid("sum exceeds S")
+    if total != S:
+        raise Invalid(f"sum is {total}, need {S}")
+    return None, {}
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a38f13a03ecffbe9a2117f71505879b5ac12dab9
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/instance.json
@@ -0,0 +1 @@
+{"F0": 122, "A": 12, "B": 13480, "S": 30474520, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/run.py b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/test.sh b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l1-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l5-s9/environment/Dockerfile b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l5-s9/environment/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9230950985dcd15a82e45cfdb316394a473aa3f2
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/environment/instance.json
@@ -0,0 +1 @@
+{"F0": 70, "A": 5, "B": 2648, "S": 681728124730224609373676, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l5-s9/solution/solve.sh b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..32b14fc5f38a7e0bc94f33d8570275ac9a0db9e9
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"indices": [16, 30]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/check.py b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..feda076c3f95e5e12198151dee30e1b8223924bc
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/check.py
@@ -0,0 +1,29 @@
+from run import Invalid, int_list
+
+
+def F(inst, n):
+    F0, A, B = inst["F0"], inst["A"], inst["B"]
+    if A == 1:
+        return F0 + n * B
+    An = A ** n
+    return An * F0 + B * (An - 1) // (A - 1)
+
+
+def check(inst, ans):
+    S = inst["S"]
+    idx = int_list(ans.get("indices"), None, 1, None, "indices")
+    if not idx:
+        raise Invalid("need at least one index")
+    if len(set(idx)) != len(idx):
+        raise Invalid("indices must be distinct")
+    total = 0
+    for n in idx:
+        # F is strictly increasing with F(n) >= n and, when A >= 2, F(n) >= 2^(n-1); bail out before big powers
+        if n > S or (inst["A"] >= 2 and n - 1 > S.bit_length()):
+            raise Invalid(f"F({n}) exceeds S")
+        total += F(inst, n)
+        if total > S:
+            raise Invalid("sum exceeds S")
+    if total != S:
+        raise Invalid(f"sum is {total}, need {S}")
+    return None, {}
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9230950985dcd15a82e45cfdb316394a473aa3f2
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/instance.json
@@ -0,0 +1 @@
+{"F0": 70, "A": 5, "B": 2648, "S": 681728124730224609373676, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/run.py b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/test.sh b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l5-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s2/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s2/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..788deff7e716f86c05b6cb80aa46eb524b37e8b6
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"W": [3, 5, 2, 3], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s2/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c5693b3bc4df7aad12a6c95756cf1240fb4c4b47
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["0111", "1021", "1001", "1110"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s2/tests/check.py b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s2/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..788deff7e716f86c05b6cb80aa46eb524b37e8b6
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"W": [3, 5, 2, 3], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s2/tests/run.py b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s2/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s5/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l1-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s5/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..92db1927145d23e72e22d8de8ebbf057c1c21698
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s5/environment/instance.json
@@ -0,0 +1 @@
+{"W": [4, 4, 4, 4], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s5/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l1-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8a0ff404629e9b44f0f9f362c3a6e71e286341a5
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["0012", "2001", "1200", "0120"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s5/tests/check.py b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s5/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..92db1927145d23e72e22d8de8ebbf057c1c21698
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/instance.json
@@ -0,0 +1 @@
+{"W": [4, 4, 4, 4], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s5/tests/run.py b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s5/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l2-s9/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l2-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l2-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l2-s9/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l2-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..302be5a06969bfbbc8ead3b7d091872dcaeee3c1
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l2-s9/environment/instance.json
@@ -0,0 +1 @@
+{"W": [9, 4, 5, 9, 7, 6], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l2-s9/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l2-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..16bf5699f3037f6ae240548ad3636992cce985be
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l2-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["021211", "002001", "100201", "020022", "122000", "111020"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l2-s9/tests/check.py b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l2-s9/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..302be5a06969bfbbc8ead3b7d091872dcaeee3c1
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/instance.json
@@ -0,0 +1 @@
+{"W": [9, 4, 5, 9, 7, 6], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l2-s9/tests/run.py b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l2-s9/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l2-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s3/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s3/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f4e9986a81cfe9ccba1120db5b556c4362492949
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"W": [16, 21, 20, 19, 17, 19, 18, 23, 17, 15, 20, 16, 18, 19, 24, 15, 15, 18], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s3/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..cfdff4045e0c3ff15107ec3129c4da18d8d5d4a6
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["001111111111111111", "201111111111111211", "110011111121111121", "112011111201110111", "111101111101110121", "111110101111120211", "111111011211110111", "111112101112121111", "111111110111111111", "111011011011111111", "110221111101002111", "111111101110111111", "111111111121011110", "111110101121101112", "111222211101110111", "101110111111111011", "110101111111111101", "111111111111201110"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s3/tests/check.py b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s3/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f4e9986a81cfe9ccba1120db5b556c4362492949
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"W": [16, 21, 20, 19, 17, 19, 18, 23, 17, 15, 20, 16, 18, 19, 24, 15, 15, 18], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s3/tests/run.py b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s3/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s4/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l5-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s4/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9bcba83425fa4252f89b6b7e037f71f3a938d53e
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s4/environment/instance.json
@@ -0,0 +1 @@
+{"W": [28, 18, 17, 30, 20, 20, 19, 21, 24, 24, 21, 20, 22, 24, 22, 14, 33, 16], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s4/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l5-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9effb37b7344f3af34f681b30711c0eb3ca08682
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["021121121001222201", "000020101211201120", "120111011120001111", "121011111212122202", "001101110201120221", "121110110002120102", "112111001211110002", "021111201112201001", "111122110011122200", "201002012022111102", "210122111000001220", "112010101020102211", "002111101121021211", "022000120122002201", "011022210110100122", "011001220100001002", "201202222201120202", "121010012021110000"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s4/tests/check.py b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s4/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9bcba83425fa4252f89b6b7e037f71f3a938d53e
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/instance.json
@@ -0,0 +1 @@
+{"W": [28, 18, 17, 30, 20, 20, 19, 21, 24, 24, 21, 20, 22, 24, 22, 14, 33, 16], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s4/tests/run.py b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s4/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l6-s1/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l6-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l6-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l6-s1/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l6-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e85bdcd9d07b23e7f4b59425bc79abd387ac207
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l6-s1/environment/instance.json
@@ -0,0 +1 @@
+{"W": [14, 41, 29, 33, 44, 36, 32, 38, 41, 45, 44, 27, 41, 33, 30, 24, 36, 28, 44, 36, 36, 35, 40, 29, 37], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l6-s1/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l6-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..19b07bd30e0ae301c94895057e8ae7354eed4715
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l6-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["0000000002002010022000001", "2010020202102220222220200", "2100200200222201002020000", "2220200110200022020010022", "2200012220020222022002212", "2022100002000022212202120", "2222020000000102021022200", "2001022002222222000002210", "2221022200022002220202010", "0022202020022022220222020", "2100222022022102020220022", "2202022000000200200020002", "0002222000020221222202021", "2002021022100022100220020", "1020002020220001020002212", "2210000000021010020202020", "2022202200200122000200211", "0020010200020200200020222", "0002001222220222220210022", "2022202200020020020020220", "2001220220002022201001220", "2222000000220200222210001", "2022010022222202002002002", "2220102110020010100002202", "1220022222001202100221000"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l6-s1/tests/check.py b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l6-s1/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e85bdcd9d07b23e7f4b59425bc79abd387ac207
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/instance.json
@@ -0,0 +1 @@
+{"W": [14, 41, 29, 33, 44, 36, 32, 38, 41, 45, 44, 27, 41, 33, 30, 24, 36, 28, 44, 36, 36, 35, 40, 29, 37], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l6-s1/tests/run.py b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l6-s1/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l6-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-shortest-path-count-l1-s3/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l1-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l1-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-shortest-path-count-l1-s3/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l1-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..47cccfee18ceae9d52ccb0bfbf0d7e62a48d410e
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l1-s3/environment/instance.json
@@ -0,0 +1 @@
+{"K": 35, "n_max": 36, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l1-s3/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l1-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4506b75a5107c2964b70a31be2725e2c2ce29413
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l1-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"n": 18, "adj": ["NNYYNNNNNNNNYNNNNN", "NNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNYNNNN", "YNNNYYNNNNNNNYNNNN", "NNYYNNYYNNNNNNNNNN", "NNYYNNYYNNNNNNNNNN", "NNNNYYNNYYNNNNNNNN", "NNNNYYNNYYNNNNNNNN", "NNNNNNYYNNYYNNNNNN", "NNNNNNYYNNYYNNNNNN", "NNNNNNNNYYNNNNNNNY", "NNNNNNNNYYNNNNNNNY", "YNNNNNNNNNNNNYNNNN", "NNYYNNNNNNNNYNYNNN", "NNNNNNNNNNNNNYNYNN", "NNNNNNNNNNNNNNYNYN", "NNNNNNNNNNNNNNNYNY", "NYNNNNNNNNYYNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l1-s3/tests/check.py b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/check.py
@@ -0,0 +1,34 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    n = as_int(ans.get("n"), "n", lo=2, hi=inst["n_max"])
+    adj = ans.get("adj")
+    if not isinstance(adj, list) or len(adj) != n:
+        raise Invalid(f"adj must be a list of {n} strings")
+    for r in adj:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"Y", "N"}:
+            raise Invalid("each row must be a string of length n over {'Y','N'}")
+    for i in range(n):
+        if adj[i][i] != "N":
+            raise Invalid("self-loop")
+        for j in range(i + 1, n):
+            if adj[i][j] != adj[j][i]:
+                raise Invalid("matrix not symmetric")
+    nb = [[j for j in range(n) if adj[i][j] == "Y"] for i in range(n)]
+    dist = [-1] * n
+    cnt = [0] * n
+    dist[0], cnt[0] = 0, 1
+    q = [0]
+    for u in q:  # BFS with exact (Python int) path counts
+        for v in nb[u]:
+            if dist[v] < 0:
+                dist[v] = dist[u] + 1
+                q.append(v)
+            if dist[v] == dist[u] + 1:
+                cnt[v] += cnt[u]
+    if dist[1] < 0:
+        raise Invalid("vertex 2 is unreachable from vertex 1")
+    if cnt[1] != inst["K"]:
+        raise Invalid(f"{cnt[1]} shortest paths, need {inst['K']}")
+    return None, {}
diff --git a/tasks/construct-rlve-shortest-path-count-l1-s3/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..47cccfee18ceae9d52ccb0bfbf0d7e62a48d410e
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/instance.json
@@ -0,0 +1 @@
+{"K": 35, "n_max": 36, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l1-s3/tests/run.py b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-shortest-path-count-l1-s3/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l1-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s1/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s1/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0ad4f92978c7ac7d75b336d999731dbed7171d20
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"K": 236, "n_max": 51, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s1/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1a43af4c1a245c131f96c7fa0f8d75bad915c95c
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"n": 24, "adj": ["NNYYNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNNNNNNNNNNNN", "YNNNYYNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNYNNNNN", "NNYYNNYYNNNNNNNNNNYNNNNN", "NNNNYYNNYYNNNNNNNNNYNNNN", "NNNNYYNNYYNNNNNNNNNYNNNN", "NNNNNNYYNNYYNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNYNN", "NNNNNNNNYYNNYYNNNNNNNYNN", "NNNNNNNNNNYYNNYYNNNNNNYN", "NNNNNNNNNNYYNNYYNNNNNNYN", "NNNNNNNNNNNNYYNNNNNNNNNY", "NNNNNNNNNNNNYYNNNNNNNNNY", "NNNNNNNNNNNNNNNNNYNNNNNN", "NNNNNNNNNNNNNNNNYNYNNNNN", "NNNNYYNNNNNNNNNNNYNYNNNN", "NNNNNNYYNNNNNNNNNNYNYNNN", "NNNNNNNNNNNNNNNNNNNYNYNN", "NNNNNNNNNNYYNNNNNNNNYNYN", "NNNNNNNNNNNNYYNNNNNNNYNY", "NYNNNNNNNNNNNNYYNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s1/tests/check.py b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/check.py
@@ -0,0 +1,34 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    n = as_int(ans.get("n"), "n", lo=2, hi=inst["n_max"])
+    adj = ans.get("adj")
+    if not isinstance(adj, list) or len(adj) != n:
+        raise Invalid(f"adj must be a list of {n} strings")
+    for r in adj:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"Y", "N"}:
+            raise Invalid("each row must be a string of length n over {'Y','N'}")
+    for i in range(n):
+        if adj[i][i] != "N":
+            raise Invalid("self-loop")
+        for j in range(i + 1, n):
+            if adj[i][j] != adj[j][i]:
+                raise Invalid("matrix not symmetric")
+    nb = [[j for j in range(n) if adj[i][j] == "Y"] for i in range(n)]
+    dist = [-1] * n
+    cnt = [0] * n
+    dist[0], cnt[0] = 0, 1
+    q = [0]
+    for u in q:  # BFS with exact (Python int) path counts
+        for v in nb[u]:
+            if dist[v] < 0:
+                dist[v] = dist[u] + 1
+                q.append(v)
+            if dist[v] == dist[u] + 1:
+                cnt[v] += cnt[u]
+    if dist[1] < 0:
+        raise Invalid("vertex 2 is unreachable from vertex 1")
+    if cnt[1] != inst["K"]:
+        raise Invalid(f"{cnt[1]} shortest paths, need {inst['K']}")
+    return None, {}
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s1/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0ad4f92978c7ac7d75b336d999731dbed7171d20
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"K": 236, "n_max": 51, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s1/tests/run.py b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s1/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s8/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s8/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..786de8d1b21fcd72b061c598cd35cd3d502b0bad
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"K": 240, "n_max": 51, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s8/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..411180b70e699a48bbbf4c67ea1a4952fc4a9012
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"n": 24, "adj": ["NNYYNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNNNNNNNNNNNN", "YNNNYYNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNYNNN", "NNNNNNYYNNYYNNNNNNNNYNNN", "NNNNNNNNYYNNYYNNNNNNNYNN", "NNNNNNNNYYNNYYNNNNNNNYNN", "NNNNNNNNNNYYNNYYNNNNNNYN", "NNNNNNNNNNYYNNYYNNNNNNYN", "NNNNNNNNNNNNYYNNNNNNNNNY", "NNNNNNNNNNNNYYNNNNNNNNNY", "NNNNNNNNNNNNNNNNNYNNNNNN", "NNNNNNNNNNNNNNNNYNYNNNNN", "NNNNNNNNNNNNNNNNNYNYNNNN", "NNNNNNNNNNNNNNNNNNYNYNNN", "NNNNNNNNYYNNNNNNNNNYNYNN", "NNNNNNNNNNYYNNNNNNNNYNYN", "NNNNNNNNNNNNYYNNNNNNNYNY", "NYNNNNNNNNNNNNYYNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s8/tests/check.py b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/check.py
@@ -0,0 +1,34 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    n = as_int(ans.get("n"), "n", lo=2, hi=inst["n_max"])
+    adj = ans.get("adj")
+    if not isinstance(adj, list) or len(adj) != n:
+        raise Invalid(f"adj must be a list of {n} strings")
+    for r in adj:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"Y", "N"}:
+            raise Invalid("each row must be a string of length n over {'Y','N'}")
+    for i in range(n):
+        if adj[i][i] != "N":
+            raise Invalid("self-loop")
+        for j in range(i + 1, n):
+            if adj[i][j] != adj[j][i]:
+                raise Invalid("matrix not symmetric")
+    nb = [[j for j in range(n) if adj[i][j] == "Y"] for i in range(n)]
+    dist = [-1] * n
+    cnt = [0] * n
+    dist[0], cnt[0] = 0, 1
+    q = [0]
+    for u in q:  # BFS with exact (Python int) path counts
+        for v in nb[u]:
+            if dist[v] < 0:
+                dist[v] = dist[u] + 1
+                q.append(v)
+            if dist[v] == dist[u] + 1:
+                cnt[v] += cnt[u]
+    if dist[1] < 0:
+        raise Invalid("vertex 2 is unreachable from vertex 1")
+    if cnt[1] != inst["K"]:
+        raise Invalid(f"{cnt[1]} shortest paths, need {inst['K']}")
+    return None, {}
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s8/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..786de8d1b21fcd72b061c598cd35cd3d502b0bad
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"K": 240, "n_max": 51, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s8/tests/run.py b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s8/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s0/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s0/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6f16cb64d47ca78c95a59e33411f90f5d969de91
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"K": 681091269143539577, "n_max": 363, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s0/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..578934fe24f8be6c0501e92dfdf01d99003979c4
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"n": 180, "adj": ["NNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "YNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", 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"NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNY", "NYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s0/tests/check.py b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/check.py
@@ -0,0 +1,34 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    n = as_int(ans.get("n"), "n", lo=2, hi=inst["n_max"])
+    adj = ans.get("adj")
+    if not isinstance(adj, list) or len(adj) != n:
+        raise Invalid(f"adj must be a list of {n} strings")
+    for r in adj:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"Y", "N"}:
+            raise Invalid("each row must be a string of length n over {'Y','N'}")
+    for i in range(n):
+        if adj[i][i] != "N":
+            raise Invalid("self-loop")
+        for j in range(i + 1, n):
+            if adj[i][j] != adj[j][i]:
+                raise Invalid("matrix not symmetric")
+    nb = [[j for j in range(n) if adj[i][j] == "Y"] for i in range(n)]
+    dist = [-1] * n
+    cnt = [0] * n
+    dist[0], cnt[0] = 0, 1
+    q = [0]
+    for u in q:  # BFS with exact (Python int) path counts
+        for v in nb[u]:
+            if dist[v] < 0:
+                dist[v] = dist[u] + 1
+                q.append(v)
+            if dist[v] == dist[u] + 1:
+                cnt[v] += cnt[u]
+    if dist[1] < 0:
+        raise Invalid("vertex 2 is unreachable from vertex 1")
+    if cnt[1] != inst["K"]:
+        raise Invalid(f"{cnt[1]} shortest paths, need {inst['K']}")
+    return None, {}
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s0/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6f16cb64d47ca78c95a59e33411f90f5d969de91
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"K": 681091269143539577, "n_max": 363, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s0/tests/run.py b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s0/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s7/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s7/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2f579ee80912ff0df132d6cd26ccf16883287eb2
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"K": 304361666097914654, "n_max": 357, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s7/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8c6f9f04853ef3e2fa4eaf9948e3e7a10831a165
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
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"NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNY", "NYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s7/tests/check.py b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/check.py
@@ -0,0 +1,34 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    n = as_int(ans.get("n"), "n", lo=2, hi=inst["n_max"])
+    adj = ans.get("adj")
+    if not isinstance(adj, list) or len(adj) != n:
+        raise Invalid(f"adj must be a list of {n} strings")
+    for r in adj:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"Y", "N"}:
+            raise Invalid("each row must be a string of length n over {'Y','N'}")
+    for i in range(n):
+        if adj[i][i] != "N":
+            raise Invalid("self-loop")
+        for j in range(i + 1, n):
+            if adj[i][j] != adj[j][i]:
+                raise Invalid("matrix not symmetric")
+    nb = [[j for j in range(n) if adj[i][j] == "Y"] for i in range(n)]
+    dist = [-1] * n
+    cnt = [0] * n
+    dist[0], cnt[0] = 0, 1
+    q = [0]
+    for u in q:  # BFS with exact (Python int) path counts
+        for v in nb[u]:
+            if dist[v] < 0:
+                dist[v] = dist[u] + 1
+                q.append(v)
+            if dist[v] == dist[u] + 1:
+                cnt[v] += cnt[u]
+    if dist[1] < 0:
+        raise Invalid("vertex 2 is unreachable from vertex 1")
+    if cnt[1] != inst["K"]:
+        raise Invalid(f"{cnt[1]} shortest paths, need {inst['K']}")
+    return None, {}
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s7/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2f579ee80912ff0df132d6cd26ccf16883287eb2
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"K": 304361666097914654, "n_max": 357, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s7/tests/run.py b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s7/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..babf96795459a0c55e482ae702a10d893bc6b58d
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 6], [0, 7], [2, 0], [3, 8]], "r_opt": 4.031128874149275, "r2_num": 65, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..72c06b2c01abb1d375ac738d03a30f8cb01d0991
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 2.5, "y": 4.0, "r": 4.031128875149275}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/check.py
@@ -0,0 +1,17 @@
+import math
+
+from run import Invalid, num
+
+TOL = 1e-6
+
+
+def check(inst, ans):
+    x, y, r = num(ans.get("x"), "x"), num(ans.get("y"), "y"), num(ans.get("r"), "r")
+    if r <= 0:
+        raise Invalid("r must be positive")
+    if r > inst["r_opt"] + TOL:
+        raise Invalid(f"r = {r} exceeds the minimum radius {inst['r_opt']} by more than {TOL}")
+    for px, py in inst["points"]:
+        if math.hypot(px - x, py - y) > r + TOL:
+            raise Invalid(f"point ({px}, {py}) is outside the circle")
+    return None, {"r": r}
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..babf96795459a0c55e482ae702a10d893bc6b58d
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 6], [0, 7], [2, 0], [3, 8]], "r_opt": 4.031128874149275, "r2_num": 65, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b6cfb82240820edf6625d6671ec3ac874ff7fec0
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 1], [2, 5], [3, 4], [4, 2]], "r_opt": 2.1368471406442104, "r2_num": 1105, "r2_den": 242, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3a616759c07f499701da0290a98f210af4221e35
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 2.0454545454545454, "y": 2.8636363636363638, "r": 2.1368471416442105}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/check.py
@@ -0,0 +1,17 @@
+import math
+
+from run import Invalid, num
+
+TOL = 1e-6
+
+
+def check(inst, ans):
+    x, y, r = num(ans.get("x"), "x"), num(ans.get("y"), "y"), num(ans.get("r"), "r")
+    if r <= 0:
+        raise Invalid("r must be positive")
+    if r > inst["r_opt"] + TOL:
+        raise Invalid(f"r = {r} exceeds the minimum radius {inst['r_opt']} by more than {TOL}")
+    for px, py in inst["points"]:
+        if math.hypot(px - x, py - y) > r + TOL:
+            raise Invalid(f"point ({px}, {py}) is outside the circle")
+    return None, {"r": r}
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b6cfb82240820edf6625d6671ec3ac874ff7fec0
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 1], [2, 5], [3, 4], [4, 2]], "r_opt": 2.1368471406442104, "r2_num": 1105, "r2_den": 242, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..20a7536299a41dc261b9785a16218c761de4ecb2
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 13], [3, 9], [5, 14], [6, 12], [10, 5], [11, 8], [15, 0], [15, 9]], "r_opt": 9.5524865872714, "r2_num": 365, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0b3721858c8214fea0b752608af10e71667beceb
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 8.0, "y": 6.5, "r": 9.5524865882714}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/check.py
@@ -0,0 +1,17 @@
+import math
+
+from run import Invalid, num
+
+TOL = 1e-6
+
+
+def check(inst, ans):
+    x, y, r = num(ans.get("x"), "x"), num(ans.get("y"), "y"), num(ans.get("r"), "r")
+    if r <= 0:
+        raise Invalid("r must be positive")
+    if r > inst["r_opt"] + TOL:
+        raise Invalid(f"r = {r} exceeds the minimum radius {inst['r_opt']} by more than {TOL}")
+    for px, py in inst["points"]:
+        if math.hypot(px - x, py - y) > r + TOL:
+            raise Invalid(f"point ({px}, {py}) is outside the circle")
+    return None, {"r": r}
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..20a7536299a41dc261b9785a16218c761de4ecb2
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 13], [3, 9], [5, 14], [6, 12], [10, 5], [11, 8], [15, 0], [15, 9]], "r_opt": 9.5524865872714, "r2_num": 365, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l2-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a21ae2d2d834619a031ae2295644f5d2b8c6f16
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 14], [1, 48], [2, 11], [2, 22], [4, 94], [5, 8], [6, 118], [13, 88], [14, 119], [16, 67], [17, 84], [17, 103], [21, 97], [23, 106], [27, 62], [28, 47], [31, 94], [36, 6], [36, 72], [37, 30], [37, 109], [39, 90], [40, 14], [48, 97], [49, 56], [51, 95], [54, 38], [54, 84], [57, 57], [60, 25], [62, 19], [62, 25], [65, 11], [65, 96], [71, 48], [73, 22], [73, 37], [75, 47], [77, 80], [78, 110], [87, 114], [89, 39], [92, 58], [93, 114], [95, 20], [95, 78], [96, 41], [96, 45], [97, 39], [98, 44], [98, 73], [104, 2], [104, 37], [106, 2], [111, 67], [114, 58], [114, 86], [115, 17], [115, 88], [116, 61]], "r_opt": 76.57675887630658, "r2_num": 5864, "r2_den": 1, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..77cd9f4c0604f6396fe65c9a9241ab301ea3b83b
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 56.0, "y": 60.0, "r": 76.57675887730659}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/check.py
@@ -0,0 +1,17 @@
+import math
+
+from run import Invalid, num
+
+TOL = 1e-6
+
+
+def check(inst, ans):
+    x, y, r = num(ans.get("x"), "x"), num(ans.get("y"), "y"), num(ans.get("r"), "r")
+    if r <= 0:
+        raise Invalid("r must be positive")
+    if r > inst["r_opt"] + TOL:
+        raise Invalid(f"r = {r} exceeds the minimum radius {inst['r_opt']} by more than {TOL}")
+    for px, py in inst["points"]:
+        if math.hypot(px - x, py - y) > r + TOL:
+            raise Invalid(f"point ({px}, {py}) is outside the circle")
+    return None, {"r": r}
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a21ae2d2d834619a031ae2295644f5d2b8c6f16
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 14], [1, 48], [2, 11], [2, 22], [4, 94], [5, 8], [6, 118], [13, 88], [14, 119], [16, 67], [17, 84], [17, 103], [21, 97], [23, 106], [27, 62], [28, 47], [31, 94], [36, 6], [36, 72], [37, 30], [37, 109], [39, 90], [40, 14], [48, 97], [49, 56], [51, 95], [54, 38], [54, 84], [57, 57], [60, 25], [62, 19], [62, 25], [65, 11], [65, 96], [71, 48], [73, 22], [73, 37], [75, 47], [77, 80], [78, 110], [87, 114], [89, 39], [92, 58], [93, 114], [95, 20], [95, 78], [96, 41], [96, 45], [97, 39], [98, 44], [98, 73], [104, 2], [104, 37], [106, 2], [111, 67], [114, 58], [114, 86], [115, 17], [115, 88], [116, 61]], "r_opt": 76.57675887630658, "r2_num": 5864, "r2_den": 1, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9892643ac2adb79395d7904d7a41a58f97b3c5b6
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[3, 114], [3, 195], [6, 22], [10, 56], [10, 175], [13, 55], [13, 116], [15, 82], [16, 231], [19, 196], [22, 115], [23, 104], [24, 119], [27, 76], [30, 46], [31, 37], [33, 14], [35, 97], [41, 44], [44, 124], [45, 125], [46, 224], [50, 101], [50, 159], [52, 87], [52, 181], [64, 56], [67, 198], [67, 240], [78, 71], [79, 196], [80, 206], [80, 216], [84, 13], [84, 108], [86, 217], [87, 23], [88, 76], [91, 165], [92, 55], [94, 147], [95, 66], [96, 17], [98, 18], [98, 134], [99, 4], [100, 164], [101, 28], [105, 116], [108, 136], [108, 215], [111, 33], [113, 210], [116, 185], [117, 222], [118, 233], [120, 239], [123, 130], [124, 195], [126, 40], [128, 9], [137, 185], [138, 95], [139, 29], [139, 157], [142, 124], [149, 65], [149, 117], [150, 12], [154, 200], [155, 28], [157, 90], [157, 213], [159, 122], [160, 65], [160, 132], [163, 171], [163, 173], [167, 119], [168, 38], [169, 24], [169, 223], [170, 6], [170, 7], [175, 128], [178, 53], [179, 60], [180, 83], [183, 228], [185, 8], [186, 209], [187, 104], [189, 215], [192, 125], [192, 169], [194, 13], [195, 93], [196, 10], [200, 44], [203, 35], [204, 162], [205, 6], [205, 153], [206, 36], [207, 240], [208, 29], [210, 132], [211, 113], [216, 16], [216, 206], [218, 135], [222, 47], [227, 80], [228, 130], [231, 217], [234, 25], [234, 221], [236, 27], [238, 37], [238, 94]], "r_opt": 151.31506864816868, "r2_num": 91585, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..03a1b4768c6e20bc517da7fbc0f6e4444ffd42b0
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 120.0, "y": 121.5, "r": 151.31506864916867}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/check.py
@@ -0,0 +1,17 @@
+import math
+
+from run import Invalid, num
+
+TOL = 1e-6
+
+
+def check(inst, ans):
+    x, y, r = num(ans.get("x"), "x"), num(ans.get("y"), "y"), num(ans.get("r"), "r")
+    if r <= 0:
+        raise Invalid("r must be positive")
+    if r > inst["r_opt"] + TOL:
+        raise Invalid(f"r = {r} exceeds the minimum radius {inst['r_opt']} by more than {TOL}")
+    for px, py in inst["points"]:
+        if math.hypot(px - x, py - y) > r + TOL:
+            raise Invalid(f"point ({px}, {py}) is outside the circle")
+    return None, {"r": r}
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9892643ac2adb79395d7904d7a41a58f97b3c5b6
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[3, 114], [3, 195], [6, 22], [10, 56], [10, 175], [13, 55], [13, 116], [15, 82], [16, 231], [19, 196], [22, 115], [23, 104], [24, 119], [27, 76], [30, 46], [31, 37], [33, 14], [35, 97], [41, 44], [44, 124], [45, 125], [46, 224], [50, 101], [50, 159], [52, 87], [52, 181], [64, 56], [67, 198], [67, 240], [78, 71], [79, 196], [80, 206], [80, 216], [84, 13], [84, 108], [86, 217], [87, 23], [88, 76], [91, 165], [92, 55], [94, 147], [95, 66], [96, 17], [98, 18], [98, 134], [99, 4], [100, 164], [101, 28], [105, 116], [108, 136], [108, 215], [111, 33], [113, 210], [116, 185], [117, 222], [118, 233], [120, 239], [123, 130], [124, 195], [126, 40], [128, 9], [137, 185], [138, 95], [139, 29], [139, 157], [142, 124], [149, 65], [149, 117], [150, 12], [154, 200], [155, 28], [157, 90], [157, 213], [159, 122], [160, 65], [160, 132], [163, 171], [163, 173], [167, 119], [168, 38], [169, 24], [169, 223], [170, 6], [170, 7], [175, 128], [178, 53], [179, 60], [180, 83], [183, 228], [185, 8], [186, 209], [187, 104], [189, 215], [192, 125], [192, 169], [194, 13], [195, 93], [196, 10], [200, 44], [203, 35], [204, 162], [205, 6], [205, 153], [206, 36], [207, 240], [208, 29], [210, 132], [211, 113], [216, 16], [216, 206], [218, 135], [222, 47], [227, 80], [228, 130], [231, 217], [234, 25], [234, 221], [236, 27], [238, 37], [238, 94]], "r_opt": 151.31506864816868, "r2_num": 91585, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l5-s0/environment/Dockerfile b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l5-s0/environment/instance.json b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..97cb205ca7c013b013a1626ff1460a1e51507bb3
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n1": 18, "n2": 26, "edges1": [[7, 15], [0, 6], [8, 9], [8, 15], [15, 17], [3, 7], [8, 13], [3, 16], [3, 11], [1, 13], [3, 15], [11, 13], [8, 10], [0, 4], [1, 3], [3, 14], [15, 16], [12, 15]], "edges2": [[6, 21], [0, 21], [15, 20], [0, 12], [11, 15], [13, 22], [5, 12], [1, 18], [7, 10], [9, 22], [6, 10], [9, 19], [5, 24], [18, 22], [7, 19], [3, 4], [15, 24], [21, 23], [1, 25], [0, 6], [5, 20], [7, 13], [4, 11], [17, 22], [22, 23], [5, 10], [17, 20], [7, 12], [10, 16], [2, 7], [5, 23], [16, 17], [4, 21], [3, 7], [15, 22], [17, 18], [16, 18], [20, 21], [4, 19], [7, 16], [5, 7], [19, 21], [0, 14], [11, 17], [9, 11], [3, 24], [7, 11], [21, 24]], "family": "rlve_subgraph_isomorphism", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l5-s0/solution/solve.sh b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..71b0c9370dbb02909499acb127874623b15158bf
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"p": [1, 24, 14, 5, 25, 8, 18, 10, 11, 4, 9, 20, 13, 15, 23, 7, 12, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/check.py b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b8467dd00c27c8902c06206c376ff7a11ac78ae0
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n1, n2 = inst["n1"], inst["n2"]
+    p = int_list(ans.get("p"), n1, 0, n2 - 1, "p")
+    if len(set(p)) != n1:
+        raise Invalid("p is not injective")
+    e1 = {(min(u, v), max(u, v)) for u, v in inst["edges1"]}
+    e2 = {(min(u, v), max(u, v)) for u, v in inst["edges2"]}
+    for u in range(n1):
+        for v in range(u + 1, n1):
+            a, b = min(p[u], p[v]), max(p[u], p[v])
+            if ((u, v) in e1) != ((a, b) in e2):
+                raise Invalid(f"pair ({u}, {v}) is not preserved")
+    return None, {}
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/instance.json b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..97cb205ca7c013b013a1626ff1460a1e51507bb3
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n1": 18, "n2": 26, "edges1": [[7, 15], [0, 6], [8, 9], [8, 15], [15, 17], [3, 7], [8, 13], [3, 16], [3, 11], [1, 13], [3, 15], [11, 13], [8, 10], [0, 4], [1, 3], [3, 14], [15, 16], [12, 15]], "edges2": [[6, 21], [0, 21], [15, 20], [0, 12], [11, 15], [13, 22], [5, 12], [1, 18], [7, 10], [9, 22], [6, 10], [9, 19], [5, 24], [18, 22], [7, 19], [3, 4], [15, 24], [21, 23], [1, 25], [0, 6], [5, 20], [7, 13], [4, 11], [17, 22], [22, 23], [5, 10], [17, 20], [7, 12], [10, 16], [2, 7], [5, 23], [16, 17], [4, 21], [3, 7], [15, 22], [17, 18], [16, 18], [20, 21], [4, 19], [7, 16], [5, 7], [19, 21], [0, 14], [11, 17], [9, 11], [3, 24], [7, 11], [21, 24]], "family": "rlve_subgraph_isomorphism", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/run.py b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/test.sh b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l5-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-ae-p45-sum-product-fp-n4000037/environment/Dockerfile b/tasks/optimize-ae-p45-sum-product-fp-n4000037/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ae-p45-sum-product-fp-n4000037/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ae-p45-sum-product-fp-n4000037/environment/instance.json b/tasks/optimize-ae-p45-sum-product-fp-n4000037/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..93908e027e19f4e153a37d8b08613da068dbb7ac
--- /dev/null
+++ b/tasks/optimize-ae-p45-sum-product-fp-n4000037/environment/instance.json
@@ -0,0 +1 @@
+{"p": 4000037, "k": 2000, "direction": "minimize", "family": "ae_p45_sum_product_fp", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p45-sum-product-fp-n4000037/solution/solve.sh b/tasks/optimize-ae-p45-sum-product-fp-n4000037/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1757768bc62f28ae8e373f26687fcbb63262a5fa
--- /dev/null
+++ b/tasks/optimize-ae-p45-sum-product-fp-n4000037/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"X": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 112, 120, 121, 125, 126, 128, 132, 135, 140, 144, 147, 20569, 20591, 20613, 70630, 70657, 70672, 70675, 70684, 70690, 70693, 70702, 70711, 70720, 70729, 70732, 70738, 70747, 70750, 70765, 70792, 95631, 95661, 95711, 95731, 95751, 95756, 95761, 95767, 95771, 95775, 95781, 95786, 95791, 95811, 95831, 95881, 95911, 141314, 141344, 141350, 141368, 141395, 141404, 141422, 141440, 141449, 141476, 141494, 141500, 141530, 166433, 166458, 166461, 166465, 166468, 166473, 166475, 166478, 166481, 166482, 166483, 166486, 166489, 166491, 166496, 166499, 166503, 166506, 166531, 187009, 187073, 187137, 191422, 191462, 191502, 191512, 191522, 191542, 191562, 191572, 191582, 191622, 191662, 212016, 212025, 212052, 212106, 212133, 212160, 212214, 212241, 212250, 237131, 237255, 262227, 262240, 262244, 262253, 262262, 262266, 262279, 282763, 282790, 282808, 282844, 282880, 282898, 282925, 287193, 287233, 287253, 287268, 287283, 287293, 287313, 287333, 287343, 287358, 287373, 287393, 287433, 332866, 332887, 332916, 332922, 332936, 332943, 332946, 332950, 332956, 332957, 332962, 332964, 332966, 332971, 332972, 332978, 332982, 332985, 332992, 333006, 333012, 333041, 333062, 353510, 353555, 353600, 357925, 357958, 357980, 357991, 358013, 358018, 358024, 358030, 358035, 358057, 358068, 358090, 358123, 378527, 378549, 378571, 378599, 378615, 378631, 378659, 378681, 378703, 383004, 383024, 383044, 383084, 383124, 383144, 383164, 403637, 403713, 428693, 428702, 428705, 428713, 428717, 428718, 428723, 428726, 428727, 428729, 428731, 428732, 428733, 428735, 428737, 428738, 428739, 428741, 428743, 428744, 428747, 428752, 428753, 428757, 428765, 428768, 428777, 474262, 474510, 478755, 478780, 478805, 478855, 478905, 478930, 478955, 499374, 499383, 499404, 499418, 499419, 499425, 499432, 499434, 499439, 499443, 499446, 499449, 499453, 499458, 499460, 499467, 499473, 499474, 499488, 499509, 499518, 503915, 524488, 524493, 524506, 524519, 524524, 570061, 570093, 570109, 570121, 570133, 570141, 570143, 570157, 570171, 570173, 570181, 570193, 570205, 570221, 570253, 574566, 574586, 574591, 574626, 574661, 574666, 574686, 595199, 595209, 595210, 595212, 595214, 595215, 595216, 595217, 595218, 595219, 595220, 595222, 595224, 595225, 595235, 640768, 640793, 640843, 640868, 640893, 640943, 640968, 645286, 645388, 665832, 665844, 665872, 665900, 665907, 665912, 665914, 665924, 665928, 665932, 665942, 665944, 665949, 665956, 665984, 666012, 666024, 670377, 670397, 670417, 690966, 690971, 691005, 691010, 715916, 715960, 715982, 716015, 716026, 716036, 716048, 716060, 716070, 716081, 716114, 716136, 716180, 736529, 736584, 736629, 736639, 736649, 736694, 736749, 761643, 761655, 761675, 761683, 761685, 761687, 761691, 761693, 761695, 761698, 761699, 761700, 761703, 761705, 761707, 761711, 761713, 761715, 761723, 761743, 761755, 786732, 786786, 807274, 807426, 832290, 832305, 832340, 832375, 832405, 832410, 832415, 832445, 832480, 832515, 832530, 857386, 857404, 857434, 857446, 857449, 857452, 857454, 857458, 857461, 857462, 857464, 857465, 857466, 857470, 857474, 857475, 857476, 857478, 857479, 857482, 857486, 857488, 857491, 857494, 857506, 857536, 857554, 903087, 903155, 928076, 928136, 928151, 928161, 928166, 928171, 928176, 928178, 928181, 928184, 928186, 928191, 928196, 928201, 928211, 928226, 928286, 953145, 953177, 953209, 953217, 953225, 953237, 953241, 953245, 953257, 953265, 953273, 953305, 953337, 978298, 978304, 998766, 998808, 998836, 998850, 998871, 998878, 998886, 998892, 998898, 998906, 998913, 998934, 998948, 998976, 999018, 1003298, 1003319, 1003343, 1003361, 1003379, 1003403, 1003424, 1023917, 1023927, 1023937, 1023940, 1023942, 1023947, 1023951, 1023952, 1023953, 1023957, 1023962, 1023964, 1023967, 1023977, 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+RLMATH_EOF
diff --git a/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/check.py b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..7184ef5e5926255a1a72ddf7fe632faebdd9012c
--- /dev/null
+++ b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/check.py
@@ -0,0 +1,15 @@
+"""Finite-field sum-product problem (AlphaEvolve problem 45): minimize max(|X+X|, |X*X|) in F_p, |X| = floor(sqrt p)."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    p, k = inst["p"], inst["k"]
+    x = int_list(ans.get("X"), k, 0, p - 1, "X")
+    if len(set(x)) != k:
+        raise Invalid("X must consist of distinct residues")
+    a = np.array(sorted(x), dtype=np.int64)
+    s = int(np.unique(np.add.outer(a, a) % p).size)
+    q = int(np.unique(np.multiply.outer(a, a) % p).size)  # products < p^2 < 2^63
+    return float(max(s, q)), {"sumset": s, "productset": q}
diff --git a/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/instance.json b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d0ca21063ef2d16bbba5984f1a04136ec88a1105
--- /dev/null
+++ b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/instance.json
@@ -0,0 +1 @@
+{"p": 4000037, "k": 2000, "direction": "minimize", "best_known": 149602.0, "baseline": 959284.0, "family": "ae_p45_sum_product_fp", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/run.py b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/test.sh b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ae-p45-sum-product-fp-n4000037/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-ae-p60-no5-on-sphere-n10/environment/Dockerfile b/tasks/optimize-ae-p60-no5-on-sphere-n10/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ae-p60-no5-on-sphere-n10/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ae-p60-no5-on-sphere-n10/environment/instance.json b/tasks/optimize-ae-p60-no5-on-sphere-n10/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f5847c8b550f4cc264b6da453378aa4705d0f354
--- /dev/null
+++ b/tasks/optimize-ae-p60-no5-on-sphere-n10/environment/instance.json
@@ -0,0 +1 @@
+{"n": 10, "max_points": 40, "direction": "maximize", "family": "ae_p60_no5_on_sphere", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p60-no5-on-sphere-n10/solution/solve.sh b/tasks/optimize-ae-p60-no5-on-sphere-n10/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2906e3d2d9963fa20dbf0ddb42ed7d4bf545657e
--- /dev/null
+++ b/tasks/optimize-ae-p60-no5-on-sphere-n10/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"points": [[8, 1, 0], [1, 5, 6], [9, 8, 6], [4, 6, 1], [8, 0, 9], [0, 1, 9], [0, 7, 4], [3, 0, 8], [9, 7, 0], [1, 7, 7], [1, 4, 9], [4, 5, 3], [5, 1, 7], [7, 4, 5], [7, 6, 1], [2, 1, 2], [9, 4, 8], [9, 5, 5], [3, 8, 1], [5, 8, 3], [7, 0, 2], [2, 2, 8], [2, 3, 2], [5, 7, 6], [0, 9, 0], [0, 2, 0], [8, 9, 1], [4, 9, 9]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/check.py b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..535715270fb95983b4b3896cda93a8746da1a961
--- /dev/null
+++ b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/check.py
@@ -0,0 +1,53 @@
+"""No 5 points of an n x n x n grid subset on a common sphere or plane (AlphaEvolve problem 60).
+
+Exact int64 test: five points are co-spherical/co-planar iff det[x, y, z, x^2+y^2+z^2, 1] = 0, evaluated as the
+4x4 determinant of differences (entries <= 3(n-1)^2, so |det| < 2^40). Upstream used float det + np.isclose."""
+import itertools
+
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def det4(m):
+    a, b, c, d = m[:, 0], m[:, 1], m[:, 2], m[:, 3]
+
+    def det3(r0, r1, r2, i, j, k):
+        return (r0[:, i] * (r1[:, j] * r2[:, k] - r1[:, k] * r2[:, j])
+                - r0[:, j] * (r1[:, i] * r2[:, k] - r1[:, k] * r2[:, i])
+                + r0[:, k] * (r1[:, i] * r2[:, j] - r1[:, j] * r2[:, i]))
+    return (a[:, 0] * det3(b, c, d, 1, 2, 3) - a[:, 1] * det3(b, c, d, 0, 2, 3)
+            + a[:, 2] * det3(b, c, d, 0, 1, 3) - a[:, 3] * det3(b, c, d, 0, 1, 2))
+
+
+def lifted(p):
+    a = np.array(p, dtype=np.int64)
+    return np.concatenate([a, (a * a).sum(1, keepdims=True)], axis=1)
+
+
+def bad_five(rows, combos):
+    """rows: (m, 4) lifted points; combos: (N, 5) index array. Returns mask of degenerate 5-sets."""
+    base = rows[combos[:, 0]]
+    m = np.stack([rows[combos[:, i]] - base for i in range(1, 5)], axis=1)
+    return det4(m) == 0
+
+
+def check(inst, ans):
+    n = inst["n"]
+    pts = ans.get("points")
+    if not isinstance(pts, list) or not (1 <= len(pts) <= inst["max_points"]):
+        raise Invalid(f"points must be a list of 1..{inst['max_points']} [x, y, z] triples")
+    p = [tuple(int_list(q, 3, 0, n - 1, "point")) for q in pts]
+    if len(set(p)) != len(p):
+        raise Invalid("points must be distinct")
+    rows = lifted(p)
+    it = itertools.combinations(range(len(p)), 5)
+    while True:
+        chunk = np.array(list(itertools.islice(it, 200000)), dtype=np.int64)
+        if len(chunk) == 0:
+            break
+        bad = bad_five(rows, chunk)
+        if bad.any():
+            q = [p[i] for i in chunk[np.argmax(bad)]]
+            raise Invalid(f"points {q} lie on a common sphere or plane")
+    return float(len(p)), {"size": len(p)}
diff --git a/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/instance.json b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5d44242092c247278d7939350bd3c24808d28228
--- /dev/null
+++ b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/instance.json
@@ -0,0 +1 @@
+{"n": 10, "max_points": 40, "direction": "maximize", "best_known": 28.0, "baseline": 20.0, "family": "ae_p60_no5_on_sphere", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/run.py b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/test.sh b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ae-p60-no5-on-sphere-n10/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-ea-kissing-d11-n605/environment/Dockerfile b/tasks/optimize-ea-kissing-d11-n605/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ea-kissing-d11-n605/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ea-kissing-d11-n605/environment/instance.json b/tasks/optimize-ea-kissing-d11-n605/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f36cd806be6784bdc7fc7f3b9124c2fcfd1b753
--- /dev/null
+++ b/tasks/optimize-ea-kissing-d11-n605/environment/instance.json
@@ -0,0 +1 @@
+{"dim": 11, "n": 605, "direction": "minimize", "progress_scale": "log", "log_floor": 0.001, "family": "ea_kissing_number", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-kissing-d11-n605/solution/solve.sh b/tasks/optimize-ea-kissing-d11-n605/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e54ee753ce589ea9d7beddc2c233e95350438b31
--- /dev/null
+++ b/tasks/optimize-ea-kissing-d11-n605/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"vectors": [[-0.9939863759901654, -0.9402300329915074, 1.5797556579109484, 0.7266414004424878, 0.9492533764263298, -0.08269420514470294, -0.53877888746077, 1.174372226101963, -0.14335550574303, -0.5751494887760122, 0.14080863273957772], [0.38775214542252784, 0.6023469389016719, -0.0713299606881812, 0.052040277237129354, 0.7886530122517591, 0.2711420113093591, 0.409803893698545, -1.809753326384127, 1.424599006578943, 0.6650883765574955, 1.014604733107526], [2.6996128898500538, 1.0793908188745975, -0.24891750082199943, -0.02108105638497597, -0.1810643965461852, -0.159110708802073, -1.7989923648227055, 1.1386656304709093, 0.5006560019595302, 1.840717033276779, -1.3665929730212598], [1.0354852755374822, -0.5020206467889974, -0.5199693809820277, -1.2590554606235846, 1.0153604293170544, -0.6290288215539477, 2.5488421255816367, 0.7524371068637923, -0.4417370225611701, 1.0041961027396191, 1.6679734004059161], [-0.658995528300114, 0.8696257582731342, 0.07466678090335396, 2.270887589809408, 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-0.027309511238700592, 0.04578164878550872, -0.9056104257731978, 0.83102122091575, 0.6912174887251117, 0.09198094691192829], [-1.9801683049177021, 0.1907991036931276, 0.8381392080757214, 0.42228697990250974, 1.3630284754636013, -0.7028743853270178, 0.38075151923839196, 0.01385024260805444, 0.5037156729337723, 0.7985922002838756, -0.013681627892561292], [-2.0828102106815343, 0.05666678004811456, -0.37262370667899947, 0.11692454365705726, -1.1574077891977117, 0.19718941888762426, -0.5949096421096263, 0.8554983215230566, -0.7481861197473157, -1.3389487438981615, -0.3865128249985956], [-1.1773128734868985, 0.5581394298522931, 0.4750553397101952, -0.6486371649981689, -0.6018423590386839, -0.4019642898141699, -0.8230013008890807, 1.3366333283365341, 0.6068230241961459, 1.3094695760550563, 0.4407722328396241], [-1.2649645757435126, 1.0374778066094041, -1.8498651289515489, -1.461095806302891, 1.2189700431616382, -0.0975650546326203, -0.34511424115047973, 0.10788339124028772, -1.4410538030159137, 2.106588720849723, -0.5041523227219028], [1.3168608536648874, 0.416399403003155, -1.4066225894780433, 1.3345132565552529, -2.1111381944943757, 1.1731787392169162, 1.2057355726868588, -0.26411408302063444, -0.15441192780341356, -0.7224782171846174, 0.44448817221268744], [1.9745269431266608, 0.0916631958249753, -0.5093907887647076, 0.7710989104772937, 0.49250959932541427, 0.14240807165329752, 1.415647421983975, -0.07161952778986055, 0.6403203634179355, 0.22052598577476745, 0.5535803601926126], [0.5619265152531993, -1.2073311160971631, 2.2248651948871876, -0.7712580335164554, 0.4057550624247745, 1.1699405782042211, -0.8214631929110675, 1.297935749432899, 0.07257155790870971, -1.1264095014799507, -0.3713175514336845], [-0.12157624778005387, 1.3547216770640302, -0.14446893976679903, 1.6826017440980456, 1.7633247086866712, 0.7927891243036984, 0.030750690965689283, -1.2429416171882133, 0.3722688023469101, 0.22474874665758224, -1.2383584484657293], [-0.8965636126451711, -0.05208346329684582, -0.7427566181697356, 0.3813066543702677, -0.5700502673203325, 0.23318148119141985, -0.03426139544392662, -0.05101248134850633, -1.5487235497679361, 1.1281215105361522, 0.007006745983049657], [-2.1710265577328762, 0.9369306483689838, 0.5516517526109177, -1.5797664622230758, -0.9808083718801404, -1.1048079033327105, -0.8769771390330326, -0.6948324928496138, -1.295184307861355, -1.2648197942306727, 1.0900290044624634], [1.731692381986656, 0.17471189895489628, -2.2649283367944544, 1.6533019382334349, 0.8445779797069376, 0.641419535246658, -0.08080506122902599, -1.085832682237906, 0.09942308968870157, -2.23408631191513, -0.7693752077058985], [-0.67068307667356, 1.4654862868948186, -0.2050710779730007, -0.6636358011717308, -0.8099887921153597, 0.4973956217055001, 0.22603194566326876, -0.1275920014902166, 0.462389090297731, 0.6802422172640072, 0.021023659676839657], [0.665695178703548, 0.0918352742401322, -0.21498048415642795, 0.8214351696176898, 1.6624893433100312, -0.8536344444148879, -0.4339895273939534, -1.1381521312109213, -1.8205300799846267, 0.09187757006354419, -0.18193330616679532], [0.8086597758622438, -2.011027427644436, 0.24270024505323937, 1.826306347511205, 0.942943482415871, 0.2058990266407265, 0.037663709162842555, -0.8739437355770443, 0.1765436929508069, -0.14623004326881756, 0.7059591754189182], [-0.45403130641321154, 0.45101409566780726, 0.7856106151622755, -0.8040909115889706, 0.29031247682617706, -0.41358822044486243, -0.7496280753427581, 0.7821081812147778, -1.3209841872464858, -1.9720254327604274, -1.0462425192250124], [0.7523964107716239, 1.013576933969708, -0.605142563828707, -0.3076145155236562, -0.5333172232840625, -0.5546661561515303, -0.06582878704131294, 0.31820589068468874, 0.08667200984433888, -0.06309996680520188, -0.35874585554879784], [-0.17524796413832652, 0.9589447549615876, 1.042089305585435, -0.6222371355032079, 0.7779629686582938, 0.1835521373766812, -0.6460010514619728, 1.098131140107744, -0.051136004710442856, 0.6812262869935775, -0.5688993695579525], [1.3590988811809017, 1.3553616526437247, 0.7720626247422054, -0.9388947134632404, -0.4919841208878735, -1.4662713416838609, -1.4969856261200416, 0.928965972930791, 0.029235030276948206, -0.5255443585946206, 2.1078937950488696], [0.017542488735818953, 0.8536876635430849, -0.4530730177578792, 1.093348835427617, 1.195629146615982, 0.7865319770749178, 2.2929032634553637, 0.5765422570534847, -1.0424198194583167, -0.868215645395189, -1.0016734628574873], [1.3564901535244447, -0.18234168182804328, -0.26193360693473994, 0.5051249102024054, 0.7720709880050032, 0.4263630350742511, -0.09473388042998285, -0.40520220674228546, 0.7261437493784757, -0.16494592274852052, 0.9802622164641571], [1.5284096074079248, 0.8312002493578878, -0.31949769377565607, 2.4560024386321233, 0.3850999174997642, 1.421461222449134, -0.2689911243803748, -1.6437967440850787, -0.1572274694733265, -1.2314823826960508, -1.079573757691429], [0.44317122511623225, 0.39427551425454516, 1.1685827476776944, -0.5730189591057856, 1.7519706528905972, -0.7450125213715626, 1.6868849372484036, 0.1760375206877068, -2.368401347770816, 0.03632521679899814, -0.5176239301976983], [0.2088222706050908, 0.5216565617647888, -0.3990506054502906, -2.689894980754565, 1.7614445486320982, -1.2047225459452682, 0.41324564053697554, -0.011464701711769533, 0.13664183304948566, -0.16145066672172126, 0.16428540340549072], [1.2081111206377297, 0.38588835504657437, 1.1038261701022256, -0.5588412578451046, 0.49112764815633125, -0.6834545603717231, 0.5661519047995413, -0.4586151086146864, -0.16863200386868407, 0.6225504902462504, 2.1004811228178557], [0.399657978921721, 0.19740402683463504, 1.028032037643594, 1.0441968949406009, -1.7477076306629082, 0.06815526457095758, -1.8486589212351237, -0.5704501325561356, -1.560962247882318, 1.3217112484625457, -1.1154212636406122], [-0.8319889091227619, -0.37902654532839036, -0.4109815654243271, -1.3472828904448908, 1.1988041205792916, -0.013056230881480111, 2.7668951757826283, -1.4401059980960076, -0.4399797409191198, 0.2673977401840845, 0.6628125107998406], [3.0903488477013927, 0.776215395710208, -0.7670949818302534, 0.6385785455467619, 0.300731597648457, 0.7986980609744123, -0.3027654638894512, -0.63087192125401, 1.8312719195186835, 0.32406141353455004, 0.8155013070704737], [-0.47218410575517733, -2.048390625713205, -2.1663768729848414, -0.9243470263845619, -1.0473703614359686, -0.512694517967413, 0.3150978838481239, 1.3524125929281907, 1.0815283386636456, -1.4359460044242776, -0.29816595476786223], [-0.5884908752087358, -0.28452581466432164, -0.1921203902382197, -1.2220108320167298, 1.307432847036849, -0.25836864636786955, 0.26666462816949754, 0.8775518133328423, -0.6825638702829548, 0.6449494424037212, -0.5294293245763199], [-1.2887305260089732, 1.4459653643021821, -0.8883755957220253, 0.9890876509993697, -2.056476179113744, 0.5589299136465624, -0.28001607460118233, -0.5375057712600104, -0.03865522147596851, -0.7529431024863862, -0.4938013661181758], [-0.20679513759037266, 1.2380220673751858, -0.21444977346732544, -0.08490786927953684, -1.455791381557005, -0.4340997508917987, 0.6328332651432089, -0.6843401935070805, -0.07982767029480936, 0.7201161554456111, -1.8011647231651648], [0.18688229628561454, -0.5398864743323033, -1.0689517283448728, -1.1223072026658294, 0.3269620727778335, 0.5725294535991473, 0.8860881709596654, 0.11525663800113684, -0.1469533243851815, -0.2248768850954705, 0.003948651072938794], [-0.8647724332434287, -0.14890268508101775, -1.0097706187417828, 0.38160541140626764, 0.0719030372842334, -0.38052303726422754, 0.3575855415748168, 0.0773321171562361, -1.6297568714545978, -1.0582078830609825, 1.182757784757653], [-2.3316919340725293, -1.237000389486217, 0.12027354746535897, -0.5562579225981283, 0.16625720908137484, -0.4529539583499886, -1.4851908482454035, 1.625085293720304, 0.20874509849898756, 0.19959575141473054, 1.7626068296146418], [-1.0171703387211941, -2.5681484596863005, -0.7503676681830561, -0.02320090583585319, -0.860231435692342, 0.4498519508201021, 1.612836818322594, -1.0464481956271, -0.0806694145919218, 0.8848509645907013, -0.5306080173561055], [-0.7841588619307361, -0.3579558502167451, -0.061413539022732784, 1.5292486328767636, -0.09337711398777117, -0.0924144159795328, 1.2112393541508695, 0.10070320576548125, 0.47694880517103394, -2.270788303845244, 0.9970785225782405], [-0.7129187585604791, 1.816846952433326, -0.459923355488933, -0.654370091801156, -0.3642300358822143, 2.2705648618127223, 1.099097574024231, -1.3100949648726155, 0.1668682375039234, 0.9926846309981133, 0.2564464904970588], [-0.4278252656098408, 1.5410034224357156, -1.3138412175352892, -0.8363755012414543, -1.0535663936451183, -0.3248325291876498, 0.2038250016745197, -2.0804768970569816, 1.2341749593582723, 0.360258199532362, 0.08918905187267243], [-2.254903898364517, 0.11669838056033811, -1.020133649874593, -1.337720845246626, 0.48686664606868857, -0.947181638249252, 0.20892162960681512, 1.0200728115743756, 0.6038691436505002, 2.6486045441118238, -0.08229739547479774], [-0.2672228111849231, 0.795365297298088, -1.275656682338119, -0.4423095872010733, -0.14533405461190982, -0.26103667621671456, -0.6994243251894973, 0.5238317744228848, -0.06552091905835437, -0.7413163423481609, 1.4540987024540561], [0.01749623474575599, -0.49184637637070244, -0.5454149627884145, -0.2739914233196557, 0.17240780619523144, -1.4485738287412546, 1.3153686949148158, -0.3582911863622961, -0.5582636746479592, -0.5277791587380178, -2.427535131627443], [0.29385690629644506, -0.9267548401711939, 0.6100948341318343, -1.6944578202703782, 0.16225869498158213, 0.8201888336734745, -1.3030253977355524, 0.05294067923791526, 1.4876615424871518, -0.29425882404650366, 0.13692738429466286], [1.1726986597540603, -1.411397180689316, -1.6198694102659605, 0.0478609443797171, 0.6874649916686566, -1.8889315318681266, -0.9384059881900543, 0.31031112821564333, 0.939016390444441, 1.0958463803060072, 0.7497316680673125], [-0.2700506941022207, -0.6051206497166525, -1.698774897821978, 0.7049367074542825, 1.1897078702231418, -0.10506318155923515, 0.4744910067884375, -0.9249698694338534, -0.5027462492179935, 1.0935909907782055, -1.1145614865720805], [-0.39593009171015453, 0.06701060132745637, -0.5575629505332743, -1.3552767474468326, -1.2019727766096846, -0.6237955440097479, 0.5974921828354793, -0.4624919645598005, 1.8361381899879845, -0.16922129943602443, -1.4841630334396765]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ea-kissing-d11-n605/tests/check.py b/tasks/optimize-ea-kissing-d11-n605/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e67c43884a1e3216148fc027eaa31c36e4ff51a4
--- /dev/null
+++ b/tasks/optimize-ea-kissing-d11-n605/tests/check.py
@@ -0,0 +1,70 @@
+"""Kissing configurations with an overlap loss (EinsteinArena kissing-number-d11 / -d11-605 / -d12, MIT).
+
+Sphere centres c_i = 2 v_i / |v_i|; loss = sum_{i<j} max(0, 2 - |c_i - c_j|) (minimize; 0 = valid kissing
+configuration).
+
+Changes vs the upstream verifier: upstream certifies loss 0 only through the sufficient test
+min |v_i - v_j|^2 >= max |v_i|^2 (in 30-80 digit Decimal arithmetic, so huge integer inputs can round) and
+otherwise sums float-ish Decimal overlaps. Here every number is read as an exact rational (floats via their
+shortest decimal repr), and a pair is overlapping iff <v_i, v_j> > 0 and 4 <v_i, v_j>^2 > |v_i|^2 |v_j|^2,
+decided in exact integer arithmetic (necessary and sufficient). The loss is 0 exactly for valid
+configurations, and every overlapping pair contributes a strictly positive amount computed from the exact
+excess 4<v_i,v_j>^2 - |v_i|^2|v_j|^2 (so an invalid configuration can never round to 0)."""
+import math
+import re
+from fractions import Fraction
+
+from run import Invalid
+
+DEC = re.compile(r"^[+-]?\d{1,40}(\.\d{1,80})?$")
+
+
+def _rat(x):
+    if isinstance(x, bool):
+        raise Invalid("coordinates must be numbers")
+    if isinstance(x, int):
+        return Fraction(x)
+    if isinstance(x, float):
+        if not math.isfinite(x):
+            raise Invalid("non-finite coordinate")
+        return Fraction(repr(x))
+    if isinstance(x, str) and DEC.fullmatch(x):
+        return Fraction(x)
+    raise Invalid("coordinates must be numbers or decimal strings")
+
+
+def check(inst, ans):
+    n, d = inst["n"], inst["dim"]
+    vs = ans.get("vectors")
+    if not isinstance(vs, list) or len(vs) != n:
+        raise Invalid(f"vectors must be a list of exactly {n} vectors")
+    rows = []
+    for v in vs:
+        if not isinstance(v, list) or len(v) != d:
+            raise Invalid(f"each vector must have exactly {d} coordinates")
+        rows.append([_rat(x) for x in v])
+    den = 1
+    for r in rows:
+        for q in r:
+            den = den * q.denominator // math.gcd(den, q.denominator)
+    R = [[int(q * den) for q in r] for r in rows]
+    N = [sum(x * x for x in r) for r in R]
+    if min(N) == 0:
+        raise Invalid("all vectors must be non-zero")
+    loss, bad = 0.0, 0
+    for i in range(n):
+        ri, Ni = R[i], N[i]
+        for j in range(i + 1, n):
+            p = sum(a * b for a, b in zip(ri, R[j]))
+            if p <= 0:
+                continue
+            NN = Ni * N[j]
+            ex = 4 * p * p - NN
+            if ex <= 0:
+                continue
+            bad += 1
+            q = float(Fraction(ex, NN))  # 4 cos^2 - 1 > 0
+            c = min(1.0, float(Fraction(p * p, NN)) ** 0.5)
+            ov = 2.0 * (q / (2 * c + 1)) / (1.0 + math.sqrt(max(0.0, 2 - 2 * c)))
+            loss += max(ov, 1e-300)
+    return loss, {"overlapping_pairs": bad}
diff --git a/tasks/optimize-ea-kissing-d11-n605/tests/instance.json b/tasks/optimize-ea-kissing-d11-n605/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e1e8798117193a38973c51a3b506f4eb79f7de5
--- /dev/null
+++ b/tasks/optimize-ea-kissing-d11-n605/tests/instance.json
@@ -0,0 +1 @@
+{"dim": 11, "n": 605, "direction": "minimize", "best_known": 1.7152471173506234, "progress_scale": "log", "log_floor": 0.001, "baseline": 1910.0812438093099, "family": "ea_kissing_number", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-kissing-d11-n605/tests/run.py b/tasks/optimize-ea-kissing-d11-n605/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ea-kissing-d11-n605/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ea-kissing-d11-n605/tests/test.sh b/tasks/optimize-ea-kissing-d11-n605/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ea-kissing-d11-n605/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-ea-tammes-n50/environment/Dockerfile b/tasks/optimize-ea-tammes-n50/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ea-tammes-n50/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ea-tammes-n50/environment/instance.json b/tasks/optimize-ea-tammes-n50/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0913de2e0262b9e688eaaa9ee2de4283b6baaa2c
--- /dev/null
+++ b/tasks/optimize-ea-tammes-n50/environment/instance.json
@@ -0,0 +1 @@
+{"n": 50, "direction": "maximize", "family": "ea_tammes", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-tammes-n50/solution/solve.sh b/tasks/optimize-ea-tammes-n50/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4130b5825099a28ccb698a14c1b343f08d3987b2
--- /dev/null
+++ b/tasks/optimize-ea-tammes-n50/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"vectors": [[0.7322901985853106, -0.580873433242494, -0.35543933323278176], [0.8668577253808234, 0.29709842023339167, -0.40036260145324254], [0.09188746042046939, 0.8178982615454883, 0.5679781055448748], [0.41753906891157594, 0.7210915371304273, -0.552890695356082], [-0.7479003654736476, 0.6359554715278511, 0.1902779061220013], [0.505801994465565, -0.03341820449736239, 0.862002068444635], [-0.9373130668768048, -0.048481761768592896, -0.3450995993011466], [0.31438814393675263, -0.8388229551939425, 0.44445038507318796], [-0.7527465493975529, -0.5247635341322129, -0.3974869376660664], [0.8097328358764708, -0.5667802456649191, 0.1519634417465671], [-0.35039337926840286, -0.5149747971085981, 0.7823205469037788], [0.7608528722093818, -0.14893360140102668, -0.6316024772152611], [0.7031992081066337, 0.6996024139865048, -0.1267569961085325], [0.16052783862765743, -0.5355084499435196, 0.8291329887687631], [-0.0829631173116482, -0.4823522455455945, -0.8720398112374551], [-0.19797421324956202, -0.872482290982598, 0.44674474010331017], [0.1745502547985098, -0.8642704767830905, -0.4717719274298806], [0.9442997680276304, 0.31119178880473675, 0.1070402666451824], [-0.48438920248932094, -0.027923825885594503, 0.8744068620840476], [-0.6555042626238464, -0.6462434634107526, 0.39074742184797967], [-0.24842750976476122, 0.11160835876493462, -0.9621992239894382], [0.27694916860990354, 0.9608364341162783, -0.00961794577849917], [-0.18716646366976272, 0.3898929511567737, 0.9016386202440627], [0.7473571578426565, 0.3221204451031153, 0.5811159070855981], [0.07581470606828906, 0.49749244658639424, -0.8641489431418999], [-0.5291907885285076, -0.8460019631842343, -0.06509829202827139], [-0.7392775647612096, 0.31816313051783696, 0.5934988665699584], [0.6257898735970058, -0.47103814864058924, 0.6216993619336356], [0.31930600444180995, 0.44433577480136294, 0.8370241303326204], [0.22612525745167922, -0.08431303325833629, -0.970442517805764], [-0.5077589635060772, 0.8333556296598351, -0.21840153271782226], [0.5374730743178054, 0.2839261574194893, -0.7940457364134451], [0.557377500854481, 0.7465391064802271, 0.36333136946445627], [-0.3815346648627622, 0.6327060625971085, -0.6738800619256544], [-0.038369176293852246, 0.9104979022134303, -0.4117297370551152], [0.9157376406447653, -0.12074800444650675, 0.38320293961365326], [-0.32822982500784675, -0.7798822686271368, -0.5329623148556649], [-0.5447609503606935, -0.2721612378041721, -0.7931984415006217], [-0.20273714329317305, 0.9637334138376233, 0.17353834671969107], [-0.8296725523645236, -0.18295159099343192, 0.5274202984394031], [0.41590583225349836, -0.5092324165254462, -0.7534618003967949], [0.9768607557168405, -0.15740225918673897, -0.14480190863118433], [-0.9768864682708631, 0.15719194937515044, 0.1448568920035228], [-0.6788742016826994, 0.21503580197205505, -0.7020608393578954], [0.012084482910697728, -0.0735915541532142, 0.9972152467898271], [-0.8469181007296209, 0.4526330520844084, -0.279021595610958], [-0.04060697495737542, -0.9988523159782288, -0.025399300182086026], [0.4600635849276428, -0.886714806932079, -0.04558891302643101], [-0.4105165258632419, 0.7118757572331307, 0.569832508950596], [-0.9286899228617197, -0.3662744606040965, 0.05812096596127289]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ea-tammes-n50/tests/check.py b/tasks/optimize-ea-tammes-n50/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..af79b2b1d2f6be5bb2dd07edd8d10ad91ffc3e4b
--- /dev/null
+++ b/tasks/optimize-ea-tammes-n50/tests/check.py
@@ -0,0 +1,16 @@
+"""Tammes problem: n points on S^2, maximize the minimum pairwise distance (EinsteinArena verifier, MIT)."""
+import itertools
+import math
+
+from run import Invalid, float_matrix
+
+
+def check(inst, ans):
+    v = float_matrix(ans.get("vectors"), inst["n"], 3, "vectors")
+    u = []
+    for x in v:
+        nr = math.sqrt(sum(t * t for t in x))
+        if nr < 1e-12:
+            raise Invalid("zero vector")
+        u.append([t / nr for t in x])
+    return min(math.dist(a, b) for a, b in itertools.combinations(u, 2)), {}
diff --git a/tasks/optimize-ea-tammes-n50/tests/instance.json b/tasks/optimize-ea-tammes-n50/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..77d816d74186bc7a08b2d1f2e06dff87a2de249c
--- /dev/null
+++ b/tasks/optimize-ea-tammes-n50/tests/instance.json
@@ -0,0 +1 @@
+{"n": 50, "direction": "maximize", "best_known": 0.5134721, "baseline": 0.12558103905862603, "family": "ea_tammes", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-tammes-n50/tests/run.py b/tasks/optimize-ea-tammes-n50/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ea-tammes-n50/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ea-tammes-n50/tests/test.sh b/tasks/optimize-ea-tammes-n50/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ea-tammes-n50/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-finch-3ap-diffs-n40/environment/Dockerfile b/tasks/optimize-finch-3ap-diffs-n40/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-finch-3ap-diffs-n40/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-finch-3ap-diffs-n40/environment/instance.json b/tasks/optimize-finch-3ap-diffs-n40/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e96633e2427ff37d33dde908c2ccf064a168591d
--- /dev/null
+++ b/tasks/optimize-finch-3ap-diffs-n40/environment/instance.json
@@ -0,0 +1 @@
+{"n": 40, "M": 400, "direction": "maximize", "family": "finch_3ap_diffs_40", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-finch-3ap-diffs-n40/solution/solve.sh b/tasks/optimize-finch-3ap-diffs-n40/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6094210c72313c0f91c70c17ee1caa814ac7bf5a
--- /dev/null
+++ b/tasks/optimize-finch-3ap-diffs-n40/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [2, 6, 14, 30, 56, 60, 106, 110, 114, 120, 126, 128, 153, 155, 162, 166, 174, 180, 186, 190, 193, 195, 196, 198, 200, 204, 206, 210, 218, 225, 226, 227, 250, 254, 276, 280, 292, 330, 342, 394]}
+RLMATH_EOF
diff --git a/tasks/optimize-finch-3ap-diffs-n40/tests/check.py b/tasks/optimize-finch-3ap-diffs-n40/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac30a01a909fcbd25818ff1325c71ecc5d13f84c
--- /dev/null
+++ b/tasks/optimize-finch-3ap-diffs-n40/tests/check.py
@@ -0,0 +1,14 @@
+"""Erdos #1097: number of distinct common differences of 3-term APs in a 40-element set A of [0, 400)
+(Finch/EFT skydiscover erdos_1097_3ap_diffs_n40, Apache-2.0). Exact integer count, as upstream. Change:
+entries must be JSON integers (upstream cast with int())."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, M = inst["n"], inst["M"]
+    A = int_list(ans.get("A"), n, 0, M - 1, "A")
+    if len(set(A)) != n:
+        raise Invalid("elements must be distinct")
+    S, L = set(A), sorted(A)
+    ds = {L[j] - L[i] for i in range(n) for j in range(i + 1, n) if 2 * L[j] - L[i] in S}
+    return float(len(ds)), {}
diff --git a/tasks/optimize-finch-3ap-diffs-n40/tests/instance.json b/tasks/optimize-finch-3ap-diffs-n40/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d644da36f35f50b65e067b9d45bab7d994c50de
--- /dev/null
+++ b/tasks/optimize-finch-3ap-diffs-n40/tests/instance.json
@@ -0,0 +1 @@
+{"n": 40, "M": 400, "direction": "maximize", "best_known": 109.0, "baseline": 19.0, "family": "finch_3ap_diffs_40", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-finch-3ap-diffs-n40/tests/run.py b/tasks/optimize-finch-3ap-diffs-n40/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-finch-3ap-diffs-n40/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-finch-3ap-diffs-n40/tests/test.sh b/tasks/optimize-finch-3ap-diffs-n40/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-finch-3ap-diffs-n40/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt