diff --git a/tasks/construct-ae-p32-spherical-design-l1-s0/environment/Dockerfile b/tasks/construct-ae-p32-spherical-design-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-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-p32-spherical-design-l1-s0/environment/instance.json b/tasks/construct-ae-p32-spherical-design-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca79c6abb85cacb5bee83b2aedcba9980178bff6
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"t": 7, "N": 32, "family": "ae_p32_spherical_designs", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p32-spherical-design-l1-s0/solution/solve.sh b/tasks/construct-ae-p32-spherical-design-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..902cc7fa04429f245f41bd06460675ee643f2a36
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-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'
+{"points": [[0.11606245518956762, -0.16610236292160294, 0.9792545693164928], [-0.39675347898353364, 0.021959702877615433, 0.9176624915316032], [0.48607965266991554, 0.3267742455138338, 0.8105215381031888], [-0.5028561752354322, -0.5750524338141748, 0.6453296563710569], [-0.028977008371302036, 0.6135860519291835, 0.7890959953413823], [0.5777480561971958, -0.47035296633303025, 0.6670646674963989], [-0.8420308379668259, 0.1041135493697409, 0.5292867245175527], [0.4881919910817507, 0.8046658299621788, 0.33790750499939154], [0.05682487551774614, -0.774372788635976, 0.6301727681695984], [-0.5062108733612531, 0.6777469568328439, 0.5333006789744942], [0.8794695462925934, 0.04158955579889673, 0.474134607461162], [-0.824292194748616, -0.526747348849163, 0.20755627708380178], [0.03579833654889291, 0.9932353461313679, 0.11046278240038192], [0.43737764389826533, -0.8976265455739514, 0.05447367528427997], [-0.9674139517139864, 0.2527458976385419, 0.015157745743229844], [0.8886047473718967, 0.4575428942323253, 0.03218855208975348], [-0.19945016049042963, -0.9765802130317549, 0.08068903887885889], [-0.5625217409955832, 0.8258384454171637, -0.03949877185761976], [0.8572022318024186, -0.5109673200807969, 0.06416176121648516], [-0.9020508634918853, -0.28444012594837104, -0.32465066521419417], [0.5380327326930923, 0.7340076582810167, -0.4144315819717673], [0.2598906488008719, -0.815213720040663, -0.5175745756152687], [-0.7070637245329644, 0.4835136486653401, -0.5160188378382152], [0.950916697141367, -0.05600374474698265, -0.30433701002682667], [-0.4784134955383967, -0.8056610046010311, -0.3493291756380935], [-0.04565799735558514, 0.8577605502323268, -0.5120177592062733], [0.6188703713672925, -0.41712374259641766, -0.6655878956276676], [-0.6087554544458175, -0.0691406036458159, -0.7903394040600269], [0.5928789130408082, 0.29380189301906434, -0.7497833301227523], [-0.21108669618117018, -0.5264950943862514, -0.8235565082509704], [-0.1545704268221741, 0.43945924916465534, -0.8848635778896362], [0.15415618062128142, -0.0564614598601123, -0.9864319416598004]]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p32-spherical-design-l1-s0/tests/check.py b/tasks/construct-ae-p32-spherical-design-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..5973c15b3df2d6228d713d9b186ced8e47dcbb48
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l1-s0/tests/check.py
@@ -0,0 +1,53 @@
+"""Spherical t-design with N points on S^2 (numerical, tolerance 1e-10 on every harmonic average).
+
+Upstream (AlphaEvolve `spherical_t_designs.ipynb`) scored sum_k dim_k/C_k(1) * sum_{i,j} C_k(<x_i,x_j>), whose
+pair sums cancel to ~1e-10 in float64 and can even go negative; its printed acceptance test
+`calculate_design_score(...) < 1e-8` compares the NEGATED error and is therefore always true (bug).  Here we
+evaluate the point averages of an orthonormal real spherical-harmonic basis directly (no cancellation).
+"""
+import numpy as np
+
+from run import Invalid, float_matrix
+
+TOL = 1e-10
+
+
+def harmonics(X, t):
+    """Rows: real spherical harmonics Y_lm (1 <= l <= t) normalised so that their mean square on S^2 is 1."""
+    ct = np.clip(X[:, 2], -1.0, 1.0)
+    st = np.sqrt(np.maximum(0.0, 1.0 - ct * ct))
+    ph = np.arctan2(X[:, 1], X[:, 0])
+    P = {(0, 0): np.ones_like(ct)}
+    for m in range(1, t + 1):
+        P[(m, m)] = (np.sqrt(3.0) if m == 1 else np.sqrt((2 * m + 1) / (2 * m))) * st * P[(m - 1, m - 1)]
+    for m in range(0, t):
+        P[(m + 1, m)] = np.sqrt(2 * m + 3) * ct * P[(m, m)]
+    for m in range(0, t + 1):
+        for l in range(m + 2, t + 1):
+            a = np.sqrt((4 * l * l - 1) / (l * l - m * m))
+            b = np.sqrt(((l - 1) ** 2 - m * m) / (4 * (l - 1) ** 2 - 1))
+            P[(l, m)] = a * (ct * P[(l - 1, m)] - b * P[(l - 2, m)])
+    rows = []
+    for l in range(1, t + 1):
+        rows.append(P[(l, 0)])
+        for m in range(1, l + 1):
+            rows.append(P[(l, m)] * np.cos(m * ph))
+            rows.append(P[(l, m)] * np.sin(m * ph))
+    return np.array(rows)
+
+
+def check(inst, ans):
+    t, n = inst["t"], inst["N"]
+    X = np.array(float_matrix(ans.get("points"), n, 3, "points"))
+    nr = np.linalg.norm(X, axis=1)
+    if nr.min() < 0.5 or nr.max() > 2.0:
+        raise Invalid("points must be (approximately) unit vectors")
+    X = X / nr[:, None]
+    G = X @ X.T
+    np.fill_diagonal(G, -1.0)
+    if G.max() > 1.0 - 1e-8:
+        raise Invalid("two points coincide (or nearly: distance < 1.4e-4)")
+    dev = np.abs(harmonics(X, t).mean(axis=1)).max()
+    if not dev <= TOL:
+        raise Invalid(f"not a {t}-design: some harmonic of degree <= {t} has point average {dev:.3e} > {TOL}")
+    return None, {"max_harmonic_average": float(dev)}
diff --git a/tasks/construct-ae-p32-spherical-design-l1-s0/tests/instance.json b/tasks/construct-ae-p32-spherical-design-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca79c6abb85cacb5bee83b2aedcba9980178bff6
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"t": 7, "N": 32, "family": "ae_p32_spherical_designs", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p32-spherical-design-l1-s0/tests/run.py b/tasks/construct-ae-p32-spherical-design-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-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-p32-spherical-design-l1-s0/tests/test.sh b/tasks/construct-ae-p32-spherical-design-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-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-ae-p38-factorial-factors-l2-s1/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-p38-factorial-factors-l2-s1/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd65b9eecbe948237ee9cd45e9ebf52009d5102b
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"N": 88, "t": 25, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s1/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b31dc0f1d0741182457ef74ba7c6e8c195d0b034
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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'
+{"factors": [150, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 37, 37, 38, 38, 38, 38, 41, 41, 43, 43, 46, 46, 46, 47, 53, 59, 61, 67, 71, 73, 79, 83]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s1/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s1/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-s1/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd65b9eecbe948237ee9cd45e9ebf52009d5102b
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"N": 88, "t": 25, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s1/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-p38-factorial-factors-l2-s1/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-p38-factorial-factors-l2-s8/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-p38-factorial-factors-l2-s8/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..43f7ba50e7c9ebc82e4c8050c2ae1142df06ad4f
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"N": 139, "t": 40, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s8/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7948820a1668ca39559a1d2ce9ccf851d036092f
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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'
+{"factors": [40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 48, 49, 49, 49, 49, 49, 51, 51, 51, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 53, 53, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 59, 59, 61, 61, 62, 62, 62, 62, 67, 67, 71, 73, 74, 74, 74, 79, 81, 81, 81, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s8/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s8/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-s8/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..43f7ba50e7c9ebc82e4c8050c2ae1142df06ad4f
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"N": 139, "t": 40, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l2-s8/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-p38-factorial-factors-l2-s8/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-p38-factorial-factors-l6-s0/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-ae-p38-factorial-factors-l6-s0/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..171004f5f5a79693c29fc83d56871cd9833aed31
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"N": 5043, "t": 1631, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s0/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2f106509af6b579df0f3c92692e6ab78ca794f04
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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'
+{"factors": [4893, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1631, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1633, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1634, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1635, 1636, 1636, 1636, 1636, 1636, 1636, 1636, 1636, 1636, 1636, 1636, 1636, 1637, 1637, 1637, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 1638, 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+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s0/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s0/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-s0/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..171004f5f5a79693c29fc83d56871cd9833aed31
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"N": 5043, "t": 1631, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s0/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-ae-p38-factorial-factors-l6-s0/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-ae-p38-factorial-factors-l6-s7/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-ae-p38-factorial-factors-l6-s7/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1aad478cfd3db47aaabc974ff436d70bfcdc0274
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"N": 8731, "t": 2851, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s7/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9e63e55588ec8d4430a7ef63a6376d3759a2b40c
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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'
+{"factors": [14255, 2851, 2851, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2852, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2853, 2854, 2854, 2854, 2854, 2854, 2854, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2855, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2856, 2857, 2857, 2857, 2858, 2858, 2858, 2858, 2858, 2858, 2859, 2859, 2859, 2859, 2859, 2859, 2859, 2859, 2859, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 2860, 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+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s7/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-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-l6-s7/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1aad478cfd3db47aaabc974ff436d70bfcdc0274
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"N": 8731, "t": 2851, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l6-s7/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-ae-p38-factorial-factors-l6-s7/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-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-ae-p52-erdos-squarefree-l2-s3/environment/Dockerfile b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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-p52-erdos-squarefree-l2-s3/environment/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2b9ff90aec29b030d2a68159878b45bc8f625d2f
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/environment/instance.json
@@ -0,0 +1 @@
+{"N": 156, "t": 6, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s3/solution/solve.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6f3206b25fb9108a5347aaafc757373cd8f98f09
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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'
+{"A": [7, 32, 57, 82, 107, 132]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s3/tests/check.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..87e15b242f211059193ba122baecdee9add99130
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/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-s3/tests/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2b9ff90aec29b030d2a68159878b45bc8f625d2f
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/tests/instance.json
@@ -0,0 +1 @@
+{"N": 156, "t": 6, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s3/tests/run.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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-p52-erdos-squarefree-l2-s3/tests/test.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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-p52-erdos-squarefree-l2-s4/environment/Dockerfile b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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-p52-erdos-squarefree-l2-s4/environment/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bd6bec0d5c219c4e166dc4d46f331d7e5a359cb6
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/environment/instance.json
@@ -0,0 +1 @@
+{"N": 241, "t": 10, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s4/solution/solve.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c95aa51469178b68838c8d965c879f48484d325c
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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'
+{"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s4/tests/check.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..87e15b242f211059193ba122baecdee9add99130
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-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-l2-s4/tests/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bd6bec0d5c219c4e166dc4d46f331d7e5a359cb6
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/tests/instance.json
@@ -0,0 +1 @@
+{"N": 241, "t": 10, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l2-s4/tests/run.py b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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-p52-erdos-squarefree-l2-s4/tests/test.sh b/tasks/construct-ae-p52-erdos-squarefree-l2-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-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-mc-all-interval-l2-s1/environment/Dockerfile b/tasks/construct-mc-all-interval-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-all-interval-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-mc-all-interval-l2-s1/environment/instance.json b/tasks/construct-mc-all-interval-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..45b1c740c7ec81636f552319b1491b8ce4124236
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 10, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l2-s1/solution/solve.sh b/tasks/construct-mc-all-interval-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5526d2a3686e270c76b5cd282e8c70dbdd9c8090
--- /dev/null
+++ b/tasks/construct-mc-all-interval-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'
+{"x": [0, 9, 1, 8, 2, 7, 3, 6, 4, 5]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-all-interval-l2-s1/tests/check.py b/tasks/construct-mc-all-interval-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e39eec264b6422a47e35921b8cdbe1fa1748307
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-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-l2-s1/tests/instance.json b/tasks/construct-mc-all-interval-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..45b1c740c7ec81636f552319b1491b8ce4124236
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 10, "fixed": [], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l2-s1/tests/run.py b/tasks/construct-mc-all-interval-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-all-interval-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-mc-all-interval-l2-s1/tests/test.sh b/tasks/construct-mc-all-interval-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-all-interval-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-mc-all-interval-l6-s0/tests/run.py b/tasks/construct-mc-all-interval-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-all-interval-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-bibd-l4-s4/environment/Dockerfile b/tasks/construct-mc-bibd-l4-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-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-bibd-l4-s4/environment/instance.json b/tasks/construct-mc-bibd-l4-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..03b3ca2f50eec5ab9f2523e60288a8a4ebedbe4a
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-s4/environment/instance.json
@@ -0,0 +1 @@
+{"v": 15, "k": 3, "lambda": 2, "b": 70, "family": "mc_bibd", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-bibd-l4-s4/solution/solve.sh b/tasks/construct-mc-bibd-l4-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..24849a265e01cc8860f13dadcbb2658b9eaa6a37
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-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'
+{"blocks": [[0, 10, 13], [0, 3, 4], [2, 7, 9], [10, 13, 14], [2, 8, 14], [2, 4, 5], [0, 5, 12], [1, 4, 10], [5, 10, 12], [0, 2, 6], [8, 9, 13], [9, 12, 13], [0, 1, 9], [9, 12, 14], [4, 9, 11], [0, 4, 8], [6, 9, 14], [5, 8, 13], [0, 12, 14], [3, 8, 14], [0, 10, 11], [4, 7, 10], [7, 8, 12], [2, 3, 13], [2, 10, 12], [10, 11, 14], [0, 1, 2], [0, 7, 8], [3, 5, 8], [3, 12, 13], [5, 6, 13], [1, 4, 13], [0, 13, 14], [0, 3, 9], [2, 4, 13], [1, 2, 5], [3, 6, 10], [1, 3, 9], [4, 7, 12], [4, 5, 14], [2, 7, 14], [1, 11, 12], [2, 11, 12], [5, 6, 10], [5, 7, 9], [4, 8, 11], [6, 8, 11], [3, 7, 11], [1, 3, 5], [7, 11, 13], [3, 6, 12], [1, 8, 10], [2, 9, 10], [3, 7, 10], [2, 3, 11], [1, 6, 14], [6, 11, 13], [2, 6, 8], [1, 11, 14], [4, 6, 12], [8, 9, 10], [1, 8, 12], [4, 6, 9], [5, 9, 11], [3, 4, 14], [1, 7, 13], [5, 7, 14], [0, 5, 11], [0, 6, 7], [1, 6, 7]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-bibd-l4-s4/tests/check.py b/tasks/construct-mc-bibd-l4-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c4b5da62477026f27ff9869fe33602fcc41e2ea9
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-s4/tests/check.py
@@ -0,0 +1,25 @@
+"""Balanced incomplete block design BIBD(v, k, lambda) (MathConstraint bibd, CC-BY-4.0).
+Answer = list of b blocks; every block is a k-subset of {0..v-1}, every pair of points lies in exactly
+lambda blocks (which forces every point to lie in r blocks). Repeated blocks are allowed, as upstream
+(its 0/1 incidence-matrix model does not forbid equal columns)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    v, k, lam, b = inst["v"], inst["k"], inst["lambda"], inst["b"]
+    blocks = ans.get("blocks")
+    if not isinstance(blocks, list) or len(blocks) != b:
+        raise Invalid(f"blocks must be a list of exactly {b} blocks")
+    pair = {}
+    for B in blocks:
+        B = int_list(B, k, 0, v - 1, "block")
+        if len(set(B)) != k:
+            raise Invalid("a block contains a repeated point")
+        for p in itertools.combinations(sorted(B), 2):
+            pair[p] = pair.get(p, 0) + 1
+    for p in itertools.combinations(range(v), 2):
+        if pair.get(p, 0) != lam:
+            raise Invalid(f"points {p} lie together in {pair.get(p, 0)} blocks, need {lam}")
+    return None, {}
diff --git a/tasks/construct-mc-bibd-l4-s4/tests/instance.json b/tasks/construct-mc-bibd-l4-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..03b3ca2f50eec5ab9f2523e60288a8a4ebedbe4a
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-s4/tests/instance.json
@@ -0,0 +1 @@
+{"v": 15, "k": 3, "lambda": 2, "b": 70, "family": "mc_bibd", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-bibd-l4-s4/tests/run.py b/tasks/construct-mc-bibd-l4-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-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-bibd-l4-s4/tests/test.sh b/tasks/construct-mc-bibd-l4-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-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-costas-array-l4-s0/environment/Dockerfile b/tasks/construct-mc-costas-array-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-costas-array-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-mc-costas-array-l4-s0/environment/instance.json b/tasks/construct-mc-costas-array-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b546184b95e4774eb9a548dbcf0ecfe84f0b4239
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 16, "fixed": [], "family": "mc_costas_array", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-costas-array-l4-s0/solution/solve.sh b/tasks/construct-mc-costas-array-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..23ae670c5c978ae5058760d4f7bdea7a5625b1b2
--- /dev/null
+++ b/tasks/construct-mc-costas-array-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'
+{"x": [14, 8, 7, 10, 2, 4, 11, 12, 3, 15, 0, 6, 1, 5, 13, 9]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-costas-array-l4-s0/tests/check.py b/tasks/construct-mc-costas-array-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c86323a5b639b23787ecd4d5f358b986bbd91b6c
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l4-s0/tests/check.py
@@ -0,0 +1,22 @@
+"""Costas array of order n (MathConstraint costas_array, CC-BY-4.0). Accepts any valid array.
+Adapted from pilot/grader.py check_costas; adds the optional fixed entries (upstream partial assignment)."""
+import itertools
+
+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")
+    for name, i, v in inst.get("fixed", []):
+        if x[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    vecs = set()
+    for i, j in itertools.combinations(range(n), 2):
+        d = (j - i, x[j] - x[i])
+        if d in vecs:
+            raise Invalid(f"repeated displacement vector {d}")
+        vecs.add(d)
+    return None, {}
diff --git a/tasks/construct-mc-costas-array-l4-s0/tests/instance.json b/tasks/construct-mc-costas-array-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b546184b95e4774eb9a548dbcf0ecfe84f0b4239
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 16, "fixed": [], "family": "mc_costas_array", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-costas-array-l4-s0/tests/run.py b/tasks/construct-mc-costas-array-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-costas-array-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-mc-costas-array-l4-s0/tests/test.sh b/tasks/construct-mc-costas-array-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-costas-array-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-mc-debruijn-l5-s2/environment/Dockerfile b/tasks/construct-mc-debruijn-l5-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-debruijn-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-debruijn-l5-s2/environment/instance.json b/tasks/construct-mc-debruijn-l5-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b24c56bf19f75a78de5813ea786e1c121f81bcb7
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s2/environment/instance.json
@@ -0,0 +1 @@
+{"b": 4, "n": 5, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l5-s2/solution/solve.sh b/tasks/construct-mc-debruijn-l5-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..42ea830831a37ccb0e86e2c2313f5f8582310d2a
--- /dev/null
+++ b/tasks/construct-mc-debruijn-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": [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, 1, 3, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 3, 0, 0, 0, 3, 1, 0, 0, 0, 3, 2, 0, 0, 0, 3, 3, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 3, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 0, 1, 1, 3, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 0, 0, 1, 2, 3, 0, 0, 1, 3, 1, 0, 0, 1, 3, 2, 0, 0, 1, 3, 3, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 3, 0, 0, 2, 1, 1, 0, 0, 2, 1, 2, 0, 0, 2, 1, 3, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 3, 0, 0, 2, 3, 1, 0, 0, 2, 3, 2, 0, 0, 2, 3, 3, 0, 0, 3, 0, 1, 0, 0, 3, 0, 2, 0, 0, 3, 0, 3, 0, 0, 3, 1, 1, 0, 0, 3, 1, 2, 0, 0, 3, 1, 3, 0, 0, 3, 2, 1, 0, 0, 3, 2, 2, 0, 0, 3, 2, 3, 0, 0, 3, 3, 1, 0, 0, 3, 3, 2, 0, 0, 3, 3, 3, 0, 1, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 3, 0, 1, 0, 2, 1, 0, 1, 0, 2, 2, 0, 1, 0, 2, 3, 0, 1, 0, 3, 1, 0, 1, 0, 3, 2, 0, 1, 0, 3, 3, 0, 1, 1, 0, 2, 0, 1, 1, 0, 3, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 3, 0, 1, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 1, 2, 3, 0, 1, 1, 3, 1, 0, 1, 1, 3, 2, 0, 1, 1, 3, 3, 0, 1, 2, 0, 2, 0, 1, 2, 0, 3, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 2, 1, 3, 0, 1, 2, 2, 1, 0, 1, 2, 2, 2, 0, 1, 2, 2, 3, 0, 1, 2, 3, 1, 0, 1, 2, 3, 2, 0, 1, 2, 3, 3, 0, 1, 3, 0, 2, 0, 1, 3, 0, 3, 0, 1, 3, 1, 1, 0, 1, 3, 1, 2, 0, 1, 3, 1, 3, 0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2, 3, 0, 1, 3, 3, 1, 0, 1, 3, 3, 2, 0, 1, 3, 3, 3, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 3, 0, 2, 0, 3, 1, 0, 2, 0, 3, 2, 0, 2, 0, 3, 3, 0, 2, 1, 0, 3, 0, 2, 1, 1, 1, 0, 2, 1, 1, 2, 0, 2, 1, 1, 3, 0, 2, 1, 2, 1, 0, 2, 1, 2, 2, 0, 2, 1, 2, 3, 0, 2, 1, 3, 1, 0, 2, 1, 3, 2, 0, 2, 1, 3, 3, 0, 2, 2, 0, 3, 0, 2, 2, 1, 1, 0, 2, 2, 1, 2, 0, 2, 2, 1, 3, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 3, 0, 2, 2, 3, 1, 0, 2, 2, 3, 2, 0, 2, 2, 3, 3, 0, 2, 3, 0, 3, 0, 2, 3, 1, 1, 0, 2, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 3, 2, 1, 0, 2, 3, 2, 2, 0, 2, 3, 2, 3, 0, 2, 3, 3, 1, 0, 2, 3, 3, 2, 0, 2, 3, 3, 3, 0, 3, 0, 3, 1, 0, 3, 0, 3, 2, 0, 3, 0, 3, 3, 0, 3, 1, 1, 1, 0, 3, 1, 1, 2, 0, 3, 1, 1, 3, 0, 3, 1, 2, 1, 0, 3, 1, 2, 2, 0, 3, 1, 2, 3, 0, 3, 1, 3, 1, 0, 3, 1, 3, 2, 0, 3, 1, 3, 3, 0, 3, 2, 1, 1, 0, 3, 2, 1, 2, 0, 3, 2, 1, 3, 0, 3, 2, 2, 1, 0, 3, 2, 2, 2, 0, 3, 2, 2, 3, 0, 3, 2, 3, 1, 0, 3, 2, 3, 2, 0, 3, 2, 3, 3, 0, 3, 3, 1, 1, 0, 3, 3, 1, 2, 0, 3, 3, 1, 3, 0, 3, 3, 2, 1, 0, 3, 3, 2, 2, 0, 3, 3, 2, 3, 0, 3, 3, 3, 1, 0, 3, 3, 3, 2, 0, 3, 3, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 1, 1, 1, 3, 2, 1, 1, 1, 3, 3, 1, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2, 2, 3, 1, 1, 2, 3, 2, 1, 1, 2, 3, 3, 1, 1, 3, 1, 2, 1, 1, 3, 1, 3, 1, 1, 3, 2, 2, 1, 1, 3, 2, 3, 1, 1, 3, 3, 2, 1, 1, 3, 3, 3, 1, 2, 1, 2, 2, 1, 2, 1, 2, 3, 1, 2, 1, 3, 2, 1, 2, 1, 3, 3, 1, 2, 2, 1, 3, 1, 2, 2, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 3, 2, 1, 2, 2, 3, 3, 1, 2, 3, 1, 3, 1, 2, 3, 2, 2, 1, 2, 3, 2, 3, 1, 2, 3, 3, 2, 1, 2, 3, 3, 3, 1, 3, 1, 3, 2, 1, 3, 1, 3, 3, 1, 3, 2, 2, 2, 1, 3, 2, 2, 3, 1, 3, 2, 3, 2, 1, 3, 2, 3, 3, 1, 3, 3, 2, 2, 1, 3, 3, 2, 3, 1, 3, 3, 3, 2, 1, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-debruijn-l5-s2/tests/check.py b/tasks/construct-mc-debruijn-l5-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c9d6f0177d2b3bde8306d74939ee9704c1501a23
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-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-l5-s2/tests/instance.json b/tasks/construct-mc-debruijn-l5-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b24c56bf19f75a78de5813ea786e1c121f81bcb7
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l5-s2/tests/instance.json
@@ -0,0 +1 @@
+{"b": 4, "n": 5, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l5-s2/tests/run.py b/tasks/construct-mc-debruijn-l5-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-debruijn-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-debruijn-l5-s2/tests/test.sh b/tasks/construct-mc-debruijn-l5-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-debruijn-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-golomb-l2-s2/environment/Dockerfile b/tasks/construct-mc-golomb-l2-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-golomb-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-golomb-l2-s2/environment/instance.json b/tasks/construct-mc-golomb-l2-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2455b77a5afa7dd7d12bcf68297bd2280eda8416
--- /dev/null
+++ b/tasks/construct-mc-golomb-l2-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 8, "max_length": 34, "fixed": [], "family": "mc_golomb", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-golomb-l2-s2/solution/solve.sh b/tasks/construct-mc-golomb-l2-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6660b5c9de5f203c3584b8ee2d137377489bbfba
--- /dev/null
+++ b/tasks/construct-mc-golomb-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'
+{"marks": [0, 1, 4, 9, 15, 22, 32, 34]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-golomb-l2-s2/tests/instance.json b/tasks/construct-mc-golomb-l2-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2455b77a5afa7dd7d12bcf68297bd2280eda8416
--- /dev/null
+++ b/tasks/construct-mc-golomb-l2-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 8, "max_length": 34, "fixed": [], "family": "mc_golomb", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-golomb-l2-s2/tests/test.sh b/tasks/construct-mc-golomb-l2-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-golomb-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-golomb-l6-s3/environment/Dockerfile b/tasks/construct-mc-golomb-l6-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-golomb-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-mc-golomb-l6-s3/environment/instance.json b/tasks/construct-mc-golomb-l6-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..21443be08561a580dc5bf9ebbb51f49747d0f67e
--- /dev/null
+++ b/tasks/construct-mc-golomb-l6-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "max_length": 283, "fixed": [], "family": "mc_golomb", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-golomb-l6-s3/solution/solve.sh b/tasks/construct-mc-golomb-l6-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6089e802e811dd8766a19067b86ce5e31b03c584
--- /dev/null
+++ b/tasks/construct-mc-golomb-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'
+{"marks": [0, 1, 8, 11, 68, 77, 94, 116, 121, 156, 158, 179, 194, 208, 212, 228, 240, 253, 259, 283]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-golomb-l6-s3/tests/check.py b/tasks/construct-mc-golomb-l6-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..84aedd6e33fee7271543bfa49ab05128e23c31ee
--- /dev/null
+++ b/tasks/construct-mc-golomb-l6-s3/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-l6-s3/tests/instance.json b/tasks/construct-mc-golomb-l6-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..21443be08561a580dc5bf9ebbb51f49747d0f67e
--- /dev/null
+++ b/tasks/construct-mc-golomb-l6-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "max_length": 283, "fixed": [], "family": "mc_golomb", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-golomb-l6-s3/tests/run.py b/tasks/construct-mc-golomb-l6-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-golomb-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-mc-golomb-l6-s3/tests/test.sh b/tasks/construct-mc-golomb-l6-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-golomb-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-mc-graceful-graph-l1-s0/environment/Dockerfile b/tasks/construct-mc-graceful-graph-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-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-graceful-graph-l1-s0/environment/instance.json b/tasks/construct-mc-graceful-graph-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b983d943629a4307f52c6128eb50676c38e72420
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"k": 2, "p": 5, "num_vertices": 10, "edges": [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l1-s0/solution/solve.sh b/tasks/construct-mc-graceful-graph-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d4fabf51f4ff001400662a7aad59df8907523570
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-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'
+{"labels": [11, 6, 4, 10, 1, 2, 12, 0, 3, 13]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-graceful-graph-l1-s0/tests/check.py b/tasks/construct-mc-graceful-graph-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..f4d33af1d63c0495c3b32d34db6ae10f0fb45923
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l1-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-l1-s0/tests/instance.json b/tasks/construct-mc-graceful-graph-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b983d943629a4307f52c6128eb50676c38e72420
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"k": 2, "p": 5, "num_vertices": 10, "edges": [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l1-s0/tests/run.py b/tasks/construct-mc-graceful-graph-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-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-graceful-graph-l1-s0/tests/test.sh b/tasks/construct-mc-graceful-graph-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-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-hadamard-l1-s0/environment/Dockerfile b/tasks/construct-mc-hadamard-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-hadamard-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-hadamard-l1-s0/environment/instance.json b/tasks/construct-mc-hadamard-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..02db493d95ea61fe6dd8e4e666c9a8eb63fef9de
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 9, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l1-s0/solution/solve.sh b/tasks/construct-mc-hadamard-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0dbc66243f488ebac659659adaa1c994f5746bf4
--- /dev/null
+++ b/tasks/construct-mc-hadamard-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'
+{"x": [1, 1, 1, -1, 1, -1, 1, -1, -1], "y": [1, 1, 1, 1, -1, -1, 1, -1, -1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-hadamard-l1-s0/tests/check.py b/tasks/construct-mc-hadamard-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc4b93160fd7473dd14935db9d712e52abdd00c2
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l1-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-l1-s0/tests/instance.json b/tasks/construct-mc-hadamard-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..02db493d95ea61fe6dd8e4e666c9a8eb63fef9de
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 9, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l1-s0/tests/run.py b/tasks/construct-mc-hadamard-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-hadamard-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-hadamard-l1-s0/tests/test.sh b/tasks/construct-mc-hadamard-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-hadamard-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-langford-l1-s1/environment/Dockerfile b/tasks/construct-mc-langford-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-langford-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-langford-l1-s1/environment/instance.json b/tasks/construct-mc-langford-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..83c5de8c5e17a3067b5a3e0a959a28cc07091181
--- /dev/null
+++ b/tasks/construct-mc-langford-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 4, "fixed": [], "family": "mc_langford", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-langford-l1-s1/solution/solve.sh b/tasks/construct-mc-langford-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..53bda82734f6a10cbe045955d28bc695a56aa174
--- /dev/null
+++ b/tasks/construct-mc-langford-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": [2, 3, 4, 2, 1, 3, 1, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-langford-l1-s1/tests/check.py b/tasks/construct-mc-langford-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4672d7eacf321991933cb280d6c940f1c4a67935
--- /dev/null
+++ b/tasks/construct-mc-langford-l1-s1/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-l1-s1/tests/instance.json b/tasks/construct-mc-langford-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..83c5de8c5e17a3067b5a3e0a959a28cc07091181
--- /dev/null
+++ b/tasks/construct-mc-langford-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 4, "fixed": [], "family": "mc_langford", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-langford-l1-s1/tests/run.py b/tasks/construct-mc-langford-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-langford-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-langford-l1-s1/tests/test.sh b/tasks/construct-mc-langford-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-langford-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-langford-l5-s0/environment/Dockerfile b/tasks/construct-mc-langford-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-langford-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-langford-l5-s0/environment/instance.json b/tasks/construct-mc-langford-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f9e047cd088c18cd6591c8c063d9d494a6873eb
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 32, "fixed": [], "family": "mc_langford", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-langford-l5-s0/solution/solve.sh b/tasks/construct-mc-langford-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..998e1d88f43fd0774a6fb87aede205c232790061
--- /dev/null
+++ b/tasks/construct-mc-langford-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": [26, 21, 23, 14, 17, 13, 32, 16, 25, 20, 1, 19, 1, 22, 2, 4, 27, 2, 14, 13, 4, 31, 17, 21, 16, 15, 23, 26, 30, 28, 20, 19, 12, 29, 25, 11, 22, 24, 10, 32, 9, 15, 18, 8, 27, 12, 7, 11, 6, 10, 9, 5, 8, 31, 7, 6, 3, 5, 28, 30, 3, 18, 24, 29]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-langford-l5-s0/tests/check.py b/tasks/construct-mc-langford-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4672d7eacf321991933cb280d6c940f1c4a67935
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s0/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-s0/tests/instance.json b/tasks/construct-mc-langford-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f9e047cd088c18cd6591c8c063d9d494a6873eb
--- /dev/null
+++ b/tasks/construct-mc-langford-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 32, "fixed": [], "family": "mc_langford", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-langford-l5-s0/tests/run.py b/tasks/construct-mc-langford-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-langford-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-langford-l5-s0/tests/test.sh b/tasks/construct-mc-langford-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-langford-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-low-autocorrelation-l6-s2/environment/Dockerfile b/tasks/construct-mc-low-autocorrelation-l6-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-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-low-autocorrelation-l6-s2/environment/instance.json b/tasks/construct-mc-low-autocorrelation-l6-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6931caca515bb75c5e990d95f92bbdde2041d54b
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l6-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 60, "bound": 266, "fixed": [], "family": "mc_low_autocorrelation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-low-autocorrelation-l6-s2/solution/solve.sh b/tasks/construct-mc-low-autocorrelation-l6-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b4deee7abdfcf835c5e6ac3a0301ae83b1831777
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-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": [-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, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-low-autocorrelation-l6-s2/tests/check.py b/tasks/construct-mc-low-autocorrelation-l6-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..8456f7b1c0ff0c9fb4bc9ae5a49074c8afa7d1aa
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l6-s2/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-l6-s2/tests/instance.json b/tasks/construct-mc-low-autocorrelation-l6-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6931caca515bb75c5e990d95f92bbdde2041d54b
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l6-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 60, "bound": 266, "fixed": [], "family": "mc_low_autocorrelation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-low-autocorrelation-l6-s2/tests/run.py b/tasks/construct-mc-low-autocorrelation-l6-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-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-low-autocorrelation-l6-s2/tests/test.sh b/tasks/construct-mc-low-autocorrelation-l6-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-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-max-independent-set-l4-s7/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-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-max-independent-set-l4-s7/environment/instance.json b/tasks/construct-mc-max-independent-set-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..114404eb4999b21ea80d0010efc4b152027897fd
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 14, "edges": [[0, 1], [0, 4], [0, 6], [0, 8], [0, 17], [0, 20], [0, 27], [0, 35], [0, 40], [0, 43], [0, 45], [0, 46], [0, 47], [0, 48], [0, 50], [0, 52], [0, 57], [1, 3], [1, 4], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [1, 21], [1, 23], [1, 27], [1, 28], [1, 29], [1, 38], [1, 47], [1, 48], [1, 53], [1, 54], [1, 55], [1, 56], [1, 59], [2, 4], [2, 6], [2, 7], [2, 9], [2, 13], [2, 16], [2, 25], [2, 29], [2, 31], [2, 32], [2, 33], [2, 37], [2, 44], [2, 46], [2, 48], [2, 49], [3, 6], [3, 10], [3, 11], [3, 12], [3, 17], [3, 18], [3, 19], [3, 20], [3, 26], [3, 27], [3, 34], [3, 36], [3, 41], [3, 51], [3, 53], [4, 8], [4, 11], [4, 13], [4, 14], [4, 16], [4, 21], [4, 22], [4, 23], [4, 30], [4, 35], [4, 37], [4, 42], [4, 45], [4, 47], [4, 48], [5, 7], [5, 9], [5, 15], [5, 23], [5, 31], [5, 35], [5, 39], [5, 40], [5, 45], [5, 49], [5, 50], [5, 52], [5, 53], [5, 55], [5, 56], [5, 57], [6, 7], [6, 12], [6, 14], [6, 23], [6, 24], [6, 25], [6, 29], [6, 43], [6, 45], [6, 46], [6, 49], [6, 52], [6, 54], [7, 8], [7, 9], [7, 10], [7, 13], [7, 18], [7, 21], [7, 24], [7, 25], [7, 26], [7, 32], [7, 34], [7, 35], [7, 41], [7, 45], [7, 47], [8, 11], [8, 12], [8, 13], [8, 14], [8, 20], [8, 26], [8, 28], [8, 34], [8, 37], [8, 39], [8, 40], [8, 50], [8, 51], [8, 56], [9, 11], [9, 15], [9, 17], [9, 21], [9, 22], [9, 24], [9, 31], [9, 33], [9, 35], [9, 38], [9, 40], [9, 44], [9, 47], [9, 52], [9, 56], [9, 57], [10, 11], [10, 15], [10, 24], [10, 25], [10, 27], [10, 28], [10, 37], [10, 42], [10, 51], [10, 54], [10, 56], [11, 12], [11, 13], [11, 14], [11, 15], [11, 21], [11, 28], [11, 29], [11, 36], [11, 39], [11, 44], [11, 49], [11, 50], [11, 55], [12, 14], [12, 17], [12, 19], [12, 22], [12, 26], [12, 27], [12, 33], [12, 34], [12, 35], [12, 40], [12, 42], [12, 43], [12, 46], [12, 49], [13, 14], [13, 16], [13, 17], [13, 20], [13, 23], [13, 27], [13, 29], [13, 30], [13, 33], [13, 41], [13, 43], [13, 44], [13, 45], [13, 51], [13, 53], [13, 55], [13, 56], [13, 57], [13, 58], [14, 15], [14, 16], [14, 17], [14, 25], [14, 26], [14, 27], [14, 31], [14, 32], [14, 33], [14, 36], [14, 42], [14, 46], [14, 52], [14, 53], [14, 55], [14, 56], [14, 57], [14, 58], [14, 59], [15, 16], [15, 20], [15, 25], [15, 26], [15, 27], [15, 30], [15, 35], [15, 38], [15, 39], [15, 44], [15, 47], [15, 51], [15, 52], [15, 59], [16, 18], [16, 20], [16, 34], [16, 36], [16, 42], [16, 43], [16, 54], [16, 56], [17, 20], [17, 23], [17, 28], [17, 32], [17, 38], [17, 46], [17, 48], [17, 50], [17, 51], [17, 52], [17, 55], [18, 19], [18, 23], [18, 24], [18, 25], [18, 31], [18, 32], [18, 33], [18, 34], [18, 36], [18, 37], [18, 43], [18, 53], [19, 21], [19, 23], [19, 24], [19, 25], [19, 28], [19, 30], [19, 36], [19, 40], [19, 43], [19, 45], [19, 46], [19, 53], [19, 57], [20, 22], [20, 25], [20, 29], [20, 31], [20, 32], [20, 44], [20, 45], [20, 49], [20, 57], [20, 59], [21, 22], [21, 26], [21, 30], [21, 32], [21, 33], [21, 34], [21, 37], [21, 42], [21, 43], [21, 51], [21, 53], [21, 57], [21, 58], [21, 59], [22, 25], [22, 30], [22, 32], [22, 35], [22, 42], [23, 26], [23, 28], [23, 30], [23, 31], [23, 37], [23, 43], [23, 45], [23, 46], [23, 48], [23, 54], [23, 55], [23, 56], [23, 57], [23, 59], [24, 26], [24, 27], [24, 28], [24, 30], [24, 31], [24, 40], [24, 54], [24, 57], [24, 58], [25, 26], [25, 27], [25, 28], [25, 31], [25, 33], [25, 34], [25, 39], [25, 40], [25, 50], [25, 53], [26, 27], [26, 29], [26, 30], [26, 32], [26, 34], [26, 37], [26, 38], [26, 42], [26, 43], [26, 48], [26, 53], [26, 55], [27, 34], [27, 36], [27, 39], [27, 47], [27, 48], [27, 52], [27, 55], [27, 57], [27, 59], [28, 31], [28, 33], [28, 35], [28, 37], [28, 39], [28, 51], [28, 57], [29, 31], [29, 33], [29, 34], [29, 42], [29, 52], [30, 33], [30, 39], [30, 44], [30, 54], [31, 43], [32, 34], [32, 39], [32, 42], [32, 46], [32, 53], [32, 55], [32, 58], [33, 35], [33, 45], [33, 49], [33, 50], [33, 56], [33, 59], [34, 48], [34, 50], [34, 54], [34, 55], [34, 59], [35, 37], [35, 38], [35, 42], [35, 43], [35, 44], [35, 46], [35, 49], [35, 52], [35, 54], [35, 56], [35, 59], [36, 46], [36, 49], [36, 51], [36, 52], [36, 56], [36, 57], [37, 39], [37, 40], [37, 44], [37, 53], [37, 58], [37, 59], [38, 40], [38, 41], [38, 49], [38, 52], [39, 42], [39, 44], [39, 45], [39, 46], [39, 47], [39, 49], [39, 50], [39, 57], [39, 59], [40, 45], [40, 46], [40, 48], [40, 49], [40, 54], [40, 55], [40, 59], [41, 42], [41, 48], [41, 49], [41, 57], [42, 43], [42, 44], [42, 45], [42, 47], [42, 48], [42, 52], [43, 54], [43, 55], [43, 57], [44, 45], [44, 46], [44, 51], [44, 52], [44, 56], [44, 59], [45, 47], [45, 49], [46, 47], [46, 52], [46, 59], [47, 54], [47, 58], [48, 49], [48, 52], [48, 56], [49, 53], [49, 54], [49, 57], [50, 51], [50, 54], [50, 58], [50, 59], [51, 53], [51, 54], [51, 56], [51, 59], [52, 54], [52, 57], [53, 54], [53, 59], [54, 56], [54, 57], [55, 56], [56, 59], [58, 59]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l4-s7/solution/solve.sh b/tasks/construct-mc-max-independent-set-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a7047a5f8f137b3f41b07000b1b6112801265900
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-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'
+{"independent_set": [6, 8, 10, 16, 22, 31, 33, 38, 44, 48, 53, 55, 57, 58]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l4-s9/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l4-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-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-mc-max-independent-set-l4-s9/environment/instance.json b/tasks/construct-mc-max-independent-set-l4-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..83f16c72c04ad8cd23e7e045a590f6b14b305f99
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 14, "edges": [[0, 7], [0, 11], [0, 13], [0, 17], [0, 34], [0, 35], [0, 38], [0, 41], [0, 42], [0, 47], [0, 48], [0, 53], [0, 56], [0, 57], [1, 4], [1, 9], [1, 10], [1, 14], [1, 19], [1, 26], [1, 28], [1, 29], [1, 34], [1, 43], [1, 45], [1, 46], [1, 48], [1, 50], [1, 54], [2, 4], [2, 6], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 16], [2, 20], [2, 21], [2, 23], [2, 24], [2, 25], [2, 28], [2, 29], [2, 33], [2, 39], [2, 40], [2, 41], [2, 44], [2, 56], [3, 5], [3, 6], [3, 16], [3, 18], [3, 20], [3, 21], [3, 38], [3, 39], [3, 40], [3, 45], [3, 47], [3, 50], [3, 51], [3, 56], [3, 59], [4, 5], [4, 6], [4, 9], [4, 10], [4, 12], [4, 14], [4, 18], [4, 19], [4, 25], [4, 33], [4, 34], [4, 35], [4, 42], [4, 43], [4, 52], [4, 55], [5, 7], [5, 13], [5, 14], [5, 15], [5, 18], [5, 24], [5, 25], [5, 27], [5, 31], [5, 37], [5, 38], [5, 39], [5, 47], [5, 50], [5, 56], [5, 59], [6, 9], [6, 13], [6, 15], [6, 16], [6, 18], [6, 25], [6, 29], [6, 34], [6, 36], [6, 38], [6, 39], [6, 42], [6, 46], [6, 51], [6, 52], [7, 8], [7, 9], [7, 10], [7, 15], [7, 19], [7, 23], [7, 27], [7, 33], [7, 38], [7, 44], [7, 53], [7, 54], [8, 11], [8, 13], [8, 17], [8, 20], [8, 26], [8, 33], [8, 35], [8, 36], [8, 40], [8, 41], [8, 42], [8, 46], [8, 48], [8, 49], [8, 52], [8, 53], [9, 10], [9, 11], [9, 16], [9, 19], [9, 26], [9, 33], [9, 36], [9, 42], [9, 48], [9, 49], [9, 52], [9, 53], [9, 54], [9, 58], [10, 12], [10, 15], [10, 16], [10, 17], [10, 21], [10, 22], [10, 26], [10, 29], [10, 34], [10, 38], [10, 39], [10, 41], [10, 42], [10, 43], [10, 44], [10, 45], [10, 51], [10, 52], [10, 56], [10, 57], [10, 59], [11, 12], [11, 17], [11, 20], [11, 25], [11, 26], [11, 27], [11, 34], [11, 36], [11, 39], [11, 40], [11, 41], [11, 45], [11, 49], [11, 53], [11, 55], [11, 57], [11, 58], [11, 59], [12, 15], [12, 23], [12, 24], [12, 26], [12, 31], [12, 33], [12, 35], [12, 41], [12, 44], [12, 50], [12, 54], [12, 55], [12, 56], [12, 57], [12, 58], [13, 15], [13, 19], [13, 21], [13, 23], [13, 25], [13, 27], [13, 30], [13, 31], [13, 40], [13, 46], [13, 47], [13, 53], [13, 54], [13, 58], [14, 19], [14, 27], [14, 34], [14, 35], [14, 36], [14, 40], [14, 45], [14, 47], [14, 48], [14, 51], [14, 53], [14, 54], [14, 56], [14, 59], [15, 23], [15, 26], [15, 29], [15, 31], [15, 32], [15, 37], [15, 39], [15, 41], [15, 44], [15, 45], [15, 46], [15, 49], [15, 53], [15, 55], [15, 59], [16, 23], [16, 24], [16, 27], [16, 36], [16, 40], [16, 41], [16, 43], [16, 46], [16, 50], [16, 54], [17, 18], [17, 19], [17, 23], [17, 27], [17, 29], [17, 31], [17, 42], [17, 44], [17, 49], [17, 55], [17, 57], [17, 59], [18, 23], [18, 25], [18, 32], [18, 33], [18, 36], [18, 40], [18, 41], [18, 48], [18, 51], [18, 54], [19, 21], [19, 24], [19, 31], [19, 32], [19, 37], [19, 38], [19, 39], [19, 43], [19, 44], [19, 45], [19, 49], [19, 50], [19, 52], [19, 53], [19, 54], [19, 59], [20, 26], [20, 34], [20, 36], [20, 48], [20, 54], [20, 58], [21, 24], [21, 27], [21, 32], [21, 35], [21, 41], [21, 44], [21, 50], [21, 51], [22, 24], [22, 27], [22, 29], [22, 31], [22, 36], [22, 40], [22, 41], [22, 43], [22, 45], [23, 33], [23, 35], [23, 38], [23, 41], [23, 47], [23, 48], [23, 51], [23, 52], [23, 58], [24, 28], [24, 30], [24, 31], [24, 33], [24, 52], [24, 54], [25, 28], [25, 34], [25, 37], [25, 38], [25, 43], [25, 45], [25, 46], [25, 53], [25, 54], [25, 55], [26, 37], [26, 40], [26, 41], [26, 43], [26, 45], [26, 46], [26, 47], [26, 48], [26, 52], [26, 53], [26, 55], [26, 56], [27, 29], [27, 33], [27, 36], [27, 43], [27, 45], [27, 47], [27, 48], [27, 51], [27, 52], [27, 54], [27, 56], [28, 32], [28, 33], [28, 34], [28, 35], [28, 36], [28, 37], [28, 38], [28, 40], [28, 41], [28, 43], [28, 44], [28, 46], [28, 48], [28, 54], [28, 56], [29, 34], [29, 42], [29, 43], [29, 44], [29, 53], [29, 58], [30, 37], [30, 38], [30, 42], [30, 43], [30, 46], [30, 53], [31, 35], [31, 38], [31, 40], [31, 41], [31, 44], [31, 46], [31, 47], [31, 50], [31, 51], [31, 59], [32, 33], [32, 37], [32, 38], [32, 40], [32, 42], [32, 49], [32, 50], [32, 54], [32, 55], [32, 56], [32, 57], [33, 34], [33, 35], [33, 41], [33, 44], [33, 47], [33, 52], [33, 53], [34, 41], [34, 42], [34, 46], [34, 47], [34, 49], [34, 55], [34, 57], [35, 39], [35, 44], [35, 45], [35, 47], [35, 49], [35, 51], [35, 56], [35, 59], [36, 39], [36, 40], [36, 41], [36, 42], [36, 43], [36, 49], [36, 50], [36, 51], [36, 59], [37, 40], [37, 45], [37, 48], [37, 49], [37, 50], [37, 54], [37, 58], [38, 39], [38, 41], [38, 43], [38, 44], [38, 49], [38, 54], [38, 57], [38, 58], [39, 50], [39, 53], [39, 58], [39, 59], [40, 43], [40, 46], [40, 51], [40, 52], [41, 47], [41, 49], [41, 52], [41, 58], [41, 59], [42, 44], [42, 45], [42, 47], [42, 49], [42, 50], [42, 51], [42, 59], [43, 49], [43, 51], [43, 53], [43, 56], [43, 59], [44, 47], [44, 49], [44, 52], [44, 53], [44, 54], [44, 55], [44, 56], [45, 49], [45, 50], [45, 51], [45, 52], [45, 54], [45, 56], [45, 58], [45, 59], [46, 47], [46, 51], [46, 52], [46, 54], [46, 55], [47, 48], [47, 53], [48, 53], [48, 56], [48, 57], [49, 52], [49, 58], [50, 52], [50, 55], [50, 59], [52, 57], [52, 58], [52, 59], [53, 56], [55, 56], [55, 59], [56, 59], [57, 58], [57, 59]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l4-s9/solution/solve.sh b/tasks/construct-mc-max-independent-set-l4-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2f45ab30b809400ffc00099e28ea37157113381e
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-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'
+{"independent_set": [7, 14, 16, 18, 20, 21, 28, 29, 30, 31, 39, 49, 55, 57]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l4-s9/tests/check.py b/tasks/construct-mc-max-independent-set-l4-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s9/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-s9/tests/instance.json b/tasks/construct-mc-max-independent-set-l4-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..83f16c72c04ad8cd23e7e045a590f6b14b305f99
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l4-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 14, "edges": [[0, 7], [0, 11], [0, 13], [0, 17], [0, 34], [0, 35], [0, 38], [0, 41], [0, 42], [0, 47], [0, 48], [0, 53], [0, 56], [0, 57], [1, 4], [1, 9], [1, 10], [1, 14], [1, 19], [1, 26], [1, 28], [1, 29], [1, 34], [1, 43], [1, 45], [1, 46], [1, 48], [1, 50], [1, 54], [2, 4], [2, 6], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 16], [2, 20], [2, 21], [2, 23], [2, 24], [2, 25], [2, 28], [2, 29], [2, 33], [2, 39], [2, 40], [2, 41], [2, 44], [2, 56], [3, 5], [3, 6], [3, 16], [3, 18], [3, 20], [3, 21], [3, 38], [3, 39], [3, 40], [3, 45], [3, 47], [3, 50], [3, 51], [3, 56], [3, 59], [4, 5], [4, 6], [4, 9], [4, 10], [4, 12], [4, 14], [4, 18], [4, 19], [4, 25], [4, 33], [4, 34], [4, 35], [4, 42], [4, 43], [4, 52], [4, 55], [5, 7], [5, 13], [5, 14], [5, 15], [5, 18], [5, 24], [5, 25], [5, 27], [5, 31], [5, 37], [5, 38], [5, 39], [5, 47], [5, 50], [5, 56], [5, 59], [6, 9], [6, 13], [6, 15], [6, 16], [6, 18], [6, 25], [6, 29], [6, 34], [6, 36], [6, 38], [6, 39], [6, 42], [6, 46], [6, 51], [6, 52], [7, 8], [7, 9], [7, 10], [7, 15], [7, 19], [7, 23], [7, 27], [7, 33], [7, 38], [7, 44], [7, 53], [7, 54], [8, 11], [8, 13], [8, 17], [8, 20], [8, 26], [8, 33], [8, 35], [8, 36], [8, 40], [8, 41], [8, 42], [8, 46], [8, 48], [8, 49], [8, 52], [8, 53], [9, 10], [9, 11], [9, 16], [9, 19], [9, 26], [9, 33], [9, 36], [9, 42], [9, 48], [9, 49], [9, 52], [9, 53], [9, 54], [9, 58], [10, 12], [10, 15], [10, 16], [10, 17], [10, 21], [10, 22], [10, 26], [10, 29], [10, 34], [10, 38], [10, 39], [10, 41], [10, 42], [10, 43], [10, 44], [10, 45], [10, 51], [10, 52], [10, 56], [10, 57], [10, 59], [11, 12], [11, 17], [11, 20], [11, 25], [11, 26], [11, 27], [11, 34], [11, 36], [11, 39], [11, 40], [11, 41], [11, 45], [11, 49], [11, 53], [11, 55], [11, 57], [11, 58], [11, 59], [12, 15], [12, 23], [12, 24], [12, 26], [12, 31], [12, 33], [12, 35], [12, 41], [12, 44], [12, 50], [12, 54], [12, 55], [12, 56], [12, 57], [12, 58], [13, 15], [13, 19], [13, 21], [13, 23], [13, 25], [13, 27], [13, 30], [13, 31], [13, 40], [13, 46], [13, 47], [13, 53], [13, 54], [13, 58], [14, 19], [14, 27], [14, 34], [14, 35], [14, 36], [14, 40], [14, 45], [14, 47], [14, 48], [14, 51], [14, 53], [14, 54], [14, 56], [14, 59], [15, 23], [15, 26], [15, 29], [15, 31], [15, 32], [15, 37], [15, 39], [15, 41], [15, 44], [15, 45], [15, 46], [15, 49], [15, 53], [15, 55], [15, 59], [16, 23], [16, 24], [16, 27], [16, 36], [16, 40], [16, 41], [16, 43], [16, 46], [16, 50], [16, 54], [17, 18], [17, 19], [17, 23], [17, 27], [17, 29], [17, 31], [17, 42], [17, 44], [17, 49], [17, 55], [17, 57], [17, 59], [18, 23], [18, 25], [18, 32], [18, 33], [18, 36], [18, 40], [18, 41], [18, 48], [18, 51], [18, 54], [19, 21], [19, 24], [19, 31], [19, 32], [19, 37], [19, 38], [19, 39], [19, 43], [19, 44], [19, 45], [19, 49], [19, 50], [19, 52], [19, 53], [19, 54], [19, 59], [20, 26], [20, 34], [20, 36], [20, 48], [20, 54], [20, 58], [21, 24], [21, 27], [21, 32], [21, 35], [21, 41], [21, 44], [21, 50], [21, 51], [22, 24], [22, 27], [22, 29], [22, 31], [22, 36], [22, 40], [22, 41], [22, 43], [22, 45], [23, 33], [23, 35], [23, 38], [23, 41], [23, 47], [23, 48], [23, 51], [23, 52], [23, 58], [24, 28], [24, 30], [24, 31], [24, 33], [24, 52], [24, 54], [25, 28], [25, 34], [25, 37], [25, 38], [25, 43], [25, 45], [25, 46], [25, 53], [25, 54], [25, 55], [26, 37], [26, 40], [26, 41], [26, 43], [26, 45], [26, 46], [26, 47], [26, 48], [26, 52], [26, 53], [26, 55], [26, 56], [27, 29], [27, 33], [27, 36], [27, 43], [27, 45], [27, 47], [27, 48], [27, 51], [27, 52], [27, 54], [27, 56], [28, 32], [28, 33], [28, 34], [28, 35], [28, 36], [28, 37], [28, 38], [28, 40], [28, 41], [28, 43], [28, 44], [28, 46], [28, 48], [28, 54], [28, 56], [29, 34], [29, 42], [29, 43], [29, 44], [29, 53], [29, 58], [30, 37], [30, 38], [30, 42], [30, 43], [30, 46], [30, 53], [31, 35], [31, 38], [31, 40], [31, 41], [31, 44], [31, 46], [31, 47], [31, 50], [31, 51], [31, 59], [32, 33], [32, 37], [32, 38], [32, 40], [32, 42], [32, 49], [32, 50], [32, 54], [32, 55], [32, 56], [32, 57], [33, 34], [33, 35], [33, 41], [33, 44], [33, 47], [33, 52], [33, 53], [34, 41], [34, 42], [34, 46], [34, 47], [34, 49], [34, 55], [34, 57], [35, 39], [35, 44], [35, 45], [35, 47], [35, 49], [35, 51], [35, 56], [35, 59], [36, 39], [36, 40], [36, 41], [36, 42], [36, 43], [36, 49], [36, 50], [36, 51], [36, 59], [37, 40], [37, 45], [37, 48], [37, 49], [37, 50], [37, 54], [37, 58], [38, 39], [38, 41], [38, 43], [38, 44], [38, 49], [38, 54], [38, 57], [38, 58], [39, 50], [39, 53], [39, 58], [39, 59], [40, 43], [40, 46], [40, 51], [40, 52], [41, 47], [41, 49], [41, 52], [41, 58], [41, 59], [42, 44], [42, 45], [42, 47], [42, 49], [42, 50], [42, 51], [42, 59], [43, 49], [43, 51], [43, 53], [43, 56], [43, 59], [44, 47], [44, 49], [44, 52], [44, 53], [44, 54], [44, 55], [44, 56], [45, 49], [45, 50], [45, 51], [45, 52], [45, 54], [45, 56], [45, 58], [45, 59], [46, 47], [46, 51], [46, 52], [46, 54], [46, 55], [47, 48], [47, 53], [48, 53], [48, 56], [48, 57], [49, 52], [49, 58], [50, 52], [50, 55], [50, 59], [52, 57], [52, 58], [52, 59], [53, 56], [55, 56], [55, 59], [56, 59], [57, 58], [57, 59]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l4-s9/tests/run.py b/tasks/construct-mc-max-independent-set-l4-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-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-mc-max-independent-set-l4-s9/tests/test.sh b/tasks/construct-mc-max-independent-set-l4-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-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-mc-non-transitive-dice-l1-s1/environment/Dockerfile b/tasks/construct-mc-non-transitive-dice-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-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-non-transitive-dice-l1-s1/environment/instance.json b/tasks/construct-mc-non-transitive-dice-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ef934edb43c8e0fd57d11528b75dbc08ddfb81c4
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 3, "m": 4, "family": "mc_non_transitive_dice", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-non-transitive-dice-l1-s1/solution/solve.sh b/tasks/construct-mc-non-transitive-dice-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bf596093cf93496b5daf2e6769de9986e6a78794
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-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'
+{"dice": [[0, 4, 5, 5], [2, 3, 3, 7], [0, 2, 6, 6]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-non-transitive-dice-l1-s1/tests/check.py b/tasks/construct-mc-non-transitive-dice-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3d5c04fa6e2819bf32f34fafe13a383437dc62a
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-l1-s1/tests/check.py
@@ -0,0 +1,18 @@
+"""Cyclically intransitive dice (MathConstraint non_transitive_dice, CC-BY-4.0): n dice with m faces in
+0..2m-1; die i beats die (i+1) mod n, i.e. #{(a, b): face_i(a) > face_{i+1}(b)} > floor(m^2 / 2).
+Face order is irrelevant (upstream additionally demanded sorted faces as a symmetry break; not required)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, m = inst["n"], inst["m"]
+    D = ans.get("dice")
+    if not isinstance(D, list) or len(D) != n:
+        raise Invalid(f"dice must be a list of {n} dice")
+    D = [int_list(d, m, 0, 2 * m - 1, "die") for d in D]
+    for i in range(n):
+        A, B = D[i], D[(i + 1) % n]
+        w = sum(1 for a in A for b in B if a > b)
+        if w <= m * m // 2:
+            raise Invalid(f"die {i} wins only {w} of {m * m} face pairs against die {(i + 1) % n}")
+    return None, {}
diff --git a/tasks/construct-mc-non-transitive-dice-l1-s1/tests/instance.json b/tasks/construct-mc-non-transitive-dice-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ef934edb43c8e0fd57d11528b75dbc08ddfb81c4
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 3, "m": 4, "family": "mc_non_transitive_dice", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-non-transitive-dice-l1-s1/tests/run.py b/tasks/construct-mc-non-transitive-dice-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-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-non-transitive-dice-l1-s1/tests/test.sh b/tasks/construct-mc-non-transitive-dice-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-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-number-partitioning-l1-s2/environment/Dockerfile b/tasks/construct-mc-number-partitioning-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-number-partitioning-l1-s2/environment/instance.json b/tasks/construct-mc-number-partitioning-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cbc3fbd204488953ea58ddd480649be60f977459
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "k": 3, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l1-s2/solution/solve.sh b/tasks/construct-mc-number-partitioning-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..97ff1c2607b28f3f12fbf9dbbb76dae4d86dc279
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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'
+{"x": [0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-number-partitioning-l1-s2/tests/check.py b/tasks/construct-mc-number-partitioning-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..67793721db8ba7d3c3979ea0e1e07091491ffa7e
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l1-s2/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-l1-s2/tests/instance.json b/tasks/construct-mc-number-partitioning-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cbc3fbd204488953ea58ddd480649be60f977459
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "k": 3, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l1-s2/tests/run.py b/tasks/construct-mc-number-partitioning-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-number-partitioning-l1-s2/tests/test.sh b/tasks/construct-mc-number-partitioning-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-number-partitioning-l1-s5/environment/Dockerfile b/tasks/construct-mc-number-partitioning-l1-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-mc-number-partitioning-l1-s5/environment/instance.json b/tasks/construct-mc-number-partitioning-l1-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cbed04ac364398dd1f7e7f4cdfead1bf3351d293
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l1-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 11, "k": 6, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l1-s5/solution/solve.sh b/tasks/construct-mc-number-partitioning-l1-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..81b1921e1f87ac82b6bf2ffc23e80155715c2c77
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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'
+{"x": [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-number-partitioning-l1-s5/tests/check.py b/tasks/construct-mc-number-partitioning-l1-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..67793721db8ba7d3c3979ea0e1e07091491ffa7e
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l1-s5/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-l1-s5/tests/instance.json b/tasks/construct-mc-number-partitioning-l1-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cbed04ac364398dd1f7e7f4cdfead1bf3351d293
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l1-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 11, "k": 6, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l1-s5/tests/run.py b/tasks/construct-mc-number-partitioning-l1-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-mc-number-partitioning-l1-s5/tests/test.sh b/tasks/construct-mc-number-partitioning-l1-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-mc-number-partitioning-l5-s3/environment/Dockerfile b/tasks/construct-mc-number-partitioning-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-number-partitioning-l5-s3/environment/instance.json b/tasks/construct-mc-number-partitioning-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4705bf67be74493d63d94aaec4d39592cbd8c524
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 6, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l5-s3/solution/solve.sh b/tasks/construct-mc-number-partitioning-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..107e61c6c02946c9909be6c713dc407b01491cdd
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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": [0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-number-partitioning-l5-s3/tests/check.py b/tasks/construct-mc-number-partitioning-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..67793721db8ba7d3c3979ea0e1e07091491ffa7e
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l5-s3/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-l5-s3/tests/instance.json b/tasks/construct-mc-number-partitioning-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4705bf67be74493d63d94aaec4d39592cbd8c524
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 6, "family": "mc_number_partitioning", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-number-partitioning-l5-s3/tests/run.py b/tasks/construct-mc-number-partitioning-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-number-partitioning-l5-s3/tests/test.sh b/tasks/construct-mc-number-partitioning-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-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-ortholatin-l3-s2/environment/Dockerfile b/tasks/construct-mc-ortholatin-l3-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-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-mc-ortholatin-l3-s2/environment/instance.json b/tasks/construct-mc-ortholatin-l3-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..34981d7778859d1666730f0790ef1f52062ce9a7
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l3-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 11, "family": "mc_ortholatin", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ortholatin-l3-s2/solution/solve.sh b/tasks/construct-mc-ortholatin-l3-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..811b221f1f45dea9d89fdd7311a28ab4c53ae28c
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-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'
+{"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], "Y": [[0, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9], [1, 3, 5, 7, 9, 0, 2, 4, 6, 8, 10], [2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 0], [3, 5, 7, 9, 0, 2, 4, 6, 8, 10, 1], [4, 6, 8, 10, 1, 3, 5, 7, 9, 0, 2], [5, 7, 9, 0, 2, 4, 6, 8, 10, 1, 3], [6, 8, 10, 1, 3, 5, 7, 9, 0, 2, 4], [7, 9, 0, 2, 4, 6, 8, 10, 1, 3, 5], [8, 10, 1, 3, 5, 7, 9, 0, 2, 4, 6], [9, 0, 2, 4, 6, 8, 10, 1, 3, 5, 7], [10, 1, 3, 5, 7, 9, 0, 2, 4, 6, 8]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ortholatin-l3-s2/tests/check.py b/tasks/construct-mc-ortholatin-l3-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5418a59fae1c86318eee903e90d75b36d8a3306
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l3-s2/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-l3-s2/tests/instance.json b/tasks/construct-mc-ortholatin-l3-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..34981d7778859d1666730f0790ef1f52062ce9a7
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l3-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 11, "family": "mc_ortholatin", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ortholatin-l3-s2/tests/run.py b/tasks/construct-mc-ortholatin-l3-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-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-mc-ortholatin-l3-s2/tests/test.sh b/tasks/construct-mc-ortholatin-l3-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-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-mc-pysms-chromatic-girth-l3-s2/environment/Dockerfile b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-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-mc-pysms-chromatic-girth-l3-s2/environment/instance.json b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d8464ae9ffa315a791d7ea95f16efa1fdead8884
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 14, "required_edges": [], "max_chromatic_number": 3, "min_edges": 20, "min_girth": 6, "family": "mc_pysms_chromatic_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l3-s2/solution/solve.sh b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f082ac108da7d325ef0b27338e2a6d2c35d155c9
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-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'
+{"edges": [[0, 11], [0, 12], [0, 13], [1, 9], [1, 10], [1, 13], [2, 8], [2, 10], [2, 12], [3, 8], [3, 9], [3, 11], [4, 7], [4, 10], [4, 11], [5, 7], [5, 9], [5, 12], [6, 7], [6, 8], [6, 13]], "coloring": [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l3-s2/tests/check.py b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l3-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-chromatic-girth-l3-s2/tests/instance.json b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d8464ae9ffa315a791d7ea95f16efa1fdead8884
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 14, "required_edges": [], "max_chromatic_number": 3, "min_edges": 20, "min_girth": 6, "family": "mc_pysms_chromatic_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l3-s2/tests/run.py b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-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-mc-pysms-chromatic-girth-l3-s2/tests/test.sh b/tasks/construct-mc-pysms-chromatic-girth-l3-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-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-mc-pysms-girth-degree-l4-s1/environment/Dockerfile b/tasks/construct-mc-pysms-girth-degree-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-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-pysms-girth-degree-l4-s1/environment/instance.json b/tasks/construct-mc-pysms-girth-degree-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9918748ec79b0715779522be8a2378030e1e3caf
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 23, "required_edges": [], "max_degree": 6, "min_degree": 3, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-girth-degree-l4-s1/solution/solve.sh b/tasks/construct-mc-pysms-girth-degree-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ea107ef130e98288b5f664141e2338db5b8e903b
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-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'
+{"edges": [[0, 20], [0, 21], [0, 22], [1, 18], [1, 19], [1, 22], [2, 17], [2, 19], [2, 21], [3, 15], [3, 16], [3, 22], [4, 14], [4, 16], [4, 21], [5, 13], [5, 16], [5, 19], [5, 20], [6, 13], [6, 15], [6, 17], [7, 13], [7, 14], [7, 18], [8, 12], [8, 15], [8, 18], [9, 11], [9, 14], [9, 17], [9, 22], [10, 11], [10, 13], [10, 21], [11, 12], [12, 20]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-girth-degree-l4-s1/tests/check.py b/tasks/construct-mc-pysms-girth-degree-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l4-s1/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-l4-s1/tests/instance.json b/tasks/construct-mc-pysms-girth-degree-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9918748ec79b0715779522be8a2378030e1e3caf
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 23, "required_edges": [], "max_degree": 6, "min_degree": 3, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-girth-degree-l4-s1/tests/run.py b/tasks/construct-mc-pysms-girth-degree-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-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-pysms-girth-degree-l4-s1/tests/test.sh b/tasks/construct-mc-pysms-girth-degree-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-girth-degree-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-pysms-independent-connectivity-l4-s1/environment/Dockerfile b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-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-pysms-independent-connectivity-l4-s1/environment/instance.json b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b638b2057f606ed58128d9f6e3899d7d8e2b7bc5
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 15, "required_edges": [[2, 5], [8, 11], [0, 2], [5, 9], [2, 10], [2, 11], [4, 13], [7, 14], [2, 13], [11, 14], [4, 6], [9, 10], [4, 14], [12, 13], [3, 4], [0, 7], [1, 5], [2, 3], [5, 8], [11, 12], [7, 10]], "max_independent_set": 4, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l4-s1/solution/solve.sh b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..202381af71f4ba7b8da0d1a923832175f9607239
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-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'
+{"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], [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], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [10, 11], [10, 12], [10, 13], [10, 14], [11, 12], [11, 13], [11, 14], [12, 13], [12, 14], [13, 14]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l4-s1/tests/check.py b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/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-independent-connectivity-l4-s1/tests/instance.json b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b638b2057f606ed58128d9f6e3899d7d8e2b7bc5
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 15, "required_edges": [[2, 5], [8, 11], [0, 2], [5, 9], [2, 10], [2, 11], [4, 13], [7, 14], [2, 13], [11, 14], [4, 6], [9, 10], [4, 14], [12, 13], [3, 4], [0, 7], [1, 5], [2, 3], [5, 8], [11, 12], [7, 10]], "max_independent_set": 4, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l4-s1/tests/run.py b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-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-pysms-independent-connectivity-l4-s1/tests/test.sh b/tasks/construct-mc-pysms-independent-connectivity-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-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-pysms-min-girth-l4-s0/environment/Dockerfile b/tasks/construct-mc-pysms-min-girth-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-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-mc-pysms-min-girth-l4-s0/environment/instance.json b/tasks/construct-mc-pysms-min-girth-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a7940a9f15a57dfbd83c6171df60cca91fe79e8f
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 14, "required_edges": [[9, 13], [4, 13]], "min_girth": 6, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s0/solution/solve.sh b/tasks/construct-mc-pysms-min-girth-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1c4371614072d14124a1ea07a224f5e6ac83f8d9
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-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'
+{"edges": [[0, 13], [1, 13], [2, 13], [3, 13], [4, 13], [5, 13], [6, 13], [7, 13], [8, 13], [9, 13], [10, 13], [11, 13], [12, 13]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s0/tests/check.py b/tasks/construct-mc-pysms-min-girth-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-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-girth-l4-s0/tests/instance.json b/tasks/construct-mc-pysms-min-girth-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a7940a9f15a57dfbd83c6171df60cca91fe79e8f
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 14, "required_edges": [[9, 13], [4, 13]], "min_girth": 6, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l4-s0/tests/run.py b/tasks/construct-mc-pysms-min-girth-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-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-mc-pysms-min-girth-l4-s0/tests/test.sh b/tasks/construct-mc-pysms-min-girth-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-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-mc-pysms-num-edges-bounds-l2-s0/environment/Dockerfile b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-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-num-edges-bounds-l2-s0/environment/instance.json b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..106d3ae88c0bb3d074a6f853254ad6dbf41653ef
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 11, "required_edges": [[1, 9], [2, 9], [6, 9], [3, 10], [5, 7], [2, 8], [7, 9], [4, 6]], "max_edges": 43, "min_edges": 32, "family": "mc_pysms_num_edges_bounds", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/solution/solve.sh b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..59583aed544d91f3e6aabdd7a51d78983946578f
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-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, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [5, 6], [5, 7], [5, 8], [5, 10], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9], [9, 10]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/tests/check.py b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-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-num-edges-bounds-l2-s0/tests/instance.json b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..106d3ae88c0bb3d074a6f853254ad6dbf41653ef
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 11, "required_edges": [[1, 9], [2, 9], [6, 9], [3, 10], [5, 7], [2, 8], [7, 9], [4, 6]], "max_edges": 43, "min_edges": 32, "family": "mc_pysms_num_edges_bounds", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/tests/run.py b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-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-num-edges-bounds-l2-s0/tests/test.sh b/tasks/construct-mc-pysms-num-edges-bounds-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-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-ramsey-l4-s0/environment/Dockerfile b/tasks/construct-mc-ramsey-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-mc-ramsey-l4-s0/environment/instance.json b/tasks/construct-mc-ramsey-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc8ee4a92c5a25d8d578135453441672dd8b3445
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 21, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s0/solution/solve.sh b/tasks/construct-mc-ramsey-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..037a1c19944cd11e36ca6e6da6f320eca2d4a304
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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'
+{"colors": [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 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-s0/tests/check.py b/tasks/construct-mc-ramsey-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s0/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-s0/tests/instance.json b/tasks/construct-mc-ramsey-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc8ee4a92c5a25d8d578135453441672dd8b3445
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 21, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s0/tests/run.py b/tasks/construct-mc-ramsey-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-mc-ramsey-l4-s0/tests/test.sh b/tasks/construct-mc-ramsey-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-mc-ramsey-l4-s7/environment/Dockerfile b/tasks/construct-mc-ramsey-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-ramsey-l4-s7/environment/instance.json b/tasks/construct-mc-ramsey-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..54b2550054d1e05c340a9570c33fcecaafdf1bd1
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "r": 5, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s7/solution/solve.sh b/tasks/construct-mc-ramsey-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..eb2466adc65e66c455a698ce8dd49da29da5b356
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ramsey-l4-s7/tests/check.py b/tasks/construct-mc-ramsey-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s7/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-s7/tests/instance.json b/tasks/construct-mc-ramsey-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..54b2550054d1e05c340a9570c33fcecaafdf1bd1
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "r": 5, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s7/tests/run.py b/tasks/construct-mc-ramsey-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-ramsey-l4-s7/tests/test.sh b/tasks/construct-mc-ramsey-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-ramsey-l4-s9/environment/Dockerfile b/tasks/construct-mc-ramsey-l4-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-mc-ramsey-l4-s9/environment/instance.json b/tasks/construct-mc-ramsey-l4-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ed30ac9064d99f69b6e6b41acbaf3356e88ab5e4
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s9/solution/solve.sh b/tasks/construct-mc-ramsey-l4-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5d601e837cc9b96a08da3773cd9afa3c0a087d74
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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'
+{"colors": [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 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-s9/tests/check.py b/tasks/construct-mc-ramsey-l4-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s9/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-s9/tests/instance.json b/tasks/construct-mc-ramsey-l4-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ed30ac9064d99f69b6e6b41acbaf3356e88ab5e4
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l4-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l4-s9/tests/run.py b/tasks/construct-mc-ramsey-l4-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-mc-ramsey-l4-s9/tests/test.sh b/tasks/construct-mc-ramsey-l4-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-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-mc-social-golfers-l1-s2/environment/Dockerfile b/tasks/construct-mc-social-golfers-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-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-social-golfers-l1-s2/environment/instance.json b/tasks/construct-mc-social-golfers-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4b78d8c0d3e30a2c58023468e6174f1ae5bb68be
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n_groups": 4, "group_size": 4, "n_weeks": 3, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l1-s2/solution/solve.sh b/tasks/construct-mc-social-golfers-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5746a4e16e4847545ae6476a7545fa1597d764fe
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-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'
+{"schedule": [[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [0, 1, 2, 3, 1, 0, 3, 2, 2, 3, 0, 1, 3, 2, 1, 0], [0, 1, 2, 3, 2, 3, 0, 1, 3, 2, 1, 0, 1, 0, 3, 2]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-social-golfers-l1-s2/tests/check.py b/tasks/construct-mc-social-golfers-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..73977815b7b6094a8491075b6dc2ae1293e44930
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l1-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-l1-s2/tests/instance.json b/tasks/construct-mc-social-golfers-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4b78d8c0d3e30a2c58023468e6174f1ae5bb68be
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n_groups": 4, "group_size": 4, "n_weeks": 3, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l1-s2/tests/run.py b/tasks/construct-mc-social-golfers-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-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-social-golfers-l1-s2/tests/test.sh b/tasks/construct-mc-social-golfers-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-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-vertex-cover-l5-s2/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l5-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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-vertex-cover-l5-s2/environment/instance.json b/tasks/construct-mc-vertex-cover-l5-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d82bc9345dd99912245e614595c7eb034d21ac1d
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 4], [0, 15], [0, 20], [0, 23], [0, 43], [0, 48], [0, 56], [0, 59], [0, 65], [0, 66], [0, 71], [0, 79], [0, 80], [0, 81], [0, 84], [0, 86], [1, 3], [1, 4], [1, 6], [1, 7], [1, 11], [1, 23], [1, 24], [1, 28], [1, 37], [1, 52], [1, 59], [1, 63], [1, 64], [1, 74], [1, 77], [1, 78], [2, 20], [2, 29], [2, 36], [2, 37], [2, 40], [2, 43], [2, 47], [2, 51], [2, 66], [2, 68], [2, 84], [2, 85], [3, 5], [3, 6], [3, 22], [3, 36], [3, 41], [3, 45], [3, 48], [3, 67], [3, 72], [4, 11], [4, 14], [4, 18], [4, 22], [4, 28], [4, 57], [4, 59], [4, 62], [4, 70], [4, 78], [4, 80], [4, 81], [4, 82], [5, 11], [5, 12], [5, 20], [5, 30], [5, 31], [5, 37], [5, 54], [5, 62], [5, 63], [5, 71], [5, 75], [5, 87], [6, 12], [6, 14], [6, 17], [6, 18], [6, 37], [6, 41], [6, 44], [6, 46], [6, 47], [6, 62], [6, 69], [6, 72], [6, 87], [7, 9], [7, 15], [7, 21], [7, 34], [7, 42], [7, 48], [7, 58], [7, 72], [7, 76], [7, 78], [7, 79], [7, 89], [8, 23], [8, 41], [8, 64], [8, 71], [9, 12], [9, 16], [9, 25], [9, 29], [9, 32], [9, 34], [9, 39], [9, 43], [9, 48], [9, 50], [9, 56], [9, 68], [9, 80], [9, 85], [10, 17], [10, 22], [10, 32], [10, 34], [10, 37], [10, 77], [11, 21], [11, 23], [11, 24], [11, 27], [11, 38], [11, 39], [11, 47], [11, 64], [11, 67], [11, 74], [11, 79], [11, 81], [12, 20], [12, 22], [12, 30], [12, 41], [12, 46], [12, 54], [12, 59], [12, 65], [12, 66], [12, 70], [12, 71], [12, 72], [12, 73], [12, 76], [12, 78], [12, 87], [13, 19], [13, 27], [13, 34], [13, 42], [13, 47], [13, 54], [13, 55], [13, 56], [13, 58], [13, 65], [13, 80], [13, 88], [14, 20], [14, 22], [14, 25], [14, 40], [14, 43], [14, 55], [14, 68], [14, 71], [15, 31], [15, 33], [15, 42], [15, 44], [15, 58], [15, 59], [15, 60], [15, 62], [15, 76], [15, 78], [15, 80], [16, 45], [16, 47], [16, 50], [16, 55], [16, 56], [16, 62], [16, 74], [16, 80], [16, 83], [17, 21], [17, 23], [17, 32], [17, 74], [17, 77], [18, 30], [18, 37], [18, 71], [18, 75], [19, 21], [19, 28], [19, 36], [19, 40], [19, 48], [19, 58], [19, 63], [19, 78], [19, 79], [19, 83], [19, 86], [19, 88], [20, 24], [20, 34], [20, 36], [20, 51], [20, 54], [20, 64], [20, 75], [20, 76], [20, 77], [20, 78], [20, 80], [20, 88], [21, 23], [21, 38], [21, 41], [21, 45], [21, 52], [21, 56], [21, 62], [21, 68], [21, 81], [21, 88], [22, 24], [22, 27], [22, 28], [22, 43], [22, 51], [22, 53], [22, 54], [22, 62], [22, 63], [22, 81], [22, 84], [22, 86], [23, 27], [23, 29], [23, 39], [23, 42], [23, 43], [23, 51], [23, 57], [23, 62], [23, 68], [24, 25], [24, 41], [24, 42], [24, 52], [24, 55], [24, 60], [24, 67], [24, 68], [24, 74], [24, 83], [24, 84], [25, 32], [25, 40], [25, 43], [25, 49], [25, 56], [25, 65], [25, 68], [25, 78], [25, 80], [25, 81], [25, 87], [26, 30], [26, 34], [26, 54], [26, 59], [26, 67], [26, 75], [26, 86], [27, 28], [27, 29], [27, 35], [27, 41], [27, 50], [27, 51], [27, 58], [27, 61], [27, 62], [27, 71], [28, 40], [28, 43], [28, 57], [28, 59], [28, 73], [28, 82], [28, 83], [29, 33], [29, 35], [29, 39], [29, 40], [29, 49], [29, 52], [29, 57], [29, 59], [29, 60], [29, 71], [29, 77], [29, 81], [30, 41], [30, 51], [30, 65], [30, 69], [30, 82], [31, 37], [31, 42], [31, 48], [31, 55], [31, 57], [31, 71], [31, 87], [32, 44], [32, 52], [32, 60], [32, 61], [32, 62], [32, 70], [32, 76], [32, 77], [32, 86], [32, 87], [32, 88], [33, 72], [33, 73], [33, 80], [33, 86], [34, 41], [34, 43], [34, 52], [34, 61], [34, 63], [34, 66], [34, 71], [34, 84], [34, 86], [35, 67], [35, 73], [35, 76], [35, 77], [36, 47], [36, 48], [36, 54], [36, 70], [36, 77], [37, 49], [37, 51], [37, 55], [37, 57], [37, 64], [37, 65], [37, 68], [37, 72], [37, 76], [37, 80], [37, 81], [38, 39], [38, 49], [38, 52], [38, 63], [38, 84], [39, 45], [39, 47], [39, 50], [39, 51], [39, 58], [39, 71], [39, 81], [40, 41], [40, 62], [40, 63], [40, 86], [41, 51], [41, 65], [41, 70], [41, 76], [41, 80], [41, 81], [41, 84], [42, 53], [42, 56], [42, 57], [42, 65], [42, 75], [42, 77], [43, 45], [43, 49], [43, 54], [43, 55], [43, 60], [43, 74], [43, 77], [43, 83], [44, 49], [44, 64], [44, 77], [44, 78], [44, 80], [44, 86], [44, 87], [45, 48], [45, 50], [45, 73], [45, 78], [45, 82], [45, 86], [46, 49], [46, 50], [46, 55], [46, 68], [46, 72], [46, 74], [46, 77], [47, 68], [47, 70], [47, 75], [47, 77], [47, 78], [47, 87], [47, 89], [48, 49], [48, 52], [48, 54], [48, 62], [49, 63], [49, 66], [49, 73], [49, 74], [49, 77], [49, 85], [49, 88], [50, 54], [50, 62], [50, 67], [50, 75], [50, 89], [51, 54], [51, 77], [51, 88], [52, 61], [52, 73], [52, 79], [52, 81], [52, 82], [53, 55], [53, 56], [53, 57], [53, 59], [53, 63], [53, 67], [53, 78], [53, 80], [53, 83], [54, 61], [54, 63], [54, 64], [54, 71], [54, 79], [55, 78], [55, 81], [56, 67], [56, 70], [56, 72], [56, 73], [56, 77], [56, 80], [57, 60], [57, 63], [57, 66], [57, 67], [57, 71], [57, 82], [57, 86], [58, 59], [58, 61], [58, 73], [58, 83], [58, 84], [58, 88], [59, 67], [59, 82], [60, 66], [60, 73], [60, 77], [60, 79], [60, 82], [60, 84], [61, 66], [61, 69], [61, 70], [61, 73], [62, 72], [62, 78], [62, 85], [62, 89], [63, 64], [63, 69], [63, 72], [63, 74], [63, 76], [63, 81], [63, 82], [63, 86], [64, 74], [64, 75], [64, 78], [64, 86], [64, 87], [64, 88], [65, 68], [65, 78], [65, 80], [66, 77], [66, 88], [67, 82], [68, 70], [68, 85], [70, 75], [71, 73], [71, 78], [72, 73], [73, 76], [73, 77], [73, 83], [73, 84], [73, 85], [73, 88], [74, 86], [75, 76], [75, 77], [75, 86], [76, 88], [77, 86], [77, 89], [78, 85], [78, 87], [79, 87], [81, 84], [83, 86], [83, 88], [84, 85]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s2/solution/solve.sh b/tasks/construct-mc-vertex-cover-l5-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3ba81632c419ed9f0edd6d39e09542adf8579d21
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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'
+{"cover": [0, 1, 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 32, 34, 35, 36, 37, 39, 41, 42, 45, 47, 48, 49, 50, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 67, 68, 71, 72, 73, 74, 75, 77, 78, 80, 83, 84, 86, 87, 88]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l5-s2/tests/check.py b/tasks/construct-mc-vertex-cover-l5-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-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-l5-s2/tests/instance.json b/tasks/construct-mc-vertex-cover-l5-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d82bc9345dd99912245e614595c7eb034d21ac1d
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 4], [0, 15], [0, 20], [0, 23], [0, 43], [0, 48], [0, 56], [0, 59], [0, 65], [0, 66], [0, 71], [0, 79], [0, 80], [0, 81], [0, 84], [0, 86], [1, 3], [1, 4], [1, 6], [1, 7], [1, 11], [1, 23], [1, 24], [1, 28], [1, 37], [1, 52], [1, 59], [1, 63], [1, 64], [1, 74], [1, 77], [1, 78], [2, 20], [2, 29], [2, 36], [2, 37], [2, 40], [2, 43], [2, 47], [2, 51], [2, 66], [2, 68], [2, 84], [2, 85], [3, 5], [3, 6], [3, 22], [3, 36], [3, 41], [3, 45], [3, 48], [3, 67], [3, 72], [4, 11], [4, 14], [4, 18], [4, 22], [4, 28], [4, 57], [4, 59], [4, 62], [4, 70], [4, 78], [4, 80], [4, 81], [4, 82], [5, 11], [5, 12], [5, 20], [5, 30], [5, 31], [5, 37], [5, 54], [5, 62], [5, 63], [5, 71], [5, 75], [5, 87], [6, 12], [6, 14], [6, 17], [6, 18], [6, 37], [6, 41], [6, 44], [6, 46], [6, 47], [6, 62], [6, 69], [6, 72], [6, 87], [7, 9], [7, 15], [7, 21], [7, 34], [7, 42], [7, 48], [7, 58], [7, 72], [7, 76], [7, 78], [7, 79], [7, 89], [8, 23], [8, 41], [8, 64], [8, 71], [9, 12], [9, 16], [9, 25], [9, 29], [9, 32], [9, 34], [9, 39], [9, 43], [9, 48], [9, 50], [9, 56], [9, 68], [9, 80], [9, 85], [10, 17], [10, 22], [10, 32], [10, 34], [10, 37], [10, 77], [11, 21], [11, 23], [11, 24], [11, 27], [11, 38], [11, 39], [11, 47], [11, 64], [11, 67], [11, 74], [11, 79], [11, 81], [12, 20], [12, 22], [12, 30], [12, 41], [12, 46], [12, 54], [12, 59], [12, 65], [12, 66], [12, 70], [12, 71], [12, 72], [12, 73], [12, 76], [12, 78], [12, 87], [13, 19], [13, 27], [13, 34], [13, 42], [13, 47], [13, 54], [13, 55], [13, 56], [13, 58], [13, 65], [13, 80], [13, 88], [14, 20], [14, 22], [14, 25], [14, 40], [14, 43], [14, 55], [14, 68], [14, 71], [15, 31], [15, 33], [15, 42], [15, 44], [15, 58], [15, 59], [15, 60], [15, 62], [15, 76], [15, 78], [15, 80], [16, 45], [16, 47], [16, 50], [16, 55], [16, 56], [16, 62], [16, 74], [16, 80], [16, 83], [17, 21], [17, 23], [17, 32], [17, 74], [17, 77], [18, 30], [18, 37], [18, 71], [18, 75], [19, 21], [19, 28], [19, 36], [19, 40], [19, 48], [19, 58], [19, 63], [19, 78], [19, 79], [19, 83], [19, 86], [19, 88], [20, 24], [20, 34], [20, 36], [20, 51], [20, 54], [20, 64], [20, 75], [20, 76], [20, 77], [20, 78], [20, 80], [20, 88], [21, 23], [21, 38], [21, 41], [21, 45], [21, 52], [21, 56], [21, 62], [21, 68], [21, 81], [21, 88], [22, 24], [22, 27], [22, 28], [22, 43], [22, 51], [22, 53], [22, 54], [22, 62], [22, 63], [22, 81], [22, 84], [22, 86], [23, 27], [23, 29], [23, 39], [23, 42], [23, 43], [23, 51], [23, 57], [23, 62], [23, 68], [24, 25], [24, 41], [24, 42], [24, 52], [24, 55], [24, 60], [24, 67], [24, 68], [24, 74], [24, 83], [24, 84], [25, 32], [25, 40], [25, 43], [25, 49], [25, 56], [25, 65], [25, 68], [25, 78], [25, 80], [25, 81], [25, 87], [26, 30], [26, 34], [26, 54], [26, 59], [26, 67], [26, 75], [26, 86], [27, 28], [27, 29], [27, 35], [27, 41], [27, 50], [27, 51], [27, 58], [27, 61], [27, 62], [27, 71], [28, 40], [28, 43], [28, 57], [28, 59], [28, 73], [28, 82], [28, 83], [29, 33], [29, 35], [29, 39], [29, 40], [29, 49], [29, 52], [29, 57], [29, 59], [29, 60], [29, 71], [29, 77], [29, 81], [30, 41], [30, 51], [30, 65], [30, 69], [30, 82], [31, 37], [31, 42], [31, 48], [31, 55], [31, 57], [31, 71], [31, 87], [32, 44], [32, 52], [32, 60], [32, 61], [32, 62], [32, 70], [32, 76], [32, 77], [32, 86], [32, 87], [32, 88], [33, 72], [33, 73], [33, 80], [33, 86], [34, 41], [34, 43], [34, 52], [34, 61], [34, 63], [34, 66], [34, 71], [34, 84], [34, 86], [35, 67], [35, 73], [35, 76], [35, 77], [36, 47], [36, 48], [36, 54], [36, 70], [36, 77], [37, 49], [37, 51], [37, 55], [37, 57], [37, 64], [37, 65], [37, 68], [37, 72], [37, 76], [37, 80], [37, 81], [38, 39], [38, 49], [38, 52], [38, 63], [38, 84], [39, 45], [39, 47], [39, 50], [39, 51], [39, 58], [39, 71], [39, 81], [40, 41], [40, 62], [40, 63], [40, 86], [41, 51], [41, 65], [41, 70], [41, 76], [41, 80], [41, 81], [41, 84], [42, 53], [42, 56], [42, 57], [42, 65], [42, 75], [42, 77], [43, 45], [43, 49], [43, 54], [43, 55], [43, 60], [43, 74], [43, 77], [43, 83], [44, 49], [44, 64], [44, 77], [44, 78], [44, 80], [44, 86], [44, 87], [45, 48], [45, 50], [45, 73], [45, 78], [45, 82], [45, 86], [46, 49], [46, 50], [46, 55], [46, 68], [46, 72], [46, 74], [46, 77], [47, 68], [47, 70], [47, 75], [47, 77], [47, 78], [47, 87], [47, 89], [48, 49], [48, 52], [48, 54], [48, 62], [49, 63], [49, 66], [49, 73], [49, 74], [49, 77], [49, 85], [49, 88], [50, 54], [50, 62], [50, 67], [50, 75], [50, 89], [51, 54], [51, 77], [51, 88], [52, 61], [52, 73], [52, 79], [52, 81], [52, 82], [53, 55], [53, 56], [53, 57], [53, 59], [53, 63], [53, 67], [53, 78], [53, 80], [53, 83], [54, 61], [54, 63], [54, 64], [54, 71], [54, 79], [55, 78], [55, 81], [56, 67], [56, 70], [56, 72], [56, 73], [56, 77], [56, 80], [57, 60], [57, 63], [57, 66], [57, 67], [57, 71], [57, 82], [57, 86], [58, 59], [58, 61], [58, 73], [58, 83], [58, 84], [58, 88], [59, 67], [59, 82], [60, 66], [60, 73], [60, 77], [60, 79], [60, 82], [60, 84], [61, 66], [61, 69], [61, 70], [61, 73], [62, 72], [62, 78], [62, 85], [62, 89], [63, 64], [63, 69], [63, 72], [63, 74], [63, 76], [63, 81], [63, 82], [63, 86], [64, 74], [64, 75], [64, 78], [64, 86], [64, 87], [64, 88], [65, 68], [65, 78], [65, 80], [66, 77], [66, 88], [67, 82], [68, 70], [68, 85], [70, 75], [71, 73], [71, 78], [72, 73], [73, 76], [73, 77], [73, 83], [73, 84], [73, 85], [73, 88], [74, 86], [75, 76], [75, 77], [75, 86], [76, 88], [77, 86], [77, 89], [78, 85], [78, 87], [79, 87], [81, 84], [83, 86], [83, 88], [84, 85]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s2/tests/run.py b/tasks/construct-mc-vertex-cover-l5-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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-vertex-cover-l5-s2/tests/test.sh b/tasks/construct-mc-vertex-cover-l5-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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-vertex-cover-l5-s5/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l5-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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-mc-vertex-cover-l5-s5/environment/instance.json b/tasks/construct-mc-vertex-cover-l5-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..749ad0ae31502f50a13bfe7e4c06a2e2d6b3444e
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 5], [0, 9], [0, 17], [0, 30], [0, 35], [0, 43], [0, 45], [0, 47], [0, 50], [0, 66], [0, 67], [0, 68], [0, 73], [0, 83], [1, 8], [1, 13], [1, 23], [1, 41], [1, 50], [1, 59], [1, 60], [1, 61], [1, 75], [1, 83], [2, 6], [2, 10], [2, 25], [2, 63], [2, 67], [2, 75], [2, 76], [2, 77], [2, 81], [3, 11], [3, 20], [3, 21], [3, 22], [3, 28], [3, 41], [3, 43], [3, 49], [3, 51], [3, 55], [3, 73], [3, 75], [3, 84], [3, 86], [4, 16], [4, 21], [4, 22], [4, 23], [4, 36], [4, 43], [4, 50], [4, 56], [4, 59], [4, 61], [4, 65], [4, 68], [4, 69], [4, 72], [4, 75], [4, 76], [4, 84], [5, 9], [5, 21], [5, 25], [5, 38], [5, 44], [5, 59], [5, 70], [5, 75], [5, 78], [5, 89], [6, 8], [6, 23], [6, 30], [6, 32], [6, 48], [6, 63], [6, 66], [6, 69], [6, 70], [6, 72], [6, 75], [6, 86], [6, 89], [7, 15], [7, 24], [7, 33], [7, 35], [7, 46], [7, 49], [7, 57], [7, 62], [7, 66], [7, 72], [7, 73], [7, 78], [7, 84], [8, 12], [8, 24], [8, 31], [8, 32], [8, 48], [8, 52], [8, 54], [8, 60], [8, 63], [8, 67], [8, 82], [8, 83], [9, 18], [9, 24], [9, 26], [9, 36], [9, 43], [9, 45], [9, 49], [9, 50], [9, 54], [9, 61], [9, 67], [9, 70], [9, 80], [9, 89], [10, 22], [10, 26], [10, 27], [10, 34], [10, 46], [10, 50], [10, 52], [10, 54], [10, 74], [10, 84], [10, 87], [11, 12], [11, 19], [11, 37], [11, 39], [11, 50], [11, 55], [11, 80], [11, 82], [11, 89], [12, 13], [12, 17], [12, 32], [12, 36], [12, 37], [12, 38], [12, 52], [12, 60], [12, 64], [12, 69], [12, 70], [12, 76], [12, 81], [13, 15], [13, 24], [13, 33], [13, 34], [13, 38], [13, 41], [13, 48], [13, 49], [13, 59], [13, 72], [13, 83], [14, 15], [14, 18], [14, 26], [14, 39], [14, 41], [14, 43], [14, 57], [14, 60], [14, 65], [14, 66], [14, 68], [14, 72], [14, 77], [14, 88], [15, 20], [15, 23], [15, 57], [15, 59], [15, 61], [15, 63], [15, 74], [15, 82], [16, 18], [16, 20], [16, 22], [16, 23], [16, 28], [16, 30], [16, 32], [16, 35], [16, 53], [16, 60], [16, 83], [17, 23], [17, 38], [17, 45], [17, 50], [17, 58], [17, 83], [17, 89], [18, 24], [18, 27], [18, 28], [18, 45], [18, 47], [18, 69], [18, 74], [18, 78], [18, 83], [19, 23], [19, 28], [19, 34], [19, 36], [19, 41], [19, 44], [19, 47], [19, 71], [19, 83], [19, 89], [20, 22], [20, 31], [20, 34], [20, 42], [20, 44], [20, 50], [20, 57], [20, 59], [20, 62], [20, 66], [20, 67], [20, 70], [20, 77], [20, 78], [20, 83], [21, 24], [21, 30], [21, 33], [21, 46], [21, 66], [21, 74], [21, 81], [21, 82], [21, 85], [22, 30], [22, 31], [22, 45], [22, 46], [22, 55], [22, 58], [22, 59], [22, 61], [22, 68], [22, 70], [22, 74], [22, 88], [23, 34], [23, 42], [23, 61], [23, 65], [24, 53], [24, 61], [24, 62], [24, 67], [24, 80], [24, 89], [25, 35], [25, 36], [25, 42], [25, 51], [25, 54], [25, 59], [25, 72], [25, 79], [25, 82], [25, 89], [26, 41], [26, 44], [26, 49], [26, 57], [26, 58], [26, 83], [26, 89], [27, 41], [27, 47], [27, 52], [27, 53], [27, 61], [27, 62], [27, 69], [27, 75], [27, 77], [28, 34], [28, 36], [28, 52], [28, 56], [28, 61], [28, 63], [28, 77], [29, 43], [29, 49], [29, 70], [29, 78], [29, 88], [29, 89], [30, 36], [30, 48], [30, 61], [30, 69], [30, 72], [30, 73], [30, 88], [31, 33], [31, 38], [31, 47], [31, 55], [31, 61], [31, 63], [31, 69], [31, 75], [31, 83], [32, 33], [32, 41], [32, 43], [32, 56], [32, 61], [32, 64], [32, 66], [32, 72], [32, 75], [32, 79], [32, 87], [33, 63], [33, 67], [33, 81], [34, 36], [34, 37], [34, 42], [34, 48], [34, 49], [34, 50], [34, 67], [34, 70], [34, 78], [34, 79], [35, 58], [35, 74], [35, 82], [36, 37], [36, 39], [36, 42], [36, 51], [36, 75], [36, 76], [36, 83], [37, 43], [37, 48], [37, 51], [37, 58], [37, 59], [37, 67], [37, 72], [38, 45], [38, 51], [38, 52], [38, 54], [38, 60], [38, 61], [38, 65], [38, 74], [38, 78], [38, 84], [39, 41], [39, 46], [39, 51], [39, 57], [39, 60], [39, 65], [39, 73], [39, 79], [40, 45], [40, 52], [40, 57], [40, 74], [40, 78], [41, 44], [41, 46], [41, 51], [41, 54], [41, 61], [41, 62], [41, 65], [41, 68], [42, 69], [42, 80], [42, 82], [43, 61], [43, 67], [43, 69], [43, 70], [43, 78], [43, 82], [43, 83], [44, 48], [44, 50], [44, 54], [44, 60], [44, 81], [44, 85], [45, 70], [45, 73], [45, 77], [46, 51], [46, 56], [46, 66], [46, 71], [46, 82], [46, 86], [46, 87], [47, 48], [47, 49], [47, 56], [47, 67], [47, 70], [47, 74], [47, 78], [48, 52], [48, 59], [48, 62], [48, 67], [48, 69], [48, 70], [48, 74], [48, 82], [49, 75], [49, 76], [49, 79], [49, 84], [49, 86], [50, 55], [50, 68], [50, 78], [50, 85], [50, 87], [51, 53], [51, 66], [51, 80], [52, 57], [52, 61], [52, 64], [52, 68], [52, 71], [52, 74], [52, 86], [53, 74], [53, 77], [53, 79], [53, 81], [53, 84], [53, 85], [53, 88], [54, 61], [54, 62], [54, 86], [55, 86], [55, 87], [56, 66], [56, 73], [56, 75], [56, 80], [56, 84], [57, 59], [57, 72], [57, 76], [57, 88], [58, 59], [58, 62], [58, 64], [58, 77], [58, 85], [59, 62], [59, 65], [59, 85], [60, 71], [60, 83], [60, 89], [62, 72], [62, 79], [63, 67], [63, 68], [63, 78], [63, 82], [63, 85], [64, 70], [64, 76], [64, 77], [65, 77], [65, 83], [66, 73], [66, 81], [67, 69], [67, 73], [67, 79], [67, 85], [68, 69], [68, 77], [68, 87], [68, 88], [69, 78], [69, 83], [69, 84], [69, 87], [70, 73], [70, 84], [72, 77], [72, 80], [72, 81], [72, 83], [73, 75], [73, 76], [73, 77], [73, 89], [74, 81], [74, 88], [74, 89], [75, 84], [75, 85], [75, 86], [76, 86], [76, 89], [77, 83], [80, 81], [82, 87], [82, 89], [83, 86], [83, 87], [84, 86], [84, 88]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s5/solution/solve.sh b/tasks/construct-mc-vertex-cover-l5-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a3343814dc24dac732aad98c090621cea69f3d1e
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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'
+{"cover": [0, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 18, 19, 20, 21, 23, 25, 30, 31, 32, 34, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 80, 81, 82, 83, 86, 88, 89]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l5-s5/tests/check.py b/tasks/construct-mc-vertex-cover-l5-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s5/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-s5/tests/instance.json b/tasks/construct-mc-vertex-cover-l5-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..749ad0ae31502f50a13bfe7e4c06a2e2d6b3444e
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l5-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 63, "edges": [[0, 5], [0, 9], [0, 17], [0, 30], [0, 35], [0, 43], [0, 45], [0, 47], [0, 50], [0, 66], [0, 67], [0, 68], [0, 73], [0, 83], [1, 8], [1, 13], [1, 23], [1, 41], [1, 50], [1, 59], [1, 60], [1, 61], [1, 75], [1, 83], [2, 6], [2, 10], [2, 25], [2, 63], [2, 67], [2, 75], [2, 76], [2, 77], [2, 81], [3, 11], [3, 20], [3, 21], [3, 22], [3, 28], [3, 41], [3, 43], [3, 49], [3, 51], [3, 55], [3, 73], [3, 75], [3, 84], [3, 86], [4, 16], [4, 21], [4, 22], [4, 23], [4, 36], [4, 43], [4, 50], [4, 56], [4, 59], [4, 61], [4, 65], [4, 68], [4, 69], [4, 72], [4, 75], [4, 76], [4, 84], [5, 9], [5, 21], [5, 25], [5, 38], [5, 44], [5, 59], [5, 70], [5, 75], [5, 78], [5, 89], [6, 8], [6, 23], [6, 30], [6, 32], [6, 48], [6, 63], [6, 66], [6, 69], [6, 70], [6, 72], [6, 75], [6, 86], [6, 89], [7, 15], [7, 24], [7, 33], [7, 35], [7, 46], [7, 49], [7, 57], [7, 62], [7, 66], [7, 72], [7, 73], [7, 78], [7, 84], [8, 12], [8, 24], [8, 31], [8, 32], [8, 48], [8, 52], [8, 54], [8, 60], [8, 63], [8, 67], [8, 82], [8, 83], [9, 18], [9, 24], [9, 26], [9, 36], [9, 43], [9, 45], [9, 49], [9, 50], [9, 54], [9, 61], [9, 67], [9, 70], [9, 80], [9, 89], [10, 22], [10, 26], [10, 27], [10, 34], [10, 46], [10, 50], [10, 52], [10, 54], [10, 74], [10, 84], [10, 87], [11, 12], [11, 19], [11, 37], [11, 39], [11, 50], [11, 55], [11, 80], [11, 82], [11, 89], [12, 13], [12, 17], [12, 32], [12, 36], [12, 37], [12, 38], [12, 52], [12, 60], [12, 64], [12, 69], [12, 70], [12, 76], [12, 81], [13, 15], [13, 24], [13, 33], [13, 34], [13, 38], [13, 41], [13, 48], [13, 49], [13, 59], [13, 72], [13, 83], [14, 15], [14, 18], [14, 26], [14, 39], [14, 41], [14, 43], [14, 57], [14, 60], [14, 65], [14, 66], [14, 68], [14, 72], [14, 77], [14, 88], [15, 20], [15, 23], [15, 57], [15, 59], [15, 61], [15, 63], [15, 74], [15, 82], [16, 18], [16, 20], [16, 22], [16, 23], [16, 28], [16, 30], [16, 32], [16, 35], [16, 53], [16, 60], [16, 83], [17, 23], [17, 38], [17, 45], [17, 50], [17, 58], [17, 83], [17, 89], [18, 24], [18, 27], [18, 28], [18, 45], [18, 47], [18, 69], [18, 74], [18, 78], [18, 83], [19, 23], [19, 28], [19, 34], [19, 36], [19, 41], [19, 44], [19, 47], [19, 71], [19, 83], [19, 89], [20, 22], [20, 31], [20, 34], [20, 42], [20, 44], [20, 50], [20, 57], [20, 59], [20, 62], [20, 66], [20, 67], [20, 70], [20, 77], [20, 78], [20, 83], [21, 24], [21, 30], [21, 33], [21, 46], [21, 66], [21, 74], [21, 81], [21, 82], [21, 85], [22, 30], [22, 31], [22, 45], [22, 46], [22, 55], [22, 58], [22, 59], [22, 61], [22, 68], [22, 70], [22, 74], [22, 88], [23, 34], [23, 42], [23, 61], [23, 65], [24, 53], [24, 61], [24, 62], [24, 67], [24, 80], [24, 89], [25, 35], [25, 36], [25, 42], [25, 51], [25, 54], [25, 59], [25, 72], [25, 79], [25, 82], [25, 89], [26, 41], [26, 44], [26, 49], [26, 57], [26, 58], [26, 83], [26, 89], [27, 41], [27, 47], [27, 52], [27, 53], [27, 61], [27, 62], [27, 69], [27, 75], [27, 77], [28, 34], [28, 36], [28, 52], [28, 56], [28, 61], [28, 63], [28, 77], [29, 43], [29, 49], [29, 70], [29, 78], [29, 88], [29, 89], [30, 36], [30, 48], [30, 61], [30, 69], [30, 72], [30, 73], [30, 88], [31, 33], [31, 38], [31, 47], [31, 55], [31, 61], [31, 63], [31, 69], [31, 75], [31, 83], [32, 33], [32, 41], [32, 43], [32, 56], [32, 61], [32, 64], [32, 66], [32, 72], [32, 75], [32, 79], [32, 87], [33, 63], [33, 67], [33, 81], [34, 36], [34, 37], [34, 42], [34, 48], [34, 49], [34, 50], [34, 67], [34, 70], [34, 78], [34, 79], [35, 58], [35, 74], [35, 82], [36, 37], [36, 39], [36, 42], [36, 51], [36, 75], [36, 76], [36, 83], [37, 43], [37, 48], [37, 51], [37, 58], [37, 59], [37, 67], [37, 72], [38, 45], [38, 51], [38, 52], [38, 54], [38, 60], [38, 61], [38, 65], [38, 74], [38, 78], [38, 84], [39, 41], [39, 46], [39, 51], [39, 57], [39, 60], [39, 65], [39, 73], [39, 79], [40, 45], [40, 52], [40, 57], [40, 74], [40, 78], [41, 44], [41, 46], [41, 51], [41, 54], [41, 61], [41, 62], [41, 65], [41, 68], [42, 69], [42, 80], [42, 82], [43, 61], [43, 67], [43, 69], [43, 70], [43, 78], [43, 82], [43, 83], [44, 48], [44, 50], [44, 54], [44, 60], [44, 81], [44, 85], [45, 70], [45, 73], [45, 77], [46, 51], [46, 56], [46, 66], [46, 71], [46, 82], [46, 86], [46, 87], [47, 48], [47, 49], [47, 56], [47, 67], [47, 70], [47, 74], [47, 78], [48, 52], [48, 59], [48, 62], [48, 67], [48, 69], [48, 70], [48, 74], [48, 82], [49, 75], [49, 76], [49, 79], [49, 84], [49, 86], [50, 55], [50, 68], [50, 78], [50, 85], [50, 87], [51, 53], [51, 66], [51, 80], [52, 57], [52, 61], [52, 64], [52, 68], [52, 71], [52, 74], [52, 86], [53, 74], [53, 77], [53, 79], [53, 81], [53, 84], [53, 85], [53, 88], [54, 61], [54, 62], [54, 86], [55, 86], [55, 87], [56, 66], [56, 73], [56, 75], [56, 80], [56, 84], [57, 59], [57, 72], [57, 76], [57, 88], [58, 59], [58, 62], [58, 64], [58, 77], [58, 85], [59, 62], [59, 65], [59, 85], [60, 71], [60, 83], [60, 89], [62, 72], [62, 79], [63, 67], [63, 68], [63, 78], [63, 82], [63, 85], [64, 70], [64, 76], [64, 77], [65, 77], [65, 83], [66, 73], [66, 81], [67, 69], [67, 73], [67, 79], [67, 85], [68, 69], [68, 77], [68, 87], [68, 88], [69, 78], [69, 83], [69, 84], [69, 87], [70, 73], [70, 84], [72, 77], [72, 80], [72, 81], [72, 83], [73, 75], [73, 76], [73, 77], [73, 89], [74, 81], [74, 88], [74, 89], [75, 84], [75, 85], [75, 86], [76, 86], [76, 89], [77, 83], [80, 81], [82, 87], [82, 89], [83, 86], [83, 87], [84, 86], [84, 88]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l5-s5/tests/run.py b/tasks/construct-mc-vertex-cover-l5-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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-mc-vertex-cover-l5-s5/tests/test.sh b/tasks/construct-mc-vertex-cover-l5-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-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-nppc-3col-l4-s2/solution/solve.sh b/tasks/construct-nppc-3col-l4-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..aff5669df97a332b70555113fcc4bf4c9f79b61f
--- /dev/null
+++ b/tasks/construct-nppc-3col-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'
+{"coloring": [0, 2, 2, 0, 0, 1, 1, 0, 2, 2, 0, 1, 0, 1, 0, 2, 0, 2, 1, 1, 2, 2, 0, 2, 1, 1, 1, 0, 2, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-3col-l4-s2/tests/check.py b/tasks/construct-nppc-3col-l4-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..72362ed9180250b6c53ce0c71867ca476ac2af20
--- /dev/null
+++ b/tasks/construct-nppc-3col-l4-s2/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-l4-s2/tests/instance.json b/tasks/construct-nppc-3col-l4-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9eed294c51329e09bce36b35579ec1f749d8066b
--- /dev/null
+++ b/tasks/construct-nppc-3col-l4-s2/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 30, "edges": [[0, 5], [0, 8], [0, 9], [0, 11], [0, 18], [0, 20], [0, 21], [0, 24], [0, 25], [0, 26], [1, 3], [1, 10], [1, 11], [1, 12], [1, 14], [1, 16], [1, 27], [2, 4], [2, 12], [2, 18], [2, 27], [3, 5], [3, 13], [3, 18], [3, 20], [3, 21], [3, 28], [4, 8], [4, 11], [4, 17], [4, 18], [4, 25], [5, 9], [5, 12], [5, 16], [5, 20], [5, 28], [6, 8], [6, 12], [6, 16], [6, 21], [6, 22], [7, 15], [7, 19], [7, 23], [7, 28], [8, 10], [8, 19], [8, 26], [9, 19], [9, 29], [10, 15], [10, 20], [10, 25], [11, 17], [11, 23], [12, 19], [12, 25], [12, 26], [12, 29], [13, 14], [14, 28], [15, 24], [15, 26], [15, 29], [16, 17], [16, 21], [16, 23], [17, 19], [17, 26], [17, 29], [18, 23], [18, 28], [21, 24], [21, 26], [22, 25], [23, 26], [24, 27], [24, 28], [26, 28]], "family": "nppc_three_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-3col-l4-s2/tests/run.py b/tasks/construct-nppc-3col-l4-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-3col-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-nppc-3col-l4-s2/tests/test.sh b/tasks/construct-nppc-3col-l4-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-3col-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-nppc-bandwidth-l3-s7/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-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-bandwidth-l3-s7/environment/instance.json b/tasks/construct-nppc-bandwidth-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3ecd2c4bc23ba512e575c7b59b55dbedb42c831c
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 4], [1, 2], [1, 7], [2, 3], [2, 7], [3, 7], [4, 5], [5, 6]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s7/solution/solve.sh b/tasks/construct-nppc-bandwidth-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0505d236a3f135618d3cb8397b853e0fc4735e63
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-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'
+{"layout": [7, 3, 2, 0, 6, 4, 5, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l3-s7/tests/check.py b/tasks/construct-nppc-bandwidth-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s7/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-s7/tests/instance.json b/tasks/construct-nppc-bandwidth-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3ecd2c4bc23ba512e575c7b59b55dbedb42c831c
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 4], [1, 2], [1, 7], [2, 3], [2, 7], [3, 7], [4, 5], [5, 6]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s7/tests/run.py b/tasks/construct-nppc-bandwidth-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-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-bandwidth-l3-s7/tests/test.sh b/tasks/construct-nppc-bandwidth-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-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-bandwidth-l3-s9/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-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-nppc-bandwidth-l3-s9/environment/instance.json b/tasks/construct-nppc-bandwidth-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7fc817a320be872241f96a03e9b11b9ea2686290
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 1], [0, 5], [1, 3], [2, 4], [3, 6], [4, 5], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s9/solution/solve.sh b/tasks/construct-nppc-bandwidth-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5f181cc34e32d6289239533e3ea6ca58fa84a4c2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-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'
+{"layout": [5, 7, 0, 6, 1, 3, 4, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l3-s9/tests/check.py b/tasks/construct-nppc-bandwidth-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s9/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-s9/tests/instance.json b/tasks/construct-nppc-bandwidth-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7fc817a320be872241f96a03e9b11b9ea2686290
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 2, "edges": [[0, 1], [0, 5], [1, 3], [2, 4], [3, 6], [4, 5], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l3-s9/tests/run.py b/tasks/construct-nppc-bandwidth-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-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-nppc-bandwidth-l3-s9/tests/test.sh b/tasks/construct-nppc-bandwidth-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-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-nppc-clique-l2-s0/environment/Dockerfile b/tasks/construct-nppc-clique-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l2-s0/environment/instance.json b/tasks/construct-nppc-clique-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b16b1c2ff1fca103d7e6d0d32b446e4380f0cf82
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 14, "k": 7, "edges": [[0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 13], [1, 4], [1, 6], [1, 7], [2, 3], [2, 5], [2, 6], [2, 9], [2, 11], [2, 12], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [4, 5], [4, 6], [4, 8], [4, 9], [4, 12], [4, 13], [5, 6], [5, 9], [5, 10], [5, 11], [5, 13], [6, 8], [6, 9], [6, 10], [6, 13], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [9, 10], [9, 11], [9, 12], [10, 11], [10, 12], [11, 12], [11, 13]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l2-s0/solution/solve.sh b/tasks/construct-nppc-clique-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7d297ff6cdf98560b2b701c83bdffea4eccf32c5
--- /dev/null
+++ b/tasks/construct-nppc-clique-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'
+{"clique": [3, 7, 8, 9, 10, 11, 12]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l2-s0/tests/check.py b/tasks/construct-nppc-clique-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s0/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-s0/tests/instance.json b/tasks/construct-nppc-clique-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b16b1c2ff1fca103d7e6d0d32b446e4380f0cf82
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 14, "k": 7, "edges": [[0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 13], [1, 4], [1, 6], [1, 7], [2, 3], [2, 5], [2, 6], [2, 9], [2, 11], [2, 12], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [4, 5], [4, 6], [4, 8], [4, 9], [4, 12], [4, 13], [5, 6], [5, 9], [5, 10], [5, 11], [5, 13], [6, 8], [6, 9], [6, 10], [6, 13], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [9, 10], [9, 11], [9, 12], [10, 11], [10, 12], [11, 12], [11, 13]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l2-s0/tests/run.py b/tasks/construct-nppc-clique-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l2-s0/tests/test.sh b/tasks/construct-nppc-clique-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l2-s7/environment/Dockerfile b/tasks/construct-nppc-clique-l2-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l2-s7/environment/instance.json b/tasks/construct-nppc-clique-l2-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..89ff92f688574c788720b0013b6ce9e0e097ce2f
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 14, "k": 7, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 8], [0, 10], [1, 3], [1, 12], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 13], [3, 6], [3, 9], [3, 11], [3, 13], [4, 5], [4, 6], [4, 7], [4, 11], [5, 8], [5, 10], [5, 11], [5, 12], [5, 13], [6, 7], [6, 8], [6, 9], [6, 10], [6, 12], [6, 13], [7, 8], [7, 9], [7, 10], [7, 13], [8, 9], [8, 10], [8, 13], [9, 10], [9, 13], [10, 12], [10, 13], [11, 13], [12, 13]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l2-s7/solution/solve.sh b/tasks/construct-nppc-clique-l2-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e66845f907ab3a32ed6d4329f9e294add0356a5a
--- /dev/null
+++ b/tasks/construct-nppc-clique-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'
+{"clique": [2, 6, 7, 8, 9, 10, 13]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l2-s7/tests/check.py b/tasks/construct-nppc-clique-l2-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-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-l2-s7/tests/instance.json b/tasks/construct-nppc-clique-l2-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..89ff92f688574c788720b0013b6ce9e0e097ce2f
--- /dev/null
+++ b/tasks/construct-nppc-clique-l2-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 14, "k": 7, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 8], [0, 10], [1, 3], [1, 12], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 13], [3, 6], [3, 9], [3, 11], [3, 13], [4, 5], [4, 6], [4, 7], [4, 11], [5, 8], [5, 10], [5, 11], [5, 12], [5, 13], [6, 7], [6, 8], [6, 9], [6, 10], [6, 12], [6, 13], [7, 8], [7, 9], [7, 10], [7, 13], [8, 9], [8, 10], [8, 13], [9, 10], [9, 13], [10, 12], [10, 13], [11, 13], [12, 13]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l2-s7/tests/run.py b/tasks/construct-nppc-clique-l2-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l2-s7/tests/test.sh b/tasks/construct-nppc-clique-l2-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l6-s1/environment/Dockerfile b/tasks/construct-nppc-clique-l6-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l6-s1/solution/solve.sh b/tasks/construct-nppc-clique-l6-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..98731f39d9278575d99a9e6d3b874d0ec3946958
--- /dev/null
+++ b/tasks/construct-nppc-clique-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'
+{"clique": [2, 10, 13, 20, 26, 27, 29, 39, 43, 46, 48, 50, 51, 56, 59, 79, 80, 84, 91, 98]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l6-s1/tests/check.py b/tasks/construct-nppc-clique-l6-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s1/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-s1/tests/instance.json b/tasks/construct-nppc-clique-l6-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b5f4f0de4b57cc9bca00330661bf2cbae5d63981
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s1/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 100, "k": 20, "edges": [[0, 1], [0, 2], [0, 6], [0, 17], [0, 18], [0, 20], [0, 24], [0, 25], [0, 27], [0, 29], [0, 30], [0, 32], [0, 35], [0, 37], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 48], [0, 49], [0, 53], [0, 54], [0, 55], [0, 56], [0, 57], [0, 59], [0, 61], [0, 65], [0, 68], [0, 70], [0, 71], [0, 75], [0, 76], [0, 80], [0, 81], [0, 83], [0, 84], [0, 86], [0, 87], [0, 88], [0, 90], [0, 91], [0, 92], [0, 93], [0, 94], [0, 95], [0, 97], [0, 99], [1, 2], [1, 7], [1, 8], [1, 9], [1, 11], [1, 19], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 30], [1, 31], [1, 33], [1, 35], [1, 36], [1, 38], [1, 39], [1, 40], [1, 41], [1, 42], [1, 44], [1, 45], [1, 46], [1, 48], [1, 49], [1, 51], [1, 52], [1, 56], [1, 58], [1, 59], [1, 61], [1, 62], [1, 63], [1, 66], [1, 68], [1, 69], [1, 70], [1, 72], [1, 73], [1, 78], [1, 79], [1, 80], [1, 82], [1, 84], [1, 88], [1, 89], [1, 91], [1, 94], [1, 95], [1, 96], [1, 97], [1, 98], [2, 5], [2, 7], [2, 8], [2, 10], [2, 11], [2, 13], [2, 16], [2, 20], [2, 22], [2, 23], [2, 24], [2, 26], [2, 27], [2, 29], [2, 32], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 42], [2, 43], [2, 44], [2, 46], [2, 47], [2, 48], [2, 49], [2, 50], [2, 51], [2, 53], [2, 54], [2, 56], [2, 58], [2, 59], [2, 62], [2, 63], [2, 65], [2, 66], [2, 68], [2, 69], [2, 75], [2, 78], [2, 79], [2, 80], [2, 83], [2, 84], [2, 87], [2, 88], [2, 89], [2, 91], [2, 92], [2, 94], [2, 96], [2, 97], [2, 98], [3, 4], [3, 5], [3, 7], [3, 10], [3, 13], [3, 15], [3, 16], [3, 20], [3, 21], [3, 22], [3, 23], [3, 26], [3, 31], [3, 32], [3, 33], [3, 37], [3, 42], [3, 43], [3, 48], [3, 49], [3, 51], [3, 53], [3, 54], [3, 63], [3, 69], [3, 70], [3, 73], [3, 75], [3, 76], [3, 80], [3, 82], [3, 83], [3, 84], [3, 85], [3, 86], [3, 88], [3, 89], [3, 90], [3, 91], [3, 93], [3, 95], [3, 96], [4, 7], [4, 9], [4, 12], [4, 13], [4, 14], [4, 16], [4, 17], [4, 20], [4, 27], [4, 28], [4, 29], [4, 31], [4, 32], [4, 33], [4, 34], [4, 35], [4, 36], [4, 40], [4, 42], [4, 43], [4, 45], [4, 50], [4, 52], [4, 53], [4, 55], [4, 59], [4, 60], [4, 61], [4, 63], [4, 64], [4, 65], [4, 66], [4, 67], [4, 68], [4, 70], [4, 71], [4, 72], [4, 74], [4, 76], [4, 77], [4, 78], [4, 79], [4, 80], [4, 84], [4, 85], [4, 86], [4, 88], [4, 91], [4, 92], [4, 93], [4, 94], [4, 95], [4, 96], [4, 97], [4, 99], [5, 6], [5, 7], [5, 8], [5, 10], [5, 11], [5, 12], [5, 16], [5, 17], [5, 18], [5, 21], [5, 22], [5, 23], [5, 24], [5, 25], [5, 27], [5, 28], [5, 29], [5, 31], [5, 32], [5, 33], [5, 37], [5, 40], [5, 43], [5, 46], [5, 49], [5, 53], [5, 55], [5, 56], [5, 59], [5, 60], [5, 61], [5, 62], [5, 66], [5, 67], [5, 69], [5, 70], [5, 71], [5, 74], [5, 75], [5, 76], [5, 78], [5, 81], [5, 85], [5, 86], [5, 87], [5, 89], [5, 92], [5, 95], [5, 96], [5, 97], [5, 99], [6, 7], [6, 9], [6, 12], [6, 14], [6, 17], [6, 19], [6, 20], [6, 22], [6, 23], [6, 27], [6, 30], [6, 33], [6, 37], [6, 38], [6, 40], [6, 41], [6, 42], [6, 44], [6, 46], [6, 48], [6, 49], [6, 54], [6, 55], [6, 56], [6, 58], [6, 59], 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95], [91, 98], [92, 93], [92, 95], [92, 96], [92, 97], [92, 98], [93, 95], [93, 96], [94, 95], [94, 96], [94, 97], [94, 99], [95, 97], [95, 98], [95, 99], [96, 99], [97, 98], [97, 99]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l6-s1/tests/run.py b/tasks/construct-nppc-clique-l6-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l6-s1/tests/test.sh b/tasks/construct-nppc-clique-l6-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l6-s8/environment/Dockerfile b/tasks/construct-nppc-clique-l6-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l6-s8/environment/instance.json b/tasks/construct-nppc-clique-l6-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8ac63dfb93967a4b981314a025b8530fa442f43a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s8/environment/instance.json
@@ -0,0 +1 @@
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[93, 95], [93, 96], [93, 97], [93, 99], [94, 95], [94, 96], [94, 99], [95, 96], [95, 99], [96, 99]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l6-s8/solution/solve.sh b/tasks/construct-nppc-clique-l6-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f73d0478c6b45ba5a659cd9889bc1fcb58edda9b
--- /dev/null
+++ b/tasks/construct-nppc-clique-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'
+{"clique": [21, 24, 28, 29, 30, 34, 40, 43, 63, 70, 76, 77, 82, 86, 89, 93, 94, 95, 96, 99]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l6-s8/tests/check.py b/tasks/construct-nppc-clique-l6-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s8/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-s8/tests/instance.json b/tasks/construct-nppc-clique-l6-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8ac63dfb93967a4b981314a025b8530fa442f43a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l6-s8/tests/instance.json
@@ -0,0 +1 @@
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[93, 95], [93, 96], [93, 97], [93, 99], [94, 95], [94, 96], [94, 99], [95, 96], [95, 99], [96, 99]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l6-s8/tests/run.py b/tasks/construct-nppc-clique-l6-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-clique-l6-s8/tests/test.sh b/tasks/construct-nppc-clique-l6-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-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-nppc-dominating-set-l3-s0/environment/Dockerfile b/tasks/construct-nppc-dominating-set-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-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-nppc-dominating-set-l3-s0/environment/instance.json b/tasks/construct-nppc-dominating-set-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5339cac6052da58e71619a5097f81ae96f99609d
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 50, "k": 20, "edges": [[0, 8], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 23], [0, 26], [0, 28], [0, 29], [0, 33], [0, 35], [0, 36], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 49], [1, 4], [1, 5], [1, 8], [1, 13], [1, 20], [1, 21], [1, 23], [1, 24], [1, 25], [1, 27], [1, 28], [1, 36], [1, 39], [1, 42], [1, 44], [2, 7], [2, 10], [2, 24], [2, 26], [2, 27], [2, 30], [2, 34], [2, 39], [2, 41], [2, 42], [2, 46], [2, 47], [2, 49], [3, 5], [3, 6], [3, 7], [3, 11], [3, 12], [3, 13], [3, 16], [3, 26], [3, 27], [3, 38], [3, 41], [3, 43], [3, 47], [3, 48], [4, 6], [4, 10], [4, 18], [4, 19], [4, 26], [4, 29], [4, 33], [4, 37], [4, 39], [4, 40], [4, 41], [4, 46], [5, 8], [5, 12], [5, 13], [5, 16], [5, 17], [5, 18], [5, 22], [5, 23], [5, 26], [5, 34], [5, 39], [5, 43], [5, 46], [5, 47], [5, 48], [6, 7], [6, 8], [6, 10], [6, 13], [6, 18], [6, 23], [6, 24], [6, 27], [6, 31], [6, 34], [6, 40], [6, 43], [6, 44], [7, 9], [7, 10], [7, 12], [7, 17], [7, 20], [7, 30], [7, 31], [7, 34], [7, 36], [7, 40], [7, 41], [7, 42], [7, 46], [8, 18], [8, 26], [8, 27], [8, 34], [8, 36], [8, 37], [8, 39], [8, 40], [8, 41], [8, 42], [8, 44], [8, 49], [9, 11], [9, 13], [9, 18], [9, 23], [9, 27], [9, 32], [9, 38], [9, 41], [9, 42], [10, 12], [10, 13], [10, 18], [10, 23], [10, 28], [10, 31], [10, 34], [10, 37], [10, 41], [10, 49], [11, 17], [11, 25], [11, 26], [11, 29], [11, 34], [11, 35], [11, 37], [11, 44], [11, 48], [12, 20], [12, 23], [12, 26], [12, 27], [12, 33], [12, 41], [12, 42], [12, 43], [12, 48], [12, 49], [13, 16], [13, 20], [13, 21], [13, 24], [13, 34], [13, 36], [13, 37], [13, 44], [13, 46], [13, 48], [13, 49], [14, 18], [14, 19], [14, 24], [14, 25], [14, 28], [14, 29], [14, 30], [14, 39], [14, 40], [14, 41], [14, 47], [14, 48], [14, 49], [15, 16], [15, 20], [15, 21], [15, 24], [15, 28], [15, 29], [15, 32], [15, 33], [15, 44], [16, 18], [16, 20], [16, 27], [16, 34], [16, 38], [16, 39], [16, 41], [16, 43], [16, 45], [16, 46], [16, 48], [17, 18], [17, 23], [17, 26], [17, 27], [17, 30], [17, 39], [17, 43], [17, 46], [18, 21], [18, 28], [18, 30], [18, 31], [18, 38], [18, 46], [19, 23], [19, 24], [19, 27], [19, 33], [19, 34], [19, 35], [19, 37], [19, 38], [19, 40], [19, 42], [19, 48], [20, 21], [20, 25], [20, 29], [20, 39], [20, 42], [20, 44], [20, 46], [20, 47], [21, 22], [21, 23], [21, 24], [21, 25], [21, 29], [21, 30], [21, 33], [21, 34], [21, 37], [21, 40], [21, 41], [21, 42], [21, 47], [22, 24], [22, 25], [22, 27], [22, 31], [22, 34], [22, 35], [22, 37], [22, 41], [22, 49], [23, 24], [23, 28], [23, 31], [23, 34], [23, 36], [23, 39], [23, 43], [23, 45], [23, 47], [23, 49], [24, 27], [24, 31], [24, 32], [24, 49], [25, 29], [25, 36], [25, 37], [25, 38], [25, 39], [25, 40], [25, 41], [25, 43], [26, 27], [26, 28], [26, 31], [26, 36], [26, 38], [26, 41], [26, 45], [26, 47], [26, 49], [27, 29], [27, 33], [27, 34], [27, 35], [27, 39], [27, 42], [27, 46], [28, 32], [28, 33], [28, 34], [28, 35], [28, 36], [29, 30], [29, 36], [29, 37], [29, 39], [29, 40], [29, 41], [29, 43], [29, 44], [29, 46], [29, 49], [30, 31], [30, 40], [30, 45], [31, 32], [31, 37], [31, 39], [31, 44], [31, 45], [32, 33], [32, 37], [32, 40], [32, 46], [32, 47], [32, 48], [33, 37], [33, 38], [33, 39], [33, 40], [33, 44], [33, 47], [34, 35], [34, 41], [34, 46], [35, 36], [35, 37], [35, 38], [35, 39], [35, 41], [35, 42], [35, 47], [35, 49], [36, 39], [36, 41], [36, 42], [36, 43], [36, 44], [36, 46], [36, 47], [37, 38], [37, 39], [37, 40], [37, 41], [37, 46], [37, 47], [38, 39], [38, 42], [38, 43], [38, 44], [38, 49], [39, 43], [39, 44], [39, 49], [40, 41], [40, 44], [40, 45], [40, 46], [40, 47], [41, 42], [41, 44], [41, 47], [42, 46], [42, 47], [43, 46], [43, 48], [44, 46], [45, 47], [45, 48], [45, 49], [46, 47], [46, 48], [47, 48], [47, 49], [48, 49]], "family": "nppc_dominating_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-dominating-set-l3-s0/solution/solve.sh b/tasks/construct-nppc-dominating-set-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1fa1b609f11fb698bec042f1a376b100c9da7b4f
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-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'
+{"dominating_set": [0, 3, 5, 6, 7, 10, 14, 19, 20, 21, 23, 24, 26, 29, 34, 35, 38, 40, 44, 48]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-dominating-set-l3-s0/tests/check.py b/tasks/construct-nppc-dominating-set-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0677a7bcbccb02297d022ffa4b5dd15da6371bff
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s0/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-l3-s0/tests/instance.json b/tasks/construct-nppc-dominating-set-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5339cac6052da58e71619a5097f81ae96f99609d
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 50, "k": 20, "edges": [[0, 8], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 23], [0, 26], [0, 28], [0, 29], [0, 33], [0, 35], [0, 36], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 49], [1, 4], [1, 5], [1, 8], [1, 13], [1, 20], [1, 21], [1, 23], [1, 24], [1, 25], [1, 27], [1, 28], [1, 36], [1, 39], [1, 42], [1, 44], [2, 7], [2, 10], [2, 24], [2, 26], [2, 27], [2, 30], [2, 34], [2, 39], [2, 41], [2, 42], [2, 46], [2, 47], [2, 49], [3, 5], [3, 6], [3, 7], [3, 11], [3, 12], [3, 13], [3, 16], [3, 26], [3, 27], [3, 38], [3, 41], [3, 43], [3, 47], [3, 48], [4, 6], [4, 10], [4, 18], [4, 19], [4, 26], [4, 29], [4, 33], [4, 37], [4, 39], [4, 40], [4, 41], [4, 46], [5, 8], [5, 12], [5, 13], [5, 16], [5, 17], [5, 18], [5, 22], [5, 23], [5, 26], [5, 34], [5, 39], [5, 43], [5, 46], [5, 47], [5, 48], [6, 7], [6, 8], [6, 10], [6, 13], [6, 18], [6, 23], [6, 24], [6, 27], [6, 31], [6, 34], [6, 40], [6, 43], [6, 44], [7, 9], [7, 10], [7, 12], [7, 17], [7, 20], [7, 30], [7, 31], [7, 34], [7, 36], [7, 40], [7, 41], [7, 42], [7, 46], [8, 18], [8, 26], [8, 27], [8, 34], [8, 36], [8, 37], [8, 39], [8, 40], [8, 41], [8, 42], [8, 44], [8, 49], [9, 11], [9, 13], [9, 18], [9, 23], [9, 27], [9, 32], [9, 38], [9, 41], [9, 42], [10, 12], [10, 13], [10, 18], [10, 23], [10, 28], [10, 31], [10, 34], [10, 37], [10, 41], [10, 49], [11, 17], [11, 25], [11, 26], [11, 29], [11, 34], [11, 35], [11, 37], [11, 44], [11, 48], [12, 20], [12, 23], [12, 26], [12, 27], [12, 33], [12, 41], [12, 42], [12, 43], [12, 48], [12, 49], [13, 16], [13, 20], [13, 21], [13, 24], [13, 34], [13, 36], [13, 37], [13, 44], [13, 46], [13, 48], [13, 49], [14, 18], [14, 19], [14, 24], [14, 25], [14, 28], [14, 29], [14, 30], [14, 39], [14, 40], [14, 41], [14, 47], [14, 48], [14, 49], [15, 16], [15, 20], [15, 21], [15, 24], [15, 28], [15, 29], [15, 32], [15, 33], [15, 44], [16, 18], [16, 20], [16, 27], [16, 34], [16, 38], [16, 39], [16, 41], [16, 43], [16, 45], [16, 46], [16, 48], [17, 18], [17, 23], [17, 26], [17, 27], [17, 30], [17, 39], [17, 43], [17, 46], [18, 21], [18, 28], [18, 30], [18, 31], [18, 38], [18, 46], [19, 23], [19, 24], [19, 27], [19, 33], [19, 34], [19, 35], [19, 37], [19, 38], [19, 40], [19, 42], [19, 48], [20, 21], [20, 25], [20, 29], [20, 39], [20, 42], [20, 44], [20, 46], [20, 47], [21, 22], [21, 23], [21, 24], [21, 25], [21, 29], [21, 30], [21, 33], [21, 34], [21, 37], [21, 40], [21, 41], [21, 42], [21, 47], [22, 24], [22, 25], [22, 27], [22, 31], [22, 34], [22, 35], [22, 37], [22, 41], [22, 49], [23, 24], [23, 28], [23, 31], [23, 34], [23, 36], [23, 39], [23, 43], [23, 45], [23, 47], [23, 49], [24, 27], [24, 31], [24, 32], [24, 49], [25, 29], [25, 36], [25, 37], [25, 38], [25, 39], [25, 40], [25, 41], [25, 43], [26, 27], [26, 28], [26, 31], [26, 36], [26, 38], [26, 41], [26, 45], [26, 47], [26, 49], [27, 29], [27, 33], [27, 34], [27, 35], [27, 39], [27, 42], [27, 46], [28, 32], [28, 33], [28, 34], [28, 35], [28, 36], [29, 30], [29, 36], [29, 37], [29, 39], [29, 40], [29, 41], [29, 43], [29, 44], [29, 46], [29, 49], [30, 31], [30, 40], [30, 45], [31, 32], [31, 37], [31, 39], [31, 44], [31, 45], [32, 33], [32, 37], [32, 40], [32, 46], [32, 47], [32, 48], [33, 37], [33, 38], [33, 39], [33, 40], [33, 44], [33, 47], [34, 35], [34, 41], [34, 46], [35, 36], [35, 37], [35, 38], [35, 39], [35, 41], [35, 42], [35, 47], [35, 49], [36, 39], [36, 41], [36, 42], [36, 43], [36, 44], [36, 46], [36, 47], [37, 38], [37, 39], [37, 40], [37, 41], [37, 46], [37, 47], [38, 39], [38, 42], [38, 43], [38, 44], [38, 49], [39, 43], [39, 44], [39, 49], [40, 41], [40, 44], [40, 45], [40, 46], [40, 47], [41, 42], [41, 44], [41, 47], [42, 46], [42, 47], [43, 46], [43, 48], [44, 46], [45, 47], [45, 48], [45, 49], [46, 47], [46, 48], [47, 48], [47, 49], [48, 49]], "family": "nppc_dominating_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-dominating-set-l3-s0/tests/run.py b/tasks/construct-nppc-dominating-set-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-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-nppc-dominating-set-l3-s0/tests/test.sh b/tasks/construct-nppc-dominating-set-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-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-nppc-dominating-set-l3-s7/environment/Dockerfile b/tasks/construct-nppc-dominating-set-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-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-dominating-set-l3-s7/environment/instance.json b/tasks/construct-nppc-dominating-set-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f046489c2f761d9c0e3f2f6ce6dc5c9ce9299fc9
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 50, "k": 20, "edges": [[0, 1], [0, 6], [0, 9], [0, 13], [0, 19], [0, 20], [0, 22], [0, 26], [0, 27], [0, 34], [0, 35], [0, 37], [0, 39], [0, 42], [1, 6], [1, 11], [1, 13], [1, 15], [1, 19], [1, 22], [1, 24], [1, 26], [1, 28], [1, 34], [1, 36], [1, 38], [1, 40], [1, 48], [2, 3], [2, 6], [2, 11], [2, 14], [2, 19], [2, 23], [2, 25], [2, 27], [2, 28], [2, 30], [2, 36], [2, 37], [2, 38], [2, 40], [2, 42], [2, 46], [2, 47], [2, 48], [3, 7], [3, 10], [3, 11], [3, 13], [3, 17], [3, 20], [3, 23], [3, 27], [3, 29], [3, 33], [3, 34], [3, 43], [3, 45], [3, 49], [4, 7], [4, 8], [4, 10], [4, 11], [4, 14], [4, 19], [4, 20], [4, 27], [4, 28], [4, 34], [4, 35], [4, 36], [4, 37], [4, 44], [5, 7], [5, 9], [5, 11], [5, 14], [5, 19], [5, 25], [5, 30], [5, 34], [5, 37], [5, 38], [5, 41], [5, 42], [5, 48], [6, 13], [6, 17], [6, 19], [6, 20], [6, 23], [6, 26], [6, 27], [6, 40], [6, 48], [6, 49], [7, 9], [7, 10], [7, 11], [7, 13], [7, 15], [7, 25], [7, 29], [7, 38], [7, 40], [7, 41], [7, 44], [7, 47], [8, 9], [8, 10], [8, 18], [8, 20], [8, 22], [8, 25], [8, 26], [8, 27], [8, 29], [8, 35], [8, 47], [8, 49], [9, 13], [9, 15], [9, 17], [9, 19], [9, 21], [9, 24], [9, 32], [9, 36], [9, 38], [9, 40], [9, 48], [10, 12], [10, 15], [10, 16], [10, 18], [10, 24], [10, 27], [10, 29], [10, 37], [10, 38], [10, 43], [10, 44], [10, 45], [10, 47], [10, 48], [11, 12], [11, 16], [11, 20], [11, 21], [11, 23], [11, 26], [11, 29], [11, 30], [11, 34], [11, 35], [11, 36], [11, 37], [11, 38], [11, 42], [11, 45], [11, 46], [11, 48], [11, 49], [12, 13], [12, 14], [12, 15], [12, 25], [12, 26], [12, 27], [12, 30], [12, 34], [12, 36], [12, 40], [12, 41], [12, 43], [12, 45], [12, 46], [12, 47], [12, 48], [12, 49], [13, 15], [13, 20], [13, 25], [13, 29], [13, 30], [13, 31], [13, 33], [13, 37], [13, 39], [13, 40], [13, 43], [13, 45], [13, 49], [14, 15], [14, 16], [14, 19], [14, 22], [14, 24], [14, 26], [14, 27], [14, 29], [14, 35], [14, 36], [14, 37], [14, 38], [14, 46], [14, 47], [15, 17], [15, 19], [15, 29], [15, 30], [15, 32], [15, 33], [15, 37], [15, 39], [15, 42], [15, 43], [15, 45], [16, 18], [16, 21], [16, 23], [16, 24], [16, 26], [16, 27], [16, 30], [16, 31], [16, 32], [16, 33], [16, 34], [16, 42], [16, 45], [17, 19], [17, 23], [17, 24], [17, 32], [17, 33], [17, 39], [17, 41], [17, 43], [17, 46], [17, 47], [18, 21], [18, 26], [18, 31], [18, 32], [18, 40], [19, 24], [19, 25], [19, 30], [19, 31], [19, 32], [19, 33], [19, 36], [19, 38], [19, 42], [19, 49], [20, 21], [20, 30], [20, 35], [20, 37], [20, 39], [20, 41], [20, 45], [20, 47], [21, 25], [21, 26], [21, 27], [21, 28], [21, 31], [21, 34], [21, 37], [21, 40], [21, 45], [21, 46], [21, 47], [22, 23], [22, 28], [22, 31], [22, 34], [22, 39], [22, 41], [22, 43], [22, 44], [22, 48], [23, 24], [23, 26], [23, 29], [23, 31], [23, 33], [23, 37], [23, 40], [23, 46], [24, 29], [24, 35], [24, 41], [24, 48], [25, 31], [25, 32], [25, 42], [25, 46], [26, 29], [26, 31], [26, 38], [26, 40], [26, 48], [27, 30], [27, 31], [27, 32], [27, 34], [27, 43], [27, 44], [27, 47], [27, 48], [28, 30], [28, 33], [28, 38], [28, 41], [28, 46], [29, 33], [29, 36], [29, 39], [29, 40], [29, 42], [29, 45], [29, 46], [29, 47], [30, 31], [30, 46], [30, 47], [31, 36], [31, 37], [31, 41], [31, 42], [31, 46], [31, 48], [32, 33], [32, 34], [32, 35], [32, 36], [32, 37], [32, 41], [32, 45], [32, 48], [32, 49], [33, 38], [33, 49], [34, 42], [34, 48], [35, 44], [35, 47], [36, 37], [36, 40], [36, 43], [36, 44], [37, 38], [37, 39], [37, 40], [37, 45], [37, 46], [37, 47], [37, 48], [37, 49], [38, 40], [38, 41], [38, 45], [38, 47], [39, 41], [39, 42], [39, 49], [40, 41], [40, 46], [41, 42], [41, 48], [42, 44], [42, 45], [42, 46], [43, 48], [43, 49], [44, 46], [45, 46], [45, 49], [46, 47], [46, 49]], "family": "nppc_dominating_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-dominating-set-l3-s7/solution/solve.sh b/tasks/construct-nppc-dominating-set-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a416d35ee15689c204660906ced0123599047224
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-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'
+{"dominating_set": [1, 4, 6, 9, 16, 18, 21, 22, 31, 32, 34, 35, 36, 37, 39, 41, 43, 44, 45, 47]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-dominating-set-l3-s7/tests/check.py b/tasks/construct-nppc-dominating-set-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0677a7bcbccb02297d022ffa4b5dd15da6371bff
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s7/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-l3-s7/tests/instance.json b/tasks/construct-nppc-dominating-set-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f046489c2f761d9c0e3f2f6ce6dc5c9ce9299fc9
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 50, "k": 20, "edges": [[0, 1], [0, 6], [0, 9], [0, 13], [0, 19], [0, 20], [0, 22], [0, 26], [0, 27], [0, 34], [0, 35], [0, 37], [0, 39], [0, 42], [1, 6], [1, 11], [1, 13], [1, 15], [1, 19], [1, 22], [1, 24], [1, 26], [1, 28], [1, 34], [1, 36], [1, 38], [1, 40], [1, 48], [2, 3], [2, 6], [2, 11], [2, 14], [2, 19], [2, 23], [2, 25], [2, 27], [2, 28], [2, 30], [2, 36], [2, 37], [2, 38], [2, 40], [2, 42], [2, 46], [2, 47], [2, 48], [3, 7], [3, 10], [3, 11], [3, 13], [3, 17], [3, 20], [3, 23], [3, 27], [3, 29], [3, 33], [3, 34], [3, 43], [3, 45], [3, 49], [4, 7], [4, 8], [4, 10], [4, 11], [4, 14], [4, 19], [4, 20], [4, 27], [4, 28], [4, 34], [4, 35], [4, 36], [4, 37], [4, 44], [5, 7], [5, 9], [5, 11], [5, 14], [5, 19], [5, 25], [5, 30], [5, 34], [5, 37], [5, 38], [5, 41], [5, 42], [5, 48], [6, 13], [6, 17], [6, 19], [6, 20], [6, 23], [6, 26], [6, 27], [6, 40], [6, 48], [6, 49], [7, 9], [7, 10], [7, 11], [7, 13], [7, 15], [7, 25], [7, 29], [7, 38], [7, 40], [7, 41], [7, 44], [7, 47], [8, 9], [8, 10], [8, 18], [8, 20], [8, 22], [8, 25], [8, 26], [8, 27], [8, 29], [8, 35], [8, 47], [8, 49], [9, 13], [9, 15], [9, 17], [9, 19], [9, 21], [9, 24], [9, 32], [9, 36], [9, 38], [9, 40], [9, 48], [10, 12], [10, 15], [10, 16], [10, 18], [10, 24], [10, 27], [10, 29], [10, 37], [10, 38], [10, 43], [10, 44], [10, 45], [10, 47], [10, 48], [11, 12], [11, 16], [11, 20], [11, 21], [11, 23], [11, 26], [11, 29], [11, 30], [11, 34], [11, 35], [11, 36], [11, 37], [11, 38], [11, 42], [11, 45], [11, 46], [11, 48], [11, 49], [12, 13], [12, 14], [12, 15], [12, 25], [12, 26], [12, 27], [12, 30], [12, 34], [12, 36], [12, 40], [12, 41], [12, 43], [12, 45], [12, 46], [12, 47], [12, 48], [12, 49], [13, 15], [13, 20], [13, 25], [13, 29], [13, 30], [13, 31], [13, 33], [13, 37], [13, 39], [13, 40], [13, 43], [13, 45], [13, 49], [14, 15], [14, 16], [14, 19], [14, 22], [14, 24], [14, 26], [14, 27], [14, 29], [14, 35], [14, 36], [14, 37], [14, 38], [14, 46], [14, 47], [15, 17], [15, 19], [15, 29], [15, 30], [15, 32], [15, 33], [15, 37], [15, 39], [15, 42], [15, 43], [15, 45], [16, 18], [16, 21], [16, 23], [16, 24], [16, 26], [16, 27], [16, 30], [16, 31], [16, 32], [16, 33], [16, 34], [16, 42], [16, 45], [17, 19], [17, 23], [17, 24], [17, 32], [17, 33], [17, 39], [17, 41], [17, 43], [17, 46], [17, 47], [18, 21], [18, 26], [18, 31], [18, 32], [18, 40], [19, 24], [19, 25], [19, 30], [19, 31], [19, 32], [19, 33], [19, 36], [19, 38], [19, 42], [19, 49], [20, 21], [20, 30], [20, 35], [20, 37], [20, 39], [20, 41], [20, 45], [20, 47], [21, 25], [21, 26], [21, 27], [21, 28], [21, 31], [21, 34], [21, 37], [21, 40], [21, 45], [21, 46], [21, 47], [22, 23], [22, 28], [22, 31], [22, 34], [22, 39], [22, 41], [22, 43], [22, 44], [22, 48], [23, 24], [23, 26], [23, 29], [23, 31], [23, 33], [23, 37], [23, 40], [23, 46], [24, 29], [24, 35], [24, 41], [24, 48], [25, 31], [25, 32], [25, 42], [25, 46], [26, 29], [26, 31], [26, 38], [26, 40], [26, 48], [27, 30], [27, 31], [27, 32], [27, 34], [27, 43], [27, 44], [27, 47], [27, 48], [28, 30], [28, 33], [28, 38], [28, 41], [28, 46], [29, 33], [29, 36], [29, 39], [29, 40], [29, 42], [29, 45], [29, 46], [29, 47], [30, 31], [30, 46], [30, 47], [31, 36], [31, 37], [31, 41], [31, 42], [31, 46], [31, 48], [32, 33], [32, 34], [32, 35], [32, 36], [32, 37], [32, 41], [32, 45], [32, 48], [32, 49], [33, 38], [33, 49], [34, 42], [34, 48], [35, 44], [35, 47], [36, 37], [36, 40], [36, 43], [36, 44], [37, 38], [37, 39], [37, 40], [37, 45], [37, 46], [37, 47], [37, 48], [37, 49], [38, 40], [38, 41], [38, 45], [38, 47], [39, 41], [39, 42], [39, 49], [40, 41], [40, 46], [41, 42], [41, 48], [42, 44], [42, 45], [42, 46], [43, 48], [43, 49], [44, 46], [45, 46], [45, 49], [46, 47], [46, 49]], "family": "nppc_dominating_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-dominating-set-l3-s7/tests/run.py b/tasks/construct-nppc-dominating-set-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-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-dominating-set-l3-s7/tests/test.sh b/tasks/construct-nppc-dominating-set-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-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-independent-set-l3-s0/environment/Dockerfile b/tasks/construct-nppc-independent-set-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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-nppc-independent-set-l3-s0/environment/instance.json b/tasks/construct-nppc-independent-set-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..20a25ba11957e9c93eb4158be67d614d5b8bc42f
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 8], [0, 10], [0, 19], [0, 21], [0, 22], [0, 23], [1, 3], [1, 4], [1, 8], [1, 9], [1, 10], [1, 19], [2, 3], [2, 4], [2, 8], [2, 9], [2, 19], [2, 22], [3, 8], [3, 10], [3, 16], [3, 19], [3, 23], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 13], [4, 20], [4, 21], [4, 22], [4, 23], [5, 8], [5, 9], [5, 15], [5, 16], [5, 18], [5, 19], [5, 22], [6, 9], [7, 8], [7, 10], [7, 18], [7, 19], [7, 21], [8, 10], [8, 11], [8, 13], [8, 17], [8, 21], [8, 22], [8, 23], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 23], [10, 12], [10, 14], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 23], [11, 16], [11, 18], [11, 19], [11, 21], [11, 22], [11, 23], [12, 16], [12, 21], [12, 22], [12, 23], [13, 16], [14, 16], [14, 18], [14, 19], [15, 16], [15, 18], [15, 19], [15, 21], [15, 23], [16, 21], [16, 23], [17, 19], [17, 23], [18, 19], [18, 20], [18, 22], [18, 23], [19, 21], [19, 23], [20, 23]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s0/solution/solve.sh b/tasks/construct-nppc-independent-set-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d7f194f69e13bf84e51a4099a3ed828a436a3715
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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'
+{"independent_set": [0, 1, 2, 5, 6, 7, 11, 12, 13, 14, 17, 20]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l3-s0/tests/check.py b/tasks/construct-nppc-independent-set-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s0/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-s0/tests/instance.json b/tasks/construct-nppc-independent-set-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..20a25ba11957e9c93eb4158be67d614d5b8bc42f
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 8], [0, 10], [0, 19], [0, 21], [0, 22], [0, 23], [1, 3], [1, 4], [1, 8], [1, 9], [1, 10], [1, 19], [2, 3], [2, 4], [2, 8], [2, 9], [2, 19], [2, 22], [3, 8], [3, 10], [3, 16], [3, 19], [3, 23], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 13], [4, 20], [4, 21], [4, 22], [4, 23], [5, 8], [5, 9], [5, 15], [5, 16], [5, 18], [5, 19], [5, 22], [6, 9], [7, 8], [7, 10], [7, 18], [7, 19], [7, 21], [8, 10], [8, 11], [8, 13], [8, 17], [8, 21], [8, 22], [8, 23], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 23], [10, 12], [10, 14], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 23], [11, 16], [11, 18], [11, 19], [11, 21], [11, 22], [11, 23], [12, 16], [12, 21], [12, 22], [12, 23], [13, 16], [14, 16], [14, 18], [14, 19], [15, 16], [15, 18], [15, 19], [15, 21], [15, 23], [16, 21], [16, 23], [17, 19], [17, 23], [18, 19], [18, 20], [18, 22], [18, 23], [19, 21], [19, 23], [20, 23]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s0/tests/run.py b/tasks/construct-nppc-independent-set-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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-nppc-independent-set-l3-s0/tests/test.sh b/tasks/construct-nppc-independent-set-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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-nppc-independent-set-l3-s7/environment/Dockerfile b/tasks/construct-nppc-independent-set-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-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-independent-set-l3-s7/environment/instance.json b/tasks/construct-nppc-independent-set-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf9bc931d9dbdc232afea9072543ace39eb55db1
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 2], [0, 5], [0, 6], [0, 9], [0, 10], [0, 11], [0, 13], [0, 16], [0, 17], [0, 18], [0, 21], [0, 23], [1, 2], [1, 4], [1, 16], [1, 18], [2, 3], [2, 8], [2, 11], [2, 12], [2, 14], [2, 15], [2, 17], [2, 21], [2, 22], [2, 23], [3, 10], [3, 11], [3, 16], [3, 17], [3, 19], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [4, 11], [4, 14], [4, 16], [4, 19], [4, 20], [4, 23], [5, 10], [5, 19], [6, 8], [6, 10], [6, 14], [6, 17], [6, 18], [7, 12], [7, 14], [7, 17], [7, 18], [8, 11], [8, 14], [8, 16], [8, 17], [8, 19], [8, 20], [8, 22], [9, 10], [9, 11], [9, 14], [9, 16], [9, 19], [10, 12], [10, 14], [10, 17], [10, 20], [10, 21], [10, 22], [11, 14], [11, 18], [11, 19], [11, 21], [11, 22], [11, 23], [12, 13], [12, 14], [12, 15], [12, 19], [12, 23], [13, 14], [13, 16], [13, 17], [14, 15], [14, 16], [14, 17], [14, 22], [14, 23], [15, 17], [15, 18], [15, 19], [16, 18], [16, 20], [16, 22], [17, 18], [17, 20], [18, 19], [18, 21], [18, 22], [19, 23]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s7/solution/solve.sh b/tasks/construct-nppc-independent-set-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7cb381bf0acee34fc93726ac6199c17ac3f35dad
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-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'
+{"independent_set": [1, 3, 5, 6, 7, 9, 13, 15, 20, 21, 22, 23]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l3-s7/tests/check.py b/tasks/construct-nppc-independent-set-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s7/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-s7/tests/instance.json b/tasks/construct-nppc-independent-set-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf9bc931d9dbdc232afea9072543ace39eb55db1
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 2], [0, 5], [0, 6], [0, 9], [0, 10], [0, 11], [0, 13], [0, 16], [0, 17], [0, 18], [0, 21], [0, 23], [1, 2], [1, 4], [1, 16], [1, 18], [2, 3], [2, 8], [2, 11], [2, 12], [2, 14], [2, 15], [2, 17], [2, 21], [2, 22], [2, 23], [3, 10], [3, 11], [3, 16], [3, 17], [3, 19], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [4, 11], [4, 14], [4, 16], [4, 19], [4, 20], [4, 23], [5, 10], [5, 19], [6, 8], [6, 10], [6, 14], [6, 17], [6, 18], [7, 12], [7, 14], [7, 17], [7, 18], [8, 11], [8, 14], [8, 16], [8, 17], [8, 19], [8, 20], [8, 22], [9, 10], [9, 11], [9, 14], [9, 16], [9, 19], [10, 12], [10, 14], [10, 17], [10, 20], [10, 21], [10, 22], [11, 14], [11, 18], [11, 19], [11, 21], [11, 22], [11, 23], [12, 13], [12, 14], [12, 15], [12, 19], [12, 23], [13, 14], [13, 16], [13, 17], [14, 15], [14, 16], [14, 17], [14, 22], [14, 23], [15, 17], [15, 18], [15, 19], [16, 18], [16, 20], [16, 22], [17, 18], [17, 20], [18, 19], [18, 21], [18, 22], [19, 23]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s7/tests/run.py b/tasks/construct-nppc-independent-set-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-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-independent-set-l3-s7/tests/test.sh b/tasks/construct-nppc-independent-set-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-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-independent-set-l3-s9/environment/Dockerfile b/tasks/construct-nppc-independent-set-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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-nppc-independent-set-l3-s9/environment/instance.json b/tasks/construct-nppc-independent-set-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3efbd4d5064907ff8a70b0400b4aeaea8594b17d
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 2], [0, 8], [0, 13], [0, 20], [0, 22], [1, 2], [1, 4], [1, 5], [1, 8], [1, 10], [2, 3], [2, 4], [2, 7], [2, 8], [2, 10], [2, 11], [2, 12], [2, 15], [2, 16], [2, 18], [2, 19], [2, 21], [2, 22], [3, 4], [3, 6], [3, 8], [3, 10], [3, 13], [3, 20], [3, 22], [3, 23], [4, 5], [4, 7], [4, 8], [4, 12], [4, 13], [4, 14], [4, 18], [4, 19], [4, 21], [4, 22], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 18], [5, 19], [5, 20], [5, 21], [5, 23], [6, 7], [6, 18], [6, 19], [6, 21], [7, 8], [7, 10], [7, 11], [7, 17], [7, 20], [7, 21], [7, 22], [8, 9], [8, 12], [8, 13], [8, 18], [8, 22], [8, 23], [9, 13], [9, 20], [9, 22], [9, 23], [10, 11], [10, 14], [10, 15], [10, 16], [10, 18], [10, 20], [10, 23], [11, 12], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 23], [12, 13], [13, 14], [13, 16], [13, 18], [13, 19], [13, 23], [14, 20], [14, 23], [15, 20], [15, 22], [15, 23], [17, 22], [17, 23], [18, 20], [18, 22], [18, 23], [19, 20], [19, 22], [20, 21], [20, 22], [20, 23], [21, 22]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s9/solution/solve.sh b/tasks/construct-nppc-independent-set-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b4efb2c8ce8f64a0a7fa142632e7cabaac2b0166
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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'
+{"independent_set": [0, 1, 3, 9, 12, 14, 15, 16, 17, 18, 19, 21]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l3-s9/tests/check.py b/tasks/construct-nppc-independent-set-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s9/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-s9/tests/instance.json b/tasks/construct-nppc-independent-set-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3efbd4d5064907ff8a70b0400b4aeaea8594b17d
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 24, "k": 12, "edges": [[0, 2], [0, 8], [0, 13], [0, 20], [0, 22], [1, 2], [1, 4], [1, 5], [1, 8], [1, 10], [2, 3], [2, 4], [2, 7], [2, 8], [2, 10], [2, 11], [2, 12], [2, 15], [2, 16], [2, 18], [2, 19], [2, 21], [2, 22], [3, 4], [3, 6], [3, 8], [3, 10], [3, 13], [3, 20], [3, 22], [3, 23], [4, 5], [4, 7], [4, 8], [4, 12], [4, 13], [4, 14], [4, 18], [4, 19], [4, 21], [4, 22], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 18], [5, 19], [5, 20], [5, 21], [5, 23], [6, 7], [6, 18], [6, 19], [6, 21], [7, 8], [7, 10], [7, 11], [7, 17], [7, 20], [7, 21], [7, 22], [8, 9], [8, 12], [8, 13], [8, 18], [8, 22], [8, 23], [9, 13], [9, 20], [9, 22], [9, 23], [10, 11], [10, 14], [10, 15], [10, 16], [10, 18], [10, 20], [10, 23], [11, 12], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 23], [12, 13], [13, 14], [13, 16], [13, 18], [13, 19], [13, 23], [14, 20], [14, 23], [15, 20], [15, 22], [15, 23], [17, 22], [17, 23], [18, 20], [18, 22], [18, 23], [19, 20], [19, 22], [20, 21], [20, 22], [20, 23], [21, 22]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l3-s9/tests/run.py b/tasks/construct-nppc-independent-set-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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-nppc-independent-set-l3-s9/tests/test.sh b/tasks/construct-nppc-independent-set-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-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-nppc-quad-diophantine-l2-s1/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-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-nppc-quad-diophantine-l2-s1/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a150e868cc64096807e6726d90f9b5469bc86945
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"a": 859, "b": 695, "c": 630079779, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s1/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..25293e9e2db57dfafa90757017cca16a87419802
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-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'
+{"x": 856, "y": 949}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s1/tests/check.py b/tasks/construct-nppc-quad-diophantine-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s1/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-s1/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a150e868cc64096807e6726d90f9b5469bc86945
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"a": 859, "b": 695, "c": 630079779, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s1/tests/run.py b/tasks/construct-nppc-quad-diophantine-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-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-nppc-quad-diophantine-l2-s1/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-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-nppc-quad-diophantine-l2-s6/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l2-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-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-nppc-quad-diophantine-l2-s6/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l2-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..10d0723560c4bfc361f87a2a6a390b6b43f1f820
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s6/environment/instance.json
@@ -0,0 +1 @@
+{"a": 603, "b": 963, "c": 2436381, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s6/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l2-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7ac5a9c037de5d16886748a6c2a833e9f125ac3d
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-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": 62, "y": 123}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s6/tests/check.py b/tasks/construct-nppc-quad-diophantine-l2-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s6/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-s6/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l2-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..10d0723560c4bfc361f87a2a6a390b6b43f1f820
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-s6/tests/instance.json
@@ -0,0 +1 @@
+{"a": 603, "b": 963, "c": 2436381, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l2-s6/tests/run.py b/tasks/construct-nppc-quad-diophantine-l2-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-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-nppc-quad-diophantine-l2-s6/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l2-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l2-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-nppc-quad-diophantine-l6-s9/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l6-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-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-l6-s9/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l6-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..987bb5a4e347c3084d37e85ec59ade23360b095e
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s9/environment/instance.json
@@ -0,0 +1 @@
+{"a": 8710231508, "b": 3870768249, "c": 5236256626610643773153378280, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s9/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l6-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..881bae274562a82df009a1bf05044c7558d4321a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-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": 775346109, "y": 3863733268}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s9/tests/check.py b/tasks/construct-nppc-quad-diophantine-l6-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-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-l6-s9/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l6-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..987bb5a4e347c3084d37e85ec59ade23360b095e
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-s9/tests/instance.json
@@ -0,0 +1 @@
+{"a": 8710231508, "b": 3870768249, "c": 5236256626610643773153378280, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l6-s9/tests/run.py b/tasks/construct-nppc-quad-diophantine-l6-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-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-l6-s9/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l6-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l6-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-l2-s1/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-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-nppc-quadratic-congruence-l2-s1/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a83728f975a4baba3a9a658b5758c76c195a4e65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"a": 768, "b": 2272, "c": 10179, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s1/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bee1fb6425bc96cce63716866b983632c809cf7b
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-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'
+{"x": 2720}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s1/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-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-l2-s1/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a83728f975a4baba3a9a658b5758c76c195a4e65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"a": 768, "b": 2272, "c": 10179, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s1/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-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-nppc-quadratic-congruence-l2-s1/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-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-nppc-quadratic-congruence-l2-s6/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l2-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-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-nppc-quadratic-congruence-l2-s6/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l2-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d08a6933bb6144f6bb668219a14f04e62b31c04a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s6/environment/instance.json
@@ -0,0 +1 @@
+{"a": 5314, "b": 5481, "c": 14113, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s6/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l2-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..888919c6d36c5e19a09b593edf81d9256f80d75e
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-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": 5069}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s6/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l2-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s6/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-s6/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l2-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d08a6933bb6144f6bb668219a14f04e62b31c04a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-s6/tests/instance.json
@@ -0,0 +1 @@
+{"a": 5314, "b": 5481, "c": 14113, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l2-s6/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l2-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-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-nppc-quadratic-congruence-l2-s6/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l2-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l2-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-nppc-quadratic-congruence-l6-s9/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l6-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-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-l6-s9/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l6-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2911a2a03f102324913fccf888ca61fdd4ca7e46
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s9/environment/instance.json
@@ -0,0 +1 @@
+{"a": 54411231287342036586557456943569560239781274087, "b": 67903019655856310312545467541604458285820320537, "c": 48293723721277017789522921140705095396913061173, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s9/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l6-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..132b4901b75f63fc40a6dae66b47911a6bc7149e
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-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": 48292796818317024962048407435450600420549279215}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s9/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l6-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-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-l6-s9/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l6-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2911a2a03f102324913fccf888ca61fdd4ca7e46
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-s9/tests/instance.json
@@ -0,0 +1 @@
+{"a": 54411231287342036586557456943569560239781274087, "b": 67903019655856310312545467541604458285820320537, "c": 48293723721277017789522921140705095396913061173, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l6-s9/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l6-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-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-l6-s9/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l6-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l6-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-vertex-cover-l4-s2/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l4-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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-nppc-vertex-cover-l4-s2/environment/instance.json b/tasks/construct-nppc-vertex-cover-l4-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..14a504d62d8ddeef708a7565f6b9cbcebd4d0f02
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s2/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 7], [0, 8], [0, 9], [0, 13], [0, 15], [0, 22], [0, 26], [0, 34], [0, 35], [0, 36], [0, 38], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 34], [1, 35], [1, 37], [1, 38], [1, 39], [2, 7], [2, 9], [2, 15], [2, 17], [2, 28], [2, 30], [2, 31], [2, 36], [2, 38], [3, 5], [3, 7], [3, 8], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 20], [3, 21], [3, 23], [3, 26], [3, 28], [3, 29], [3, 30], [3, 32], [3, 33], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [3, 39], [4, 7], [4, 8], [4, 13], [4, 18], [4, 28], [4, 30], [4, 34], [4, 35], [5, 7], [5, 13], [5, 15], [5, 17], [5, 18], [5, 26], [5, 28], [5, 29], [5, 38], [5, 39], [6, 8], [6, 13], [6, 15], [6, 26], [6, 28], [6, 29], [6, 30], [6, 31], [6, 34], [7, 8], [7, 9], [7, 13], [7, 14], [7, 17], [7, 18], [7, 22], [7, 25], [7, 26], [7, 28], [7, 30], [7, 33], [7, 36], [7, 37], [7, 38], [7, 39], [8, 9], [8, 11], [8, 14], [8, 16], [8, 17], [8, 18], [8, 22], [8, 25], [8, 26], [8, 27], [8, 29], [8, 30], [8, 31], [8, 33], [8, 35], [8, 37], [8, 38], [8, 39], [9, 10], [9, 13], [9, 15], [9, 17], [9, 18], [9, 21], [9, 22], [9, 24], [9, 26], [9, 27], [9, 28], [9, 29], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 36], [9, 38], [10, 13], [10, 17], [10, 18], [10, 22], [10, 26], [10, 28], [10, 29], [10, 31], [10, 36], [11, 13], [11, 15], [11, 22], [11, 28], [11, 30], [11, 31], [11, 34], [11, 39], [12, 13], [12, 17], [12, 18], [12, 22], [12, 28], [12, 29], [12, 31], [12, 35], [12, 39], [13, 14], [13, 15], [13, 17], [13, 19], [13, 20], [13, 22], [13, 23], [13, 24], [13, 26], [13, 28], [13, 31], [13, 33], [13, 34], [13, 35], [13, 36], [13, 37], [13, 38], [13, 39], [14, 15], [14, 17], [14, 18], [14, 28], [14, 30], [14, 35], [14, 36], [14, 38], [14, 39], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 26], [15, 28], [15, 29], [15, 30], [15, 32], [15, 33], [15, 34], [15, 35], [15, 36], [15, 38], [15, 39], [16, 22], [16, 26], [16, 28], [16, 29], [16, 34], [16, 36], [16, 38], [16, 39], [17, 18], [17, 21], [17, 22], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 30], [17, 31], [17, 32], [17, 33], [17, 35], [17, 38], [18, 19], [18, 22], [18, 25], [18, 26], [18, 28], [18, 30], [18, 33], [18, 34], [18, 35], [18, 36], [18, 37], [18, 38], [18, 39], [19, 22], [19, 28], [19, 29], [19, 31], [19, 35], [19, 38], [19, 39], [20, 26], [20, 30], [20, 34], [20, 35], [21, 22], [21, 29], [21, 30], [21, 31], [21, 34], [21, 35], [21, 38], [22, 23], [22, 26], [22, 27], [22, 28], [22, 30], [22, 31], [22, 33], [22, 34], [22, 39], [23, 31], [23, 34], [24, 29], [24, 34], [24, 35], [24, 36], [24, 38], [25, 28], [25, 29], [25, 30], [25, 31], [25, 34], [25, 35], [25, 39], [26, 27], [26, 28], [26, 29], [26, 30], [26, 31], [26, 36], [26, 38], [26, 39], [27, 30], [27, 35], [27, 38], [27, 39], [28, 30], [28, 31], [28, 32], [28, 34], [28, 35], [28, 36], [28, 37], [28, 38], [28, 39], [29, 30], [29, 31], [29, 33], [29, 35], [29, 36], [29, 38], [30, 31], [30, 33], [30, 34], [30, 36], [30, 38], [30, 39], [31, 32], [31, 34], [31, 35], [31, 36], [31, 38], [31, 39], [32, 34], [32, 35], [32, 36], [32, 38], [33, 34], [33, 36], [33, 38], [34, 35], [34, 36], [34, 37], [34, 38], [34, 39], [35, 36], [35, 37], [35, 39], [36, 37], [36, 38], [36, 39], [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-s2/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l4-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e99fe414858418c5995eb4cd8419e4c0ea39e173
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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'
+{"cover": [1, 3, 7, 8, 9, 13, 15, 17, 18, 22, 26, 28, 29, 30, 31, 34, 35, 36, 38, 39]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l4-s2/tests/check.py b/tasks/construct-nppc-vertex-cover-l4-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s2/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-s2/tests/instance.json b/tasks/construct-nppc-vertex-cover-l4-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..14a504d62d8ddeef708a7565f6b9cbcebd4d0f02
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s2/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 7], [0, 8], [0, 9], [0, 13], [0, 15], [0, 22], [0, 26], [0, 34], [0, 35], [0, 36], [0, 38], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 34], [1, 35], [1, 37], [1, 38], [1, 39], [2, 7], [2, 9], [2, 15], [2, 17], [2, 28], [2, 30], [2, 31], [2, 36], [2, 38], [3, 5], [3, 7], [3, 8], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 20], [3, 21], [3, 23], [3, 26], [3, 28], [3, 29], [3, 30], [3, 32], [3, 33], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [3, 39], [4, 7], [4, 8], [4, 13], [4, 18], [4, 28], [4, 30], [4, 34], [4, 35], [5, 7], [5, 13], [5, 15], [5, 17], [5, 18], [5, 26], [5, 28], [5, 29], [5, 38], [5, 39], [6, 8], [6, 13], [6, 15], [6, 26], [6, 28], [6, 29], [6, 30], [6, 31], [6, 34], [7, 8], [7, 9], [7, 13], [7, 14], [7, 17], [7, 18], [7, 22], [7, 25], [7, 26], [7, 28], [7, 30], [7, 33], [7, 36], [7, 37], [7, 38], [7, 39], [8, 9], [8, 11], [8, 14], [8, 16], [8, 17], [8, 18], [8, 22], [8, 25], [8, 26], [8, 27], [8, 29], [8, 30], [8, 31], [8, 33], [8, 35], [8, 37], [8, 38], [8, 39], [9, 10], [9, 13], [9, 15], [9, 17], [9, 18], [9, 21], [9, 22], [9, 24], [9, 26], [9, 27], [9, 28], [9, 29], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 36], [9, 38], [10, 13], [10, 17], [10, 18], [10, 22], [10, 26], [10, 28], [10, 29], [10, 31], [10, 36], [11, 13], [11, 15], [11, 22], [11, 28], [11, 30], [11, 31], [11, 34], [11, 39], [12, 13], [12, 17], [12, 18], [12, 22], [12, 28], [12, 29], [12, 31], [12, 35], [12, 39], [13, 14], [13, 15], [13, 17], [13, 19], [13, 20], [13, 22], [13, 23], [13, 24], [13, 26], [13, 28], [13, 31], [13, 33], [13, 34], [13, 35], [13, 36], [13, 37], [13, 38], [13, 39], [14, 15], [14, 17], [14, 18], [14, 28], [14, 30], [14, 35], [14, 36], [14, 38], [14, 39], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 26], [15, 28], [15, 29], [15, 30], [15, 32], [15, 33], [15, 34], [15, 35], [15, 36], [15, 38], [15, 39], [16, 22], [16, 26], [16, 28], [16, 29], [16, 34], [16, 36], [16, 38], [16, 39], [17, 18], [17, 21], [17, 22], [17, 24], [17, 25], [17, 26], [17, 27], [17, 28], [17, 29], [17, 30], [17, 31], [17, 32], [17, 33], [17, 35], [17, 38], [18, 19], [18, 22], [18, 25], [18, 26], [18, 28], [18, 30], [18, 33], [18, 34], [18, 35], [18, 36], [18, 37], [18, 38], [18, 39], [19, 22], [19, 28], [19, 29], [19, 31], [19, 35], [19, 38], [19, 39], [20, 26], [20, 30], [20, 34], [20, 35], [21, 22], [21, 29], [21, 30], [21, 31], [21, 34], [21, 35], [21, 38], [22, 23], [22, 26], [22, 27], [22, 28], [22, 30], [22, 31], [22, 33], [22, 34], [22, 39], [23, 31], [23, 34], [24, 29], [24, 34], [24, 35], [24, 36], [24, 38], [25, 28], [25, 29], [25, 30], [25, 31], [25, 34], [25, 35], [25, 39], [26, 27], [26, 28], [26, 29], [26, 30], [26, 31], [26, 36], [26, 38], [26, 39], [27, 30], [27, 35], [27, 38], [27, 39], [28, 30], [28, 31], [28, 32], [28, 34], [28, 35], [28, 36], [28, 37], [28, 38], [28, 39], [29, 30], [29, 31], [29, 33], [29, 35], [29, 36], [29, 38], [30, 31], [30, 33], [30, 34], [30, 36], [30, 38], [30, 39], [31, 32], [31, 34], [31, 35], [31, 36], [31, 38], [31, 39], [32, 34], [32, 35], [32, 36], [32, 38], [33, 34], [33, 36], [33, 38], [34, 35], [34, 36], [34, 37], [34, 38], [34, 39], [35, 36], [35, 37], [35, 39], [36, 37], [36, 38], [36, 39], [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-s2/tests/run.py b/tasks/construct-nppc-vertex-cover-l4-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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-nppc-vertex-cover-l4-s2/tests/test.sh b/tasks/construct-nppc-vertex-cover-l4-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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-nppc-vertex-cover-l4-s5/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l4-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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-nppc-vertex-cover-l4-s5/environment/instance.json b/tasks/construct-nppc-vertex-cover-l4-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a81dc2958da0de609cbda522286410e10a9a59dd
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s5/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 16], [0, 17], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 30], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 39], [1, 2], [1, 4], [1, 6], [1, 9], [1, 10], [1, 11], [1, 12], [1, 14], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 34], [1, 36], [1, 37], [1, 38], [1, 39], [2, 5], [2, 6], [2, 10], [2, 11], [2, 12], [2, 14], [2, 17], [2, 20], [2, 21], [2, 22], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [2, 38], [3, 10], [3, 11], [3, 14], [3, 17], [3, 21], [3, 23], [3, 26], [3, 29], [3, 32], [3, 38], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 14], [4, 15], [4, 16], [4, 17], [4, 19], [4, 21], [4, 22], [4, 24], [4, 26], [4, 28], [4, 29], [4, 30], [4, 31], [4, 32], [4, 33], [4, 35], [4, 36], [4, 38], [4, 39], [5, 11], [5, 16], [5, 17], [5, 26], [5, 29], [5, 32], [5, 33], [5, 38], [6, 8], [6, 10], [6, 12], [6, 15], [6, 16], [6, 17], [6, 18], [6, 20], [6, 21], [6, 23], [6, 25], [6, 26], [6, 28], [6, 30], [6, 31], [6, 32], [6, 33], [6, 34], [6, 36], [6, 37], [6, 38], [6, 39], [7, 10], [7, 16], [7, 21], [7, 23], [7, 26], [7, 29], [7, 30], [7, 33], [8, 16], [8, 21], [8, 26], [8, 29], [8, 32], [9, 14], [9, 16], [9, 17], [9, 23], [9, 29], [9, 31], [9, 32], [9, 33], [10, 11], [10, 15], [10, 16], [10, 17], [10, 23], [10, 26], [10, 27], [10, 30], [10, 31], [10, 32], [10, 33], [10, 34], [10, 36], [10, 37], [10, 39], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 18], [11, 22], [11, 23], [11, 24], [11, 30], [11, 31], [11, 32], [11, 33], [11, 34], [11, 35], [11, 36], [11, 38], [12, 14], [12, 16], [12, 17], [12, 23], [12, 29], [12, 30], [12, 31], [13, 14], [13, 16], [13, 17], [13, 22], [13, 29], [13, 30], [14, 16], [14, 17], [14, 18], [14, 19], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 25], [14, 26], [14, 29], [14, 30], [14, 31], [14, 32], [14, 33], [14, 37], [14, 38], [15, 22], [15, 26], [15, 32], [16, 18], [16, 23], [16, 24], [16, 26], [16, 30], [16, 31], [16, 32], [16, 33], [16, 36], [16, 38], [16, 39], [17, 21], [17, 22], [17, 23], [17, 24], [17, 32], [17, 33], [17, 35], [17, 37], [17, 39], [18, 22], [18, 23], [18, 31], [18, 32], [18, 33], [19, 22], [19, 23], [19, 26], [19, 29], [19, 30], [19, 33], [20, 21], [20, 23], [20, 26], [20, 31], [20, 32], [21, 23], [21, 24], [21, 26], [21, 27], [21, 30], [21, 31], [21, 32], [21, 35], [21, 36], [21, 38], [21, 39], [22, 23], [22, 32], [22, 33], [22, 34], [22, 35], [22, 39], [23, 28], [23, 29], [23, 31], [23, 34], [23, 35], [23, 36], [23, 38], [23, 39], [24, 30], [24, 32], [24, 38], [25, 26], [25, 30], [25, 31], [25, 38], [26, 28], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 34], [26, 36], [26, 38], [27, 30], [27, 32], [27, 33], [27, 38], [28, 30], [28, 38], [29, 30], [29, 31], [29, 32], [29, 33], [29, 34], [29, 36], [29, 37], [29, 38], [29, 39], [30, 31], [30, 32], [30, 36], [30, 38], [30, 39], [31, 32], [31, 34], [31, 35], [31, 36], [31, 37], [31, 38], [32, 33], [32, 34], [32, 35], [32, 36], [32, 37], [33, 36], [33, 37], [33, 38], [34, 38], [35, 38]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s5/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l4-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..80989e2cce201366228cee5b19a95c62e16961c1
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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'
+{"cover": [0, 1, 2, 4, 6, 10, 11, 14, 16, 17, 21, 22, 23, 26, 29, 30, 31, 32, 33, 38]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l4-s5/tests/check.py b/tasks/construct-nppc-vertex-cover-l4-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s5/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-s5/tests/instance.json b/tasks/construct-nppc-vertex-cover-l4-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a81dc2958da0de609cbda522286410e10a9a59dd
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l4-s5/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 16], [0, 17], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 30], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 39], [1, 2], [1, 4], [1, 6], [1, 9], [1, 10], [1, 11], [1, 12], [1, 14], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 34], [1, 36], [1, 37], [1, 38], [1, 39], [2, 5], [2, 6], [2, 10], [2, 11], [2, 12], [2, 14], [2, 17], [2, 20], [2, 21], [2, 22], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [2, 38], [3, 10], [3, 11], [3, 14], [3, 17], [3, 21], [3, 23], [3, 26], [3, 29], [3, 32], [3, 38], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 14], [4, 15], [4, 16], [4, 17], [4, 19], [4, 21], [4, 22], [4, 24], [4, 26], [4, 28], [4, 29], [4, 30], [4, 31], [4, 32], [4, 33], [4, 35], [4, 36], [4, 38], [4, 39], [5, 11], [5, 16], [5, 17], [5, 26], [5, 29], [5, 32], [5, 33], [5, 38], [6, 8], [6, 10], [6, 12], [6, 15], [6, 16], [6, 17], [6, 18], [6, 20], [6, 21], [6, 23], [6, 25], [6, 26], [6, 28], [6, 30], [6, 31], [6, 32], [6, 33], [6, 34], [6, 36], [6, 37], [6, 38], [6, 39], [7, 10], [7, 16], [7, 21], [7, 23], [7, 26], [7, 29], [7, 30], [7, 33], [8, 16], [8, 21], [8, 26], [8, 29], [8, 32], [9, 14], [9, 16], [9, 17], [9, 23], [9, 29], [9, 31], [9, 32], [9, 33], [10, 11], [10, 15], [10, 16], [10, 17], [10, 23], [10, 26], [10, 27], [10, 30], [10, 31], [10, 32], [10, 33], [10, 34], [10, 36], [10, 37], [10, 39], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 18], [11, 22], [11, 23], [11, 24], [11, 30], [11, 31], [11, 32], [11, 33], [11, 34], [11, 35], [11, 36], [11, 38], [12, 14], [12, 16], [12, 17], [12, 23], [12, 29], [12, 30], [12, 31], [13, 14], [13, 16], [13, 17], [13, 22], [13, 29], [13, 30], [14, 16], [14, 17], [14, 18], [14, 19], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 25], [14, 26], [14, 29], [14, 30], [14, 31], [14, 32], [14, 33], [14, 37], [14, 38], [15, 22], [15, 26], [15, 32], [16, 18], [16, 23], [16, 24], [16, 26], [16, 30], [16, 31], [16, 32], [16, 33], [16, 36], [16, 38], [16, 39], [17, 21], [17, 22], [17, 23], [17, 24], [17, 32], [17, 33], [17, 35], [17, 37], [17, 39], [18, 22], [18, 23], [18, 31], [18, 32], [18, 33], [19, 22], [19, 23], [19, 26], [19, 29], [19, 30], [19, 33], [20, 21], [20, 23], [20, 26], [20, 31], [20, 32], [21, 23], [21, 24], [21, 26], [21, 27], [21, 30], [21, 31], [21, 32], [21, 35], [21, 36], [21, 38], [21, 39], [22, 23], [22, 32], [22, 33], [22, 34], [22, 35], [22, 39], [23, 28], [23, 29], [23, 31], [23, 34], [23, 35], [23, 36], [23, 38], [23, 39], [24, 30], [24, 32], [24, 38], [25, 26], [25, 30], [25, 31], [25, 38], [26, 28], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 34], [26, 36], [26, 38], [27, 30], [27, 32], [27, 33], [27, 38], [28, 30], [28, 38], [29, 30], [29, 31], [29, 32], [29, 33], [29, 34], [29, 36], [29, 37], [29, 38], [29, 39], [30, 31], [30, 32], [30, 36], [30, 38], [30, 39], [31, 32], [31, 34], [31, 35], [31, 36], [31, 37], [31, 38], [32, 33], [32, 34], [32, 35], [32, 36], [32, 37], [33, 36], [33, 37], [33, 38], [34, 38], [35, 38]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l4-s5/tests/run.py b/tasks/construct-nppc-vertex-cover-l4-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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-nppc-vertex-cover-l4-s5/tests/test.sh b/tasks/construct-nppc-vertex-cover-l4-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-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-rg-graph-color-l2-s1/environment/Dockerfile b/tasks/construct-rg-graph-color-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-graph-color-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-rg-graph-color-l2-s1/environment/instance.json b/tasks/construct-rg-graph-color-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..58ce37d81a92f575270df20db387e4f056a32bc3
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"num_vertices": 10, "num_colors": 4, "edges": [[0, 4], [0, 6], [0, 7], [1, 2], [1, 7], [2, 8], [2, 9], [3, 8], [4, 9], [5, 6], [5, 7], [5, 8], [6, 8], [7, 8]], "family": "rg_graph_color", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-graph-color-l2-s1/solution/solve.sh b/tasks/construct-rg-graph-color-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..403435a69eac597a59fc336a396bf565629796da
--- /dev/null
+++ b/tasks/construct-rg-graph-color-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'
+{"coloring": [1, 1, 2, 1, 2, 1, 2, 2, 3, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rg-graph-color-l2-s1/tests/check.py b/tasks/construct-rg-graph-color-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e9328912405d1c894970c90415be62bf9556ed36
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l2-s1/tests/check.py
@@ -0,0 +1,13 @@
+"""Proper colouring with colours 1..k (Reasoning Gym graph_color, Apache-2.0). Any valid colouring.
+Upstream note: its verifier checks `color in allowed_colors`, so True (== 1) and 1.0 were accepted as
+colours, and extra keys were ignored. Here colours must be ints in 1..k, one per vertex."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_vertices"], inst["num_colors"]
+    c = int_list(ans.get("coloring"), n, 1, k, "coloring")
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"adjacent vertices {u} and {v} share colour {c[u]}")
+    return None, {}
diff --git a/tasks/construct-rg-graph-color-l2-s1/tests/instance.json b/tasks/construct-rg-graph-color-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..58ce37d81a92f575270df20db387e4f056a32bc3
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"num_vertices": 10, "num_colors": 4, "edges": [[0, 4], [0, 6], [0, 7], [1, 2], [1, 7], [2, 8], [2, 9], [3, 8], [4, 9], [5, 6], [5, 7], [5, 8], [6, 8], [7, 8]], "family": "rg_graph_color", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-graph-color-l2-s1/tests/run.py b/tasks/construct-rg-graph-color-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-graph-color-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-rg-graph-color-l2-s1/tests/test.sh b/tasks/construct-rg-graph-color-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-graph-color-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-rg-graph-color-l6-s9/environment/Dockerfile b/tasks/construct-rg-graph-color-l6-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-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-graph-color-l6-s9/environment/instance.json b/tasks/construct-rg-graph-color-l6-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4b71ec13f90851aa473d68c5e1ad219f8c6f376e
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-s9/environment/instance.json
@@ -0,0 +1 @@
+{"num_vertices": 40, "num_colors": 3, "edges": [[0, 14], [0, 19], [1, 4], [1, 15], [1, 30], [2, 8], [2, 17], [2, 21], [3, 21], [3, 25], [3, 33], [3, 39], [4, 13], [4, 26], [4, 32], [4, 36], [5, 12], [5, 14], [6, 16], [6, 29], [7, 25], [7, 29], [8, 13], [8, 28], [8, 33], [8, 34], [9, 12], [9, 27], [9, 34], [10, 11], [10, 14], [10, 15], [10, 32], [11, 12], [11, 21], [11, 22], [11, 33], [11, 34], [12, 20], [12, 24], [13, 20], [13, 30], [13, 32], [13, 37], [14, 16], [14, 25], [14, 33], [15, 22], [15, 36], [16, 31], [16, 38], [17, 24], [17, 35], [18, 30], [20, 21], [21, 22], [22, 28], [22, 30], [22, 34], [23, 25], [23, 32], [24, 25], [25, 27], [26, 32], [27, 33], [27, 34], [28, 31], [30, 36], [31, 36], [31, 37]], "family": "rg_graph_color", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-graph-color-l6-s9/solution/solve.sh b/tasks/construct-rg-graph-color-l6-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..08f6001a8f6de22a3a844e2e6e604048b8c91493
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-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'
+{"coloring": [1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 3, 2, 1, 2, 2, 3, 1, 1, 1, 3, 1, 2, 3, 2, 2, 1, 3, 3, 3, 1, 3, 2, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rg-graph-color-l6-s9/tests/check.py b/tasks/construct-rg-graph-color-l6-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e9328912405d1c894970c90415be62bf9556ed36
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-s9/tests/check.py
@@ -0,0 +1,13 @@
+"""Proper colouring with colours 1..k (Reasoning Gym graph_color, Apache-2.0). Any valid colouring.
+Upstream note: its verifier checks `color in allowed_colors`, so True (== 1) and 1.0 were accepted as
+colours, and extra keys were ignored. Here colours must be ints in 1..k, one per vertex."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_vertices"], inst["num_colors"]
+    c = int_list(ans.get("coloring"), n, 1, k, "coloring")
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"adjacent vertices {u} and {v} share colour {c[u]}")
+    return None, {}
diff --git a/tasks/construct-rg-graph-color-l6-s9/tests/instance.json b/tasks/construct-rg-graph-color-l6-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4b71ec13f90851aa473d68c5e1ad219f8c6f376e
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-s9/tests/instance.json
@@ -0,0 +1 @@
+{"num_vertices": 40, "num_colors": 3, "edges": [[0, 14], [0, 19], [1, 4], [1, 15], [1, 30], [2, 8], [2, 17], [2, 21], [3, 21], [3, 25], [3, 33], [3, 39], [4, 13], [4, 26], [4, 32], [4, 36], [5, 12], [5, 14], [6, 16], [6, 29], [7, 25], [7, 29], [8, 13], [8, 28], [8, 33], [8, 34], [9, 12], [9, 27], [9, 34], [10, 11], [10, 14], [10, 15], [10, 32], [11, 12], [11, 21], [11, 22], [11, 33], [11, 34], [12, 20], [12, 24], [13, 20], [13, 30], [13, 32], [13, 37], [14, 16], [14, 25], [14, 33], [15, 22], [15, 36], [16, 31], [16, 38], [17, 24], [17, 35], [18, 30], [20, 21], [21, 22], [22, 28], [22, 30], [22, 34], [23, 25], [23, 32], [24, 25], [25, 27], [26, 32], [27, 33], [27, 34], [28, 31], [30, 36], [31, 36], [31, 37]], "family": "rg_graph_color", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-graph-color-l6-s9/tests/run.py b/tasks/construct-rg-graph-color-l6-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-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-graph-color-l6-s9/tests/test.sh b/tasks/construct-rg-graph-color-l6-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-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-s4/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l1-s4/environment/instance.json b/tasks/construct-rg-intermediate-integration-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..243493818a4409a7d6c7b45ed2b46edfdbf81833
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "2*(9*x + 5)**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-s4/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c2c510e5c089ce6503e7b8a086e7163e5f195235
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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'
+{"antiderivative": "729*x**4/2 + 810*x**3 + 675*x**2 + 250*x + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l1-s4/tests/check.py b/tasks/construct-rg-intermediate-integration-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s4/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-s4/tests/instance.json b/tasks/construct-rg-intermediate-integration-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..243493818a4409a7d6c7b45ed2b46edfdbf81833
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "2*(9*x + 5)**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-s4/tests/run.py b/tasks/construct-rg-intermediate-integration-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l1-s4/tests/test.sh b/tasks/construct-rg-intermediate-integration-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l5-s2/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l5-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l5-s2/environment/instance.json b/tasks/construct-rg-intermediate-integration-l5-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f9f1a7ff30bbecf183f050936beedca5ac568111
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s2/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "2*x*sin(3*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-s2/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l5-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..47d9e356abab18cc498fe7d0600f84374d21bcf6
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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'
+{"antiderivative": "-2*x*cos(3*x)/3 + 2*sin(3*x)/9 + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l5-s2/tests/check.py b/tasks/construct-rg-intermediate-integration-l5-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s2/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-s2/tests/instance.json b/tasks/construct-rg-intermediate-integration-l5-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f9f1a7ff30bbecf183f050936beedca5ac568111
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s2/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "2*x*sin(3*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-s2/tests/run.py b/tasks/construct-rg-intermediate-integration-l5-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l5-s2/tests/test.sh b/tasks/construct-rg-intermediate-integration-l5-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l5-s5/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l5-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l5-s5/environment/instance.json b/tasks/construct-rg-intermediate-integration-l5-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e398a9eedfa02bd8639d1530d9a2b0991325b956
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s5/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "3*x*cos(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-s5/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l5-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9dba5ac9b413d0e062c9482e649a211538cb963d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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'
+{"antiderivative": "3*x*sin(x) + 3*cos(x) + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l5-s5/tests/check.py b/tasks/construct-rg-intermediate-integration-l5-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-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-l5-s5/tests/instance.json b/tasks/construct-rg-intermediate-integration-l5-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e398a9eedfa02bd8639d1530d9a2b0991325b956
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l5-s5/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "3*x*cos(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-s5/tests/run.py b/tasks/construct-rg-intermediate-integration-l5-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-intermediate-integration-l5-s5/tests/test.sh b/tasks/construct-rg-intermediate-integration-l5-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-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-rg-simple-integration-l2-s0/environment/Dockerfile b/tasks/construct-rg-simple-integration-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l2-s0/environment/instance.json b/tasks/construct-rg-simple-integration-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a3a46b00ff33a5553522fa3d076c6c38dc68606f
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "7*x**4 - 3*x**2", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l2-s0/solution/solve.sh b/tasks/construct-rg-simple-integration-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..92ebab78e899a23f8dd766b7b00cbee500db746f
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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'
+{"antiderivative": "7*x**5/5 - x**3 + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-simple-integration-l2-s0/tests/check.py b/tasks/construct-rg-simple-integration-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s0/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-simple-integration-l2-s0/tests/instance.json b/tasks/construct-rg-simple-integration-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a3a46b00ff33a5553522fa3d076c6c38dc68606f
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "7*x**4 - 3*x**2", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l2-s0/tests/run.py b/tasks/construct-rg-simple-integration-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l2-s0/tests/test.sh b/tasks/construct-rg-simple-integration-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l2-s7/environment/Dockerfile b/tasks/construct-rg-simple-integration-l2-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l2-s7/environment/instance.json b/tasks/construct-rg-simple-integration-l2-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3df9c2e79ef06c354e620f3e2ff83eb33970b596
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s7/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "X", "integrand": "-21*X**5/2 + 4*X/3 - 1/4", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l2-s7/solution/solve.sh b/tasks/construct-rg-simple-integration-l2-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..942188a0c93d74161345b340ae3ad0d5f16564c7
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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'
+{"antiderivative": "-7*X**6/4 + 2*X**2/3 - X/4 + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-simple-integration-l2-s7/tests/check.py b/tasks/construct-rg-simple-integration-l2-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-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-simple-integration-l2-s7/tests/instance.json b/tasks/construct-rg-simple-integration-l2-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3df9c2e79ef06c354e620f3e2ff83eb33970b596
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s7/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "X", "integrand": "-21*X**5/2 + 4*X/3 - 1/4", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l2-s7/tests/run.py b/tasks/construct-rg-simple-integration-l2-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l2-s7/tests/test.sh b/tasks/construct-rg-simple-integration-l2-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l6-s6/environment/Dockerfile b/tasks/construct-rg-simple-integration-l6-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-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-simple-integration-l6-s6/environment/instance.json b/tasks/construct-rg-simple-integration-l6-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a68f885d752c4a0ea69bdb461eb882d723819c9
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s6/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "X", "integrand": "33*X**10 - 70*X**6 - 12*X - 8 - 2/(5*X**2) - 129/(20*X**7)", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l6-s6/solution/solve.sh b/tasks/construct-rg-simple-integration-l6-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..337e1dfc7aa7692c432b69e21afec3aff834ecbb
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-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": "3*X**11 - 10*X**7 - 6*X**2 - 8*X + 2/(5*X) + 43/(40*X**6) + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-simple-integration-l6-s6/tests/check.py b/tasks/construct-rg-simple-integration-l6-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-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-simple-integration-l6-s6/tests/instance.json b/tasks/construct-rg-simple-integration-l6-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a68f885d752c4a0ea69bdb461eb882d723819c9
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s6/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "X", "integrand": "33*X**10 - 70*X**6 - 12*X - 8 - 2/(5*X**2) - 129/(20*X**7)", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l6-s6/tests/run.py b/tasks/construct-rg-simple-integration-l6-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-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-simple-integration-l6-s6/tests/test.sh b/tasks/construct-rg-simple-integration-l6-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-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-simple-integration-l6-s8/environment/Dockerfile b/tasks/construct-rg-simple-integration-l6-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l6-s8/environment/instance.json b/tasks/construct-rg-simple-integration-l6-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf4d7f37e7b75b1fa3b45358df7607da1793d842
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s8/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "45*x**9 - 30*x**4/7 - 18*x - 9/x**4 + 16/(3*x**5) + 24/x**7 - 81/x**10", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l6-s8/solution/solve.sh b/tasks/construct-rg-simple-integration-l6-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..83e2b01f9bf6295a946f538b28e937d670bdfa21
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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'
+{"antiderivative": "9*x**10/2 - 6*x**5/7 - 9*x**2 + 3/x**3 - 4/(3*x**4) - 4/x**6 + 9/x**9 + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-simple-integration-l6-s8/tests/check.py b/tasks/construct-rg-simple-integration-l6-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-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-simple-integration-l6-s8/tests/instance.json b/tasks/construct-rg-simple-integration-l6-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf4d7f37e7b75b1fa3b45358df7607da1793d842
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s8/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "45*x**9 - 30*x**4/7 - 18*x - 9/x**4 + 16/(3*x**5) + 24/x**7 - 81/x**10", "family": "rg_simple_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-simple-integration-l6-s8/tests/run.py b/tasks/construct-rg-simple-integration-l6-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rg-simple-integration-l6-s8/tests/test.sh b/tasks/construct-rg-simple-integration-l6-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-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-rlve-antiderivative-l3-s0/environment/Dockerfile b/tasks/construct-rlve-antiderivative-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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-rlve-antiderivative-l3-s0/environment/instance.json b/tasks/construct-rlve-antiderivative-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..40fb489eced61596e717e1d117fddb318f116bbc
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"f_prime": "(x*cos(x) + sin(x))*sin(x*sin(x))*sin(sin(cos(x*sin(x))))*cos(cos(x*sin(x)))", "max_ops": 40, "max_len": 860, "family": "rlve_antiderivative", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-antiderivative-l3-s0/solution/solve.sh b/tasks/construct-rlve-antiderivative-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..48300ffa8a920dd661c7fc791aa4777d60e58804
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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'
+{"F": "cos(sin(cos(x*sin(x))))"}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-antiderivative-l3-s0/tests/check.py b/tasks/construct-rlve-antiderivative-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c6b30b93bbbb7795b54d973e43f25b23c82cb7fc
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s0/tests/check.py
@@ -0,0 +1,107 @@
+"""Antiderivative check. The answer string is tokenised against a whitelist (x, integers, + - * / ** ( ) and a few
+elementary functions) before sympy parses it, so no Python eval of untrusted text and no `integrate`/`Integral`."""
+import re
+import signal
+
+import sympy
+from sympy.parsing.sympy_parser import auto_number, parse_expr
+
+from run import Invalid
+
+x = sympy.Symbol("x")
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "exp": sympy.exp, "log": sympy.log,
+         "sqrt": sympy.sqrt, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "E": sympy.E, "pi": sympy.pi, "x": x}
+TOK = re.compile(r"\s*(?:(\d+)|([A-Za-z]+)|(\*\*|[-+*/()]))")
+NPTS = 40
+
+
+def safe_parse(s, max_len):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("F must be a non-empty string")
+    if len(s) > max_len:
+        raise Invalid("expression too long")
+    pos = 0
+    while pos < len(s):
+        m = TOK.match(s, pos)
+        if not m or m.end() == pos:
+            if s[pos:].strip() == "":
+                break
+            raise Invalid(f"illegal character near position {pos}")
+        if m.group(1) and len(m.group(1)) > 12:
+            raise Invalid("integer literal too long")
+        if m.group(2) and m.group(2) not in FUNCS:
+            raise Invalid(f"unknown name {m.group(2)!r}")
+        pos = m.end()
+    try:
+        e = parse_expr(s, local_dict=dict(FUNCS), global_dict={"__builtins__": {}, "Integer": sympy.Integer},
+                       transformations=(auto_number,))
+    except Invalid:
+        raise
+    except Exception as ex:
+        raise Invalid(f"cannot parse F: {type(ex).__name__}")
+    if not isinstance(e, sympy.Expr):
+        raise Invalid("F is not an expression")
+    if e.free_symbols - {x}:
+        raise Invalid("F may only contain the variable x")
+    return e
+
+
+def _val(e, pt):
+    v = e.evalf(40, subs={x: pt})
+    if not v.is_number or v.has(sympy.zoo, sympy.nan, sympy.oo, -sympy.oo):
+        return None
+    return v
+
+
+class _Timeout(Exception):
+    pass
+
+
+def _alarm(*_):
+    raise _Timeout()
+
+
+def check(inst, ans):
+    old = None
+    try:
+        old = signal.signal(signal.SIGALRM, _alarm)
+        signal.alarm(40)
+    except ValueError:  # not in main thread
+        old = None
+    try:
+        return _check(inst, ans)
+    except _Timeout:
+        raise Invalid("evaluation timed out")
+    except RecursionError:
+        raise Invalid("expression too deep")
+    finally:
+        if old is not None:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+
+
+def _check(inst, ans):
+    F = safe_parse(ans.get("F"), inst["max_len"])
+    if sympy.count_ops(F) > inst["max_ops"]:
+        raise Invalid("expression too complex")
+    if any(isinstance(a, sympy.Rational) and max(abs(a.p), abs(a.q)) > 10 ** 12 for a in F.atoms(sympy.Rational)):
+        raise Invalid("numeric constants too large")
+    D = sympy.diff(F, x)
+    f = sympy.sympify(inst["f_prime"])  # trusted instance data
+    ok = 0
+    for k in range(NPTS):
+        pt = sympy.Rational(2 * k + 1, NPTS // 2 * 2) * 2 - 2 + sympy.Rational(1, 997)
+        vf = _val(f, pt)
+        if vf is None:
+            continue
+        vd = _val(D, pt)
+        if vd is None:
+            continue
+        err = sympy.Abs(vd - vf).evalf(40)
+        if err > sympy.Float("1e-20", 40) * (1 + sympy.Abs(vf).evalf(40)):
+            raise Invalid(f"F'(x) != f(x) at x = {float(pt):.4f}")
+        ok += 1
+    if ok < NPTS // 4:
+        raise Invalid("F' could not be compared with f on enough test points")
+    return None, {"points_checked": ok}
diff --git a/tasks/construct-rlve-antiderivative-l3-s0/tests/instance.json b/tasks/construct-rlve-antiderivative-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..40fb489eced61596e717e1d117fddb318f116bbc
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"f_prime": "(x*cos(x) + sin(x))*sin(x*sin(x))*sin(sin(cos(x*sin(x))))*cos(cos(x*sin(x)))", "max_ops": 40, "max_len": 860, "family": "rlve_antiderivative", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-antiderivative-l3-s0/tests/run.py b/tasks/construct-rlve-antiderivative-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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-rlve-antiderivative-l3-s0/tests/test.sh b/tasks/construct-rlve-antiderivative-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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-rlve-antiderivative-l3-s9/environment/Dockerfile b/tasks/construct-rlve-antiderivative-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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-antiderivative-l3-s9/environment/instance.json b/tasks/construct-rlve-antiderivative-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..77f0d195789071a387c6ecfc196e36b94d6ab96e
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"f_prime": "-sin(2*x)/2 - 1", "max_ops": 36, "max_len": 700, "family": "rlve_antiderivative", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-antiderivative-l3-s9/solution/solve.sh b/tasks/construct-rlve-antiderivative-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..205a9de387dbcf299fdd443fa09874b2d46f2a48
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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'
+{"F": "-x + cos(2*x)/4"}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-antiderivative-l3-s9/tests/check.py b/tasks/construct-rlve-antiderivative-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c6b30b93bbbb7795b54d973e43f25b23c82cb7fc
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s9/tests/check.py
@@ -0,0 +1,107 @@
+"""Antiderivative check. The answer string is tokenised against a whitelist (x, integers, + - * / ** ( ) and a few
+elementary functions) before sympy parses it, so no Python eval of untrusted text and no `integrate`/`Integral`."""
+import re
+import signal
+
+import sympy
+from sympy.parsing.sympy_parser import auto_number, parse_expr
+
+from run import Invalid
+
+x = sympy.Symbol("x")
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "exp": sympy.exp, "log": sympy.log,
+         "sqrt": sympy.sqrt, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "E": sympy.E, "pi": sympy.pi, "x": x}
+TOK = re.compile(r"\s*(?:(\d+)|([A-Za-z]+)|(\*\*|[-+*/()]))")
+NPTS = 40
+
+
+def safe_parse(s, max_len):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("F must be a non-empty string")
+    if len(s) > max_len:
+        raise Invalid("expression too long")
+    pos = 0
+    while pos < len(s):
+        m = TOK.match(s, pos)
+        if not m or m.end() == pos:
+            if s[pos:].strip() == "":
+                break
+            raise Invalid(f"illegal character near position {pos}")
+        if m.group(1) and len(m.group(1)) > 12:
+            raise Invalid("integer literal too long")
+        if m.group(2) and m.group(2) not in FUNCS:
+            raise Invalid(f"unknown name {m.group(2)!r}")
+        pos = m.end()
+    try:
+        e = parse_expr(s, local_dict=dict(FUNCS), global_dict={"__builtins__": {}, "Integer": sympy.Integer},
+                       transformations=(auto_number,))
+    except Invalid:
+        raise
+    except Exception as ex:
+        raise Invalid(f"cannot parse F: {type(ex).__name__}")
+    if not isinstance(e, sympy.Expr):
+        raise Invalid("F is not an expression")
+    if e.free_symbols - {x}:
+        raise Invalid("F may only contain the variable x")
+    return e
+
+
+def _val(e, pt):
+    v = e.evalf(40, subs={x: pt})
+    if not v.is_number or v.has(sympy.zoo, sympy.nan, sympy.oo, -sympy.oo):
+        return None
+    return v
+
+
+class _Timeout(Exception):
+    pass
+
+
+def _alarm(*_):
+    raise _Timeout()
+
+
+def check(inst, ans):
+    old = None
+    try:
+        old = signal.signal(signal.SIGALRM, _alarm)
+        signal.alarm(40)
+    except ValueError:  # not in main thread
+        old = None
+    try:
+        return _check(inst, ans)
+    except _Timeout:
+        raise Invalid("evaluation timed out")
+    except RecursionError:
+        raise Invalid("expression too deep")
+    finally:
+        if old is not None:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+
+
+def _check(inst, ans):
+    F = safe_parse(ans.get("F"), inst["max_len"])
+    if sympy.count_ops(F) > inst["max_ops"]:
+        raise Invalid("expression too complex")
+    if any(isinstance(a, sympy.Rational) and max(abs(a.p), abs(a.q)) > 10 ** 12 for a in F.atoms(sympy.Rational)):
+        raise Invalid("numeric constants too large")
+    D = sympy.diff(F, x)
+    f = sympy.sympify(inst["f_prime"])  # trusted instance data
+    ok = 0
+    for k in range(NPTS):
+        pt = sympy.Rational(2 * k + 1, NPTS // 2 * 2) * 2 - 2 + sympy.Rational(1, 997)
+        vf = _val(f, pt)
+        if vf is None:
+            continue
+        vd = _val(D, pt)
+        if vd is None:
+            continue
+        err = sympy.Abs(vd - vf).evalf(40)
+        if err > sympy.Float("1e-20", 40) * (1 + sympy.Abs(vf).evalf(40)):
+            raise Invalid(f"F'(x) != f(x) at x = {float(pt):.4f}")
+        ok += 1
+    if ok < NPTS // 4:
+        raise Invalid("F' could not be compared with f on enough test points")
+    return None, {"points_checked": ok}
diff --git a/tasks/construct-rlve-antiderivative-l3-s9/tests/instance.json b/tasks/construct-rlve-antiderivative-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..77f0d195789071a387c6ecfc196e36b94d6ab96e
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"f_prime": "-sin(2*x)/2 - 1", "max_ops": 36, "max_len": 700, "family": "rlve_antiderivative", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-antiderivative-l3-s9/tests/run.py b/tasks/construct-rlve-antiderivative-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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-antiderivative-l3-s9/tests/test.sh b/tasks/construct-rlve-antiderivative-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-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-bezout-identity-l2-s4/environment/Dockerfile b/tasks/construct-rlve-bezout-identity-l2-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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-bezout-identity-l2-s4/environment/instance.json b/tasks/construct-rlve-bezout-identity-l2-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..11fa1f67f84d0f66bc75558435cabd891da1bd44
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l2-s4/environment/instance.json
@@ -0,0 +1 @@
+{"A": [3, -102, 105, 9], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-bezout-identity-l2-s4/solution/solve.sh b/tasks/construct-rlve-bezout-identity-l2-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..73e439dfbcf1a18ab64533feb7128416679821ce
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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": [1, 0, 0, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-bezout-identity-l2-s4/tests/check.py b/tasks/construct-rlve-bezout-identity-l2-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b4cb860ed36974a12b71adc9a0fa3f1ad85c814a
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l2-s4/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-l2-s4/tests/instance.json b/tasks/construct-rlve-bezout-identity-l2-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..11fa1f67f84d0f66bc75558435cabd891da1bd44
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l2-s4/tests/instance.json
@@ -0,0 +1 @@
+{"A": [3, -102, 105, 9], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-bezout-identity-l2-s4/tests/run.py b/tasks/construct-rlve-bezout-identity-l2-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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-bezout-identity-l2-s4/tests/test.sh b/tasks/construct-rlve-bezout-identity-l2-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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-bezout-identity-l6-s5/environment/Dockerfile b/tasks/construct-rlve-bezout-identity-l6-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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-bezout-identity-l6-s5/environment/instance.json b/tasks/construct-rlve-bezout-identity-l6-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aed4c074008d9b1644b117d844e52669f7ef181d
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l6-s5/environment/instance.json
@@ -0,0 +1 @@
+{"A": [90, -30434, -858, -8804, -15114, 20198, 18568, 7604, -11974, -1562, -9286, -1772], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-bezout-identity-l6-s5/solution/solve.sh b/tasks/construct-rlve-bezout-identity-l6-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..33474dcd4ac85276031973e5b02da7d6c382d962
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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": [-4396, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-bezout-identity-l6-s5/tests/check.py b/tasks/construct-rlve-bezout-identity-l6-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b4cb860ed36974a12b71adc9a0fa3f1ad85c814a
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l6-s5/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-l6-s5/tests/instance.json b/tasks/construct-rlve-bezout-identity-l6-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aed4c074008d9b1644b117d844e52669f7ef181d
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l6-s5/tests/instance.json
@@ -0,0 +1 @@
+{"A": [90, -30434, -858, -8804, -15114, 20198, 18568, 7604, -11974, -1562, -9286, -1772], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-bezout-identity-l6-s5/tests/run.py b/tasks/construct-rlve-bezout-identity-l6-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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-bezout-identity-l6-s5/tests/test.sh b/tasks/construct-rlve-bezout-identity-l6-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-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-construct-hack-interval-l1-s0/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-rlve-construct-hack-interval-l1-s0/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..11f49976987954d7f52101972c770f5b280989ee
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 52, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s0/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c390f8933bfd8314241f9f066b3d9f6a715c4263
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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'
+{"L": 3, "R": 13}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s0/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s0/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-s0/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..11f49976987954d7f52101972c770f5b280989ee
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 52, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s0/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-rlve-construct-hack-interval-l1-s0/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-rlve-construct-hack-interval-l1-s7/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l1-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-construct-hack-interval-l1-s7/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l1-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa4306f051f3e9a603fc89aabeeffe5ebae390e5
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s7/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 30, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s7/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l1-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c567eb1dd00b89beb7a9e248b538581bd62a18b6
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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'
+{"L": 4, "R": 8}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s7/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l1-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-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-l1-s7/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l1-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa4306f051f3e9a603fc89aabeeffe5ebae390e5
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l1-s7/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 30, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l1-s7/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l1-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-construct-hack-interval-l1-s7/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l1-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-construct-hack-interval-l5-s1/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-rlve-construct-hack-interval-l5-s1/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d0906ef92f7688ce977547c05f82653514f18d5c
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 674321634672658, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s1/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..13f0ddfb87b1a9678c84b13f46015818890166e0
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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'
+{"L": 443216346726580, "R": 543216346726579}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s1/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s1/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-s1/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d0906ef92f7688ce977547c05f82653514f18d5c
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 674321634672658, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s1/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-rlve-construct-hack-interval-l5-s1/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-rlve-construct-hack-interval-l5-s8/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l5-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-construct-hack-interval-l5-s8/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..304b0e84e6818c64b8c70f8f919777c41f3841c5
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s8/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 544748334121030, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s8/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l5-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5903c8ed5e53320d70723f5548e035712334b57e
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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'
+{"L": 236980009452360, "R": 336980009452359}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s8/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l5-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s8/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-s8/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l5-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..304b0e84e6818c64b8c70f8f919777c41f3841c5
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l5-s8/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 544748334121030, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l5-s8/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l5-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-construct-hack-interval-l5-s8/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l5-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-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-crt-l1-s8/environment/Dockerfile b/tasks/construct-rlve-crt-l1-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-rlve-crt-l1-s8/environment/instance.json b/tasks/construct-rlve-crt-l1-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2a66f260e646f70a2abbeac61067c1563d131ace
--- /dev/null
+++ b/tasks/construct-rlve-crt-l1-s8/environment/instance.json
@@ -0,0 +1 @@
+{"moduli": [14, 13], "residues": [2, 3], "family": "rlve_crt", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-crt-l1-s8/solution/solve.sh b/tasks/construct-rlve-crt-l1-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..705a22748a7b60f74829857496f39d20f161dbde
--- /dev/null
+++ b/tasks/construct-rlve-crt-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'
+{"x": 16}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-crt-l1-s8/tests/check.py b/tasks/construct-rlve-crt-l1-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..886d95606ef325930b24794c0959c2ba7b254ebd
--- /dev/null
+++ b/tasks/construct-rlve-crt-l1-s8/tests/check.py
@@ -0,0 +1,11 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    x = as_int(ans.get("x"), "x", lo=0)
+    if x.bit_length() > 20000:
+        raise Invalid("x is unreasonably large")
+    for a, b in zip(inst["residues"], inst["moduli"]):
+        if x % b != a:
+            raise Invalid(f"x mod {b} = {x % b}, need {a}")
+    return None, {}
diff --git a/tasks/construct-rlve-crt-l1-s8/tests/instance.json b/tasks/construct-rlve-crt-l1-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2a66f260e646f70a2abbeac61067c1563d131ace
--- /dev/null
+++ b/tasks/construct-rlve-crt-l1-s8/tests/instance.json
@@ -0,0 +1 @@
+{"moduli": [14, 13], "residues": [2, 3], "family": "rlve_crt", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-crt-l1-s8/tests/run.py b/tasks/construct-rlve-crt-l1-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-rlve-crt-l1-s8/tests/test.sh b/tasks/construct-rlve-crt-l1-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-rlve-crt-l5-s0/environment/Dockerfile b/tasks/construct-rlve-crt-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-crt-l5-s0/environment/instance.json b/tasks/construct-rlve-crt-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6f7dbbdc4f9b80169382e2c5a9f0bd8ef76d15db
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"moduli": [158298035, 1499470965, 947951029, 354154797, 699828353, 287902062], "residues": [124385906, 366193326, 917713262, 94890306, 466007585, 138251919], "family": "rlve_crt", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-crt-l5-s0/solution/solve.sh b/tasks/construct-rlve-crt-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fafd1085012e70afe5f3e7fddbe92115022b323a
--- /dev/null
+++ b/tasks/construct-rlve-crt-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'
+{"x": 1865664291}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-crt-l5-s0/tests/check.py b/tasks/construct-rlve-crt-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..886d95606ef325930b24794c0959c2ba7b254ebd
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s0/tests/check.py
@@ -0,0 +1,11 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    x = as_int(ans.get("x"), "x", lo=0)
+    if x.bit_length() > 20000:
+        raise Invalid("x is unreasonably large")
+    for a, b in zip(inst["residues"], inst["moduli"]):
+        if x % b != a:
+            raise Invalid(f"x mod {b} = {x % b}, need {a}")
+    return None, {}
diff --git a/tasks/construct-rlve-crt-l5-s0/tests/instance.json b/tasks/construct-rlve-crt-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6f7dbbdc4f9b80169382e2c5a9f0bd8ef76d15db
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"moduli": [158298035, 1499470965, 947951029, 354154797, 699828353, 287902062], "residues": [124385906, 366193326, 917713262, 94890306, 466007585, 138251919], "family": "rlve_crt", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-crt-l5-s0/tests/run.py b/tasks/construct-rlve-crt-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-crt-l5-s0/tests/test.sh b/tasks/construct-rlve-crt-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-rlve-crt-l5-s7/environment/Dockerfile b/tasks/construct-rlve-crt-l5-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-crt-l5-s7/environment/instance.json b/tasks/construct-rlve-crt-l5-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b93f0b4530603e7d54123daca31ca655114cbf1d
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s7/environment/instance.json
@@ -0,0 +1 @@
+{"moduli": [3138480415, 4411274497, 3506412757, 2829265016, 247255816, 2724611332], "residues": [2068962579, 796168497, 1701030237, 2378177978, 15070858, 2482831662], "family": "rlve_crt", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-crt-l5-s7/solution/solve.sh b/tasks/construct-rlve-crt-l5-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1f1d6039dd59a41416dc175b3a641d24728a4f49
--- /dev/null
+++ b/tasks/construct-rlve-crt-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'
+{"x": 5207442994}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-crt-l5-s7/tests/check.py b/tasks/construct-rlve-crt-l5-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..886d95606ef325930b24794c0959c2ba7b254ebd
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s7/tests/check.py
@@ -0,0 +1,11 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    x = as_int(ans.get("x"), "x", lo=0)
+    if x.bit_length() > 20000:
+        raise Invalid("x is unreasonably large")
+    for a, b in zip(inst["residues"], inst["moduli"]):
+        if x % b != a:
+            raise Invalid(f"x mod {b} = {x % b}, need {a}")
+    return None, {}
diff --git a/tasks/construct-rlve-crt-l5-s7/tests/instance.json b/tasks/construct-rlve-crt-l5-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b93f0b4530603e7d54123daca31ca655114cbf1d
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s7/tests/instance.json
@@ -0,0 +1 @@
+{"moduli": [3138480415, 4411274497, 3506412757, 2829265016, 247255816, 2724611332], "residues": [2068962579, 796168497, 1701030237, 2378177978, 15070858, 2482831662], "family": "rlve_crt", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-crt-l5-s7/tests/run.py b/tasks/construct-rlve-crt-l5-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-crt-l5-s7/tests/test.sh b/tasks/construct-rlve-crt-l5-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-crt-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-distinct-subset-sum-permutation-l4-s0/environment/Dockerfile b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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-distinct-subset-sum-permutation-l4-s0/environment/instance.json b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd029bd7a8a38df2f2c0f22d478decc095a23559
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"A": [4, 16, 10, 6, 23, 1, 19, 11, 13, 20, 3, 24, 9, 26], "family": "rlve_distinct_subset_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/solution/solve.sh b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6e9ae1b33f4d1d0eb44449cc48f4e64157f9253b
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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'
+{"B": [6, 19, 11, 9, 24, 3, 20, 13, 16, 23, 4, 26, 10, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/tests/check.py b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..06bbbcf872c2fca05785f40fdfdcf85a5e5a0e7c
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/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-l4-s0/tests/instance.json b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd029bd7a8a38df2f2c0f22d478decc095a23559
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"A": [4, 16, 10, 6, 23, 1, 19, 11, 13, 20, 3, 24, 9, 26], "family": "rlve_distinct_subset_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/tests/run.py b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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-distinct-subset-sum-permutation-l4-s0/tests/test.sh b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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-distinct-subset-sum-permutation-l4-s7/environment/Dockerfile b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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-distinct-subset-sum-permutation-l4-s7/environment/instance.json b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..207d9f684d9403e99fd8f315d71855116ec4af45
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"A": [23, 17, 27, 18, 7, 12, 26, 11, 0, 3, 16, 9, 13, 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-l4-s7/solution/solve.sh b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b94d2909e81809c918a685206595c2b0a9c2faa5
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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'
+{"B": [26, 18, 0, 23, 9, 13, 27, 12, 2, 7, 17, 11, 16, 3]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/tests/check.py b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..06bbbcf872c2fca05785f40fdfdcf85a5e5a0e7c
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/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-l4-s7/tests/instance.json b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..207d9f684d9403e99fd8f315d71855116ec4af45
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"A": [23, 17, 27, 18, 7, 12, 26, 11, 0, 3, 16, 9, 13, 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-l4-s7/tests/run.py b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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-distinct-subset-sum-permutation-l4-s7/tests/test.sh b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-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-even-degree-partition-l1-s1/environment/Dockerfile b/tasks/construct-rlve-even-degree-partition-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-rlve-even-degree-partition-l1-s1/environment/instance.json b/tasks/construct-rlve-even-degree-partition-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d39b03a7f1c0e50b8aa0fa5f12f74fc7b448a0e
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 5, "edges": [[1, 4], [2, 4]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s1/solution/solve.sh b/tasks/construct-rlve-even-degree-partition-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fc4e8ab45ff4d58ae544b0547e2e4c040c7c9db0
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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'
+{"groups": [2, 1, 1, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s1/tests/check.py b/tasks/construct-rlve-even-degree-partition-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c7f0f71ea6d10264ececcc933b97a4a0e6eaf8e
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s1/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-l1-s1/tests/instance.json b/tasks/construct-rlve-even-degree-partition-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d39b03a7f1c0e50b8aa0fa5f12f74fc7b448a0e
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 5, "edges": [[1, 4], [2, 4]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s1/tests/run.py b/tasks/construct-rlve-even-degree-partition-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-rlve-even-degree-partition-l1-s1/tests/test.sh b/tasks/construct-rlve-even-degree-partition-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-rlve-even-degree-partition-l1-s6/environment/Dockerfile b/tasks/construct-rlve-even-degree-partition-l1-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l1-s6/environment/instance.json b/tasks/construct-rlve-even-degree-partition-l1-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..15efadb1d12db16e2feec68822d2bb558aa2bcd6
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 5, "edges": [[0, 1], [0, 2], [0, 3], [1, 4], [2, 4], [3, 4]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s6/solution/solve.sh b/tasks/construct-rlve-even-degree-partition-l1-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f9cbdd2874a1d448993749d364c39c70fa327105
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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'
+{"groups": [2, 2, 2, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s6/tests/check.py b/tasks/construct-rlve-even-degree-partition-l1-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c7f0f71ea6d10264ececcc933b97a4a0e6eaf8e
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s6/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-l1-s6/tests/instance.json b/tasks/construct-rlve-even-degree-partition-l1-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..15efadb1d12db16e2feec68822d2bb558aa2bcd6
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 5, "edges": [[0, 1], [0, 2], [0, 3], [1, 4], [2, 4], [3, 4]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s6/tests/run.py b/tasks/construct-rlve-even-degree-partition-l1-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l1-s6/tests/test.sh b/tasks/construct-rlve-even-degree-partition-l1-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l5-s7/environment/Dockerfile b/tasks/construct-rlve-even-degree-partition-l5-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l5-s7/environment/instance.json b/tasks/construct-rlve-even-degree-partition-l5-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c4510cab818379bd93f49d326bb7036e36a586fc
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 28, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 9], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [1, 2], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 18], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 27], [2, 5], [2, 6], [2, 7], [2, 9], [2, 11], [2, 14], [2, 15], [2, 16], [2, 19], [2, 21], [2, 23], [2, 24], [2, 25], [2, 26], [2, 27], [3, 6], [3, 9], [3, 11], [3, 16], [3, 17], [3, 19], [3, 20], [3, 22], [3, 23], [3, 24], [3, 25], [3, 27], [4, 5], [4, 6], [4, 9], [4, 11], [4, 14], [4, 17], [4, 20], [4, 21], [4, 22], [4, 24], [4, 25], [4, 26], [4, 27], [5, 6], [5, 7], [5, 9], [5, 10], [5, 11], [5, 14], [5, 18], [5, 19], [5, 24], [5, 25], [5, 27], [6, 8], [6, 9], [6, 10], [6, 11], [6, 14], [6, 15], [6, 16], [6, 17], [6, 18], [6, 20], [6, 22], [6, 23], [6, 24], [6, 25], [6, 26], [6, 27], [7, 8], [7, 9], [7, 11], [7, 12], [7, 13], [7, 14], [7, 16], [7, 17], [7, 19], [7, 20], [7, 21], [7, 23], [7, 24], [7, 25], [7, 26], [7, 27], [8, 9], [8, 11], [8, 14], [8, 19], [8, 20], [8, 25], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 17], [9, 18], [9, 20], [9, 21], [9, 23], [9, 24], [9, 25], [9, 26], [9, 27], [10, 11], [10, 14], [10, 16], [10, 19], [10, 20], [10, 27], [11, 12], [11, 13], [11, 14], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 22], [11, 23], [11, 24], [11, 26], [11, 27], [12, 14], [12, 16], [12, 17], [12, 19], [12, 21], [12, 22], [12, 24], [12, 25], [12, 26], [12, 27], [13, 14], [13, 15], [13, 17], [13, 19], [13, 20], [13, 21], [13, 23], [13, 24], [13, 26], [13, 27], [14, 15], [14, 16], [14, 17], [14, 18], [14, 21], [14, 23], [14, 26], [15, 16], [15, 19], [15, 20], [15, 21], [15, 22], [15, 24], [15, 25], [15, 26], [15, 27], [16, 20], [16, 21], [16, 24], [17, 19], [17, 20], [17, 21], [17, 25], [17, 26], [17, 27], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 25], [18, 26], [18, 27], [19, 20], [19, 22], [19, 26], [19, 27], [20, 21], [20, 22], [20, 23], [20, 24], [20, 27], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [22, 23], [22, 24], [22, 25], [22, 26], [22, 27], [23, 24], [23, 25], [23, 26], [23, 27], [24, 25], [24, 26], [24, 27], [25, 26], [25, 27], [26, 27]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s7/solution/solve.sh b/tasks/construct-rlve-even-degree-partition-l5-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7b0529f798c640462de41ede865ca287c513d9b1
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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'
+{"groups": [1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s7/tests/check.py b/tasks/construct-rlve-even-degree-partition-l5-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c7f0f71ea6d10264ececcc933b97a4a0e6eaf8e
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s7/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-l5-s7/tests/instance.json b/tasks/construct-rlve-even-degree-partition-l5-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c4510cab818379bd93f49d326bb7036e36a586fc
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 28, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 9], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [1, 2], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 18], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 27], [2, 5], [2, 6], [2, 7], [2, 9], [2, 11], [2, 14], [2, 15], [2, 16], [2, 19], [2, 21], [2, 23], [2, 24], [2, 25], [2, 26], [2, 27], [3, 6], [3, 9], [3, 11], [3, 16], [3, 17], [3, 19], [3, 20], [3, 22], [3, 23], [3, 24], [3, 25], [3, 27], [4, 5], [4, 6], [4, 9], [4, 11], [4, 14], [4, 17], [4, 20], [4, 21], [4, 22], [4, 24], [4, 25], [4, 26], [4, 27], [5, 6], [5, 7], [5, 9], [5, 10], [5, 11], [5, 14], [5, 18], [5, 19], [5, 24], [5, 25], [5, 27], [6, 8], [6, 9], [6, 10], [6, 11], [6, 14], [6, 15], [6, 16], [6, 17], [6, 18], [6, 20], [6, 22], [6, 23], [6, 24], [6, 25], [6, 26], [6, 27], [7, 8], [7, 9], [7, 11], [7, 12], [7, 13], [7, 14], [7, 16], [7, 17], [7, 19], [7, 20], [7, 21], [7, 23], [7, 24], [7, 25], [7, 26], [7, 27], [8, 9], [8, 11], [8, 14], [8, 19], [8, 20], [8, 25], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 17], [9, 18], [9, 20], [9, 21], [9, 23], [9, 24], [9, 25], [9, 26], [9, 27], [10, 11], [10, 14], [10, 16], [10, 19], [10, 20], [10, 27], [11, 12], [11, 13], [11, 14], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 22], [11, 23], [11, 24], [11, 26], [11, 27], [12, 14], [12, 16], [12, 17], [12, 19], [12, 21], [12, 22], [12, 24], [12, 25], [12, 26], [12, 27], [13, 14], [13, 15], [13, 17], [13, 19], [13, 20], [13, 21], [13, 23], [13, 24], [13, 26], [13, 27], [14, 15], [14, 16], [14, 17], [14, 18], [14, 21], [14, 23], [14, 26], [15, 16], [15, 19], [15, 20], [15, 21], [15, 22], [15, 24], [15, 25], [15, 26], [15, 27], [16, 20], [16, 21], [16, 24], [17, 19], [17, 20], [17, 21], [17, 25], [17, 26], [17, 27], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 25], [18, 26], [18, 27], [19, 20], [19, 22], [19, 26], [19, 27], [20, 21], [20, 22], [20, 23], [20, 24], [20, 27], [21, 22], [21, 23], [21, 24], [21, 25], [21, 26], [21, 27], [22, 23], [22, 24], [22, 25], [22, 26], [22, 27], [23, 24], [23, 25], [23, 26], [23, 27], [24, 25], [24, 26], [24, 27], [25, 26], [25, 27], [26, 27]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s7/tests/run.py b/tasks/construct-rlve-even-degree-partition-l5-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l5-s7/tests/test.sh b/tasks/construct-rlve-even-degree-partition-l5-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l5-s9/environment/Dockerfile b/tasks/construct-rlve-even-degree-partition-l5-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l5-s9/environment/instance.json b/tasks/construct-rlve-even-degree-partition-l5-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..67fcb6733b04d75861425dc963aa9ed8d804d9d5
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 28, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 10], [0, 13], [0, 15], [0, 16], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 25], [0, 26], [0, 27], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 21], [1, 22], [1, 24], [1, 26], [1, 27], [2, 3], [2, 5], [2, 6], [2, 8], [2, 10], [2, 11], [2, 13], [2, 15], [2, 16], [2, 18], [2, 19], [3, 4], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 16], [3, 17], [3, 18], [3, 20], [3, 21], [3, 22], [3, 24], [3, 25], [3, 27], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 15], [4, 16], [4, 18], [4, 20], [4, 21], [4, 23], [4, 25], [5, 6], [5, 9], [5, 10], [5, 13], [5, 15], [5, 16], [5, 20], [5, 21], [5, 22], [5, 24], [5, 25], [5, 26], [5, 27], [6, 8], [6, 10], [6, 11], [6, 13], [6, 14], [6, 15], [6, 16], [6, 17], [6, 18], [6, 19], [6, 20], [6, 21], [6, 22], [6, 23], [6, 25], [6, 26], [7, 8], [7, 10], [7, 11], [7, 13], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 27], [8, 9], [8, 10], [8, 11], [8, 15], [8, 18], [8, 19], [8, 20], [8, 24], [8, 25], [8, 26], [9, 10], [9, 11], [9, 15], [9, 16], [9, 18], [9, 20], [9, 25], [9, 27], [10, 12], [10, 13], [10, 16], [10, 18], [10, 20], [10, 23], [10, 27], [11, 13], [11, 14], [11, 15], [11, 16], [11, 18], [11, 19], [11, 21], [11, 22], [11, 23], [11, 25], [12, 13], [12, 15], [12, 18], [13, 15], [13, 16], [13, 18], [13, 19], [13, 26], [14, 15], [14, 18], [14, 19], [14, 20], [14, 26], [15, 16], [15, 17], [15, 18], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 27], [16, 18], [16, 19], [16, 23], [16, 26], [17, 18], [17, 19], [17, 20], [17, 26], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [19, 21], [19, 22], [19, 23], [19, 25], [19, 26], [19, 27], [20, 22], [20, 23], [20, 24], [20, 27], [21, 24], [21, 26], [22, 23], [22, 25], [22, 26], [23, 26], [23, 27], [24, 25], [24, 27], [25, 26], [25, 27]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s9/solution/solve.sh b/tasks/construct-rlve-even-degree-partition-l5-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f4fe18f8f25746e8b6b5e38988f06f1c8158669a
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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'
+{"groups": [2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s9/tests/check.py b/tasks/construct-rlve-even-degree-partition-l5-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c7f0f71ea6d10264ececcc933b97a4a0e6eaf8e
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s9/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-l5-s9/tests/instance.json b/tasks/construct-rlve-even-degree-partition-l5-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..67fcb6733b04d75861425dc963aa9ed8d804d9d5
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 28, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 10], [0, 13], [0, 15], [0, 16], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 25], [0, 26], [0, 27], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 21], [1, 22], [1, 24], [1, 26], [1, 27], [2, 3], [2, 5], [2, 6], [2, 8], [2, 10], [2, 11], [2, 13], [2, 15], [2, 16], [2, 18], [2, 19], [3, 4], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 16], [3, 17], [3, 18], [3, 20], [3, 21], [3, 22], [3, 24], [3, 25], [3, 27], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 15], [4, 16], [4, 18], [4, 20], [4, 21], [4, 23], [4, 25], [5, 6], [5, 9], [5, 10], [5, 13], [5, 15], [5, 16], [5, 20], [5, 21], [5, 22], [5, 24], [5, 25], [5, 26], [5, 27], [6, 8], [6, 10], [6, 11], [6, 13], [6, 14], [6, 15], [6, 16], [6, 17], [6, 18], [6, 19], [6, 20], [6, 21], [6, 22], [6, 23], [6, 25], [6, 26], [7, 8], [7, 10], [7, 11], [7, 13], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 27], [8, 9], [8, 10], [8, 11], [8, 15], [8, 18], [8, 19], [8, 20], [8, 24], [8, 25], [8, 26], [9, 10], [9, 11], [9, 15], [9, 16], [9, 18], [9, 20], [9, 25], [9, 27], [10, 12], [10, 13], [10, 16], [10, 18], [10, 20], [10, 23], [10, 27], [11, 13], [11, 14], [11, 15], [11, 16], [11, 18], [11, 19], [11, 21], [11, 22], [11, 23], [11, 25], [12, 13], [12, 15], [12, 18], [13, 15], [13, 16], [13, 18], [13, 19], [13, 26], [14, 15], [14, 18], [14, 19], [14, 20], [14, 26], [15, 16], [15, 17], [15, 18], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 27], [16, 18], [16, 19], [16, 23], [16, 26], [17, 18], [17, 19], [17, 20], [17, 26], [18, 19], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 26], [18, 27], [19, 21], [19, 22], [19, 23], [19, 25], [19, 26], [19, 27], [20, 22], [20, 23], [20, 24], [20, 27], [21, 24], [21, 26], [22, 23], [22, 25], [22, 26], [23, 26], [23, 27], [24, 25], [24, 27], [25, 26], [25, 27]], "family": "rlve_even_degree_partition", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s9/tests/run.py b/tasks/construct-rlve-even-degree-partition-l5-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-even-degree-partition-l5-s9/tests/test.sh b/tasks/construct-rlve-even-degree-partition-l5-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-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-graph-isomorphism-l3-s4/environment/Dockerfile b/tasks/construct-rlve-graph-isomorphism-l3-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-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-graph-isomorphism-l3-s4/environment/instance.json b/tasks/construct-rlve-graph-isomorphism-l3-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ae7b1595136d136f06012fff0436fb871e0f9d24
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges1": [[3, 7], [3, 10], [2, 11], [5, 9], [0, 6], [2, 3], [0, 2], [1, 11], [3, 9], [2, 5], [0, 8], [1, 4], [9, 11], [1, 9], [2, 8], [10, 11], [1, 2], [8, 11], [4, 7], [4, 5], [6, 8], [0, 5], [1, 8], [6, 10], [1, 7], [3, 8], [3, 4], [4, 10], [2, 6], [5, 8], [2, 9], [7, 10], [4, 8], [3, 6], [7, 9], [9, 10], [6, 11], [0, 4], [3, 11], [1, 3], [0, 10], [4, 6], [0, 7], [0, 3], [4, 9], [2, 4], [7, 11], [1, 10], [8, 10]], "edges2": [[0, 11], [2, 8], [5, 8], [7, 8], [8, 11], [2, 11], [1, 5], [10, 11], [0, 8], [4, 6], [1, 10], [4, 9], [5, 9], [5, 11], [4, 5], [7, 10], [0, 9], [1, 4], [5, 6], [7, 9], [2, 9], [4, 7], [2, 4], [5, 10], [1, 11], [7, 11], [0, 10], [3, 11], [2, 7], [6, 7], [5, 7], [6, 10], [3, 8], [2, 3], [9, 10], [6, 8], [2, 6], [0, 7], [0, 5], [0, 2], [0, 3], [2, 10], [3, 10], [3, 7], [3, 4], [6, 9], [8, 9], [1, 9], [4, 10]], "family": "rlve_graph_isomorphism", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-graph-isomorphism-l3-s4/solution/solve.sh b/tasks/construct-rlve-graph-isomorphism-l3-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2ad524c74c8862f457b0346d8751b71ed9c65e64
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-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'
+{"p": [4, 0, 5, 7, 10, 1, 6, 3, 9, 11, 2, 8]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-graph-isomorphism-l3-s4/tests/check.py b/tasks/construct-rlve-graph-isomorphism-l3-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..64b755f5ab12e7270811ccfc2f02d104715517b7
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-s4/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-l3-s4/tests/instance.json b/tasks/construct-rlve-graph-isomorphism-l3-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ae7b1595136d136f06012fff0436fb871e0f9d24
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-s4/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges1": [[3, 7], [3, 10], [2, 11], [5, 9], [0, 6], [2, 3], [0, 2], [1, 11], [3, 9], [2, 5], [0, 8], [1, 4], [9, 11], [1, 9], [2, 8], [10, 11], [1, 2], [8, 11], [4, 7], [4, 5], [6, 8], [0, 5], [1, 8], [6, 10], [1, 7], [3, 8], [3, 4], [4, 10], [2, 6], [5, 8], [2, 9], [7, 10], [4, 8], [3, 6], [7, 9], [9, 10], [6, 11], [0, 4], [3, 11], [1, 3], [0, 10], [4, 6], [0, 7], [0, 3], [4, 9], [2, 4], [7, 11], [1, 10], [8, 10]], "edges2": [[0, 11], [2, 8], [5, 8], [7, 8], [8, 11], [2, 11], [1, 5], [10, 11], [0, 8], [4, 6], [1, 10], [4, 9], [5, 9], [5, 11], [4, 5], [7, 10], [0, 9], [1, 4], [5, 6], [7, 9], [2, 9], [4, 7], [2, 4], [5, 10], [1, 11], [7, 11], [0, 10], [3, 11], [2, 7], [6, 7], [5, 7], [6, 10], [3, 8], [2, 3], [9, 10], [6, 8], [2, 6], [0, 7], [0, 5], [0, 2], [0, 3], [2, 10], [3, 10], [3, 7], [3, 4], [6, 9], [8, 9], [1, 9], [4, 10]], "family": "rlve_graph_isomorphism", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-graph-isomorphism-l3-s4/tests/run.py b/tasks/construct-rlve-graph-isomorphism-l3-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-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-graph-isomorphism-l3-s4/tests/test.sh b/tasks/construct-rlve-graph-isomorphism-l3-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-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-grid-parity-construction-l3-s3/environment/Dockerfile b/tasks/construct-rlve-grid-parity-construction-l3-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-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-grid-parity-construction-l3-s3/environment/instance.json b/tasks/construct-rlve-grid-parity-construction-l3-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bfddb223ae93661c9f77c41a0bb1bb6beb6bcb21
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-s3/environment/instance.json
@@ -0,0 +1 @@
+{"parity": ["101010", "000011", "000110", "011001"], "family": "rlve_grid_parity_construction", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-grid-parity-construction-l3-s3/solution/solve.sh b/tasks/construct-rlve-grid-parity-construction-l3-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f448ff467c130a20f5d039df04ec93ba1f969570
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-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'
+{"grid": ["111110", "110111", "111111", "101111"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-grid-parity-construction-l3-s3/tests/check.py b/tasks/construct-rlve-grid-parity-construction-l3-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..89d5d286593348d0000ac10db74e1c6242be6c97
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-s3/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-l3-s3/tests/instance.json b/tasks/construct-rlve-grid-parity-construction-l3-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bfddb223ae93661c9f77c41a0bb1bb6beb6bcb21
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-s3/tests/instance.json
@@ -0,0 +1 @@
+{"parity": ["101010", "000011", "000110", "011001"], "family": "rlve_grid_parity_construction", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-grid-parity-construction-l3-s3/tests/run.py b/tasks/construct-rlve-grid-parity-construction-l3-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-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-grid-parity-construction-l3-s3/tests/test.sh b/tasks/construct-rlve-grid-parity-construction-l3-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-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-imp-party-l4-s3/environment/Dockerfile b/tasks/construct-rlve-imp-party-l4-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-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-imp-party-l4-s3/environment/instance.json b/tasks/construct-rlve-imp-party-l4-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b83356b9f44ea4591a7c4a2de65d1ada14ec410
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 12], [0, 13], [0, 18], [0, 20], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [0, 31], [0, 33], [0, 34], [0, 35], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 12], [1, 13], [1, 18], [1, 20], [1, 22], [1, 23], [1, 24], [1, 26], [1, 28], [1, 29], [1, 31], [1, 33], [1, 34], [1, 35], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 12], [2, 13], [2, 17], [2, 18], [2, 20], [2, 22], [2, 23], [2, 24], [2, 26], [2, 28], [2, 29], [2, 30], [2, 31], [2, 33], [2, 34], [2, 35], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 12], [3, 13], [3, 16], [3, 18], [3, 20], [3, 22], [3, 23], [3, 24], [3, 26], [3, 28], [3, 29], [3, 31], [3, 33], [3, 34], [3, 35], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 18], [4, 20], [4, 22], [4, 23], [4, 24], [4, 26], [4, 27], [4, 28], [4, 29], [4, 31], [4, 33], [4, 34], [4, 35], [5, 6], [5, 7], [5, 8], [5, 9], [5, 12], [5, 13], [5, 16], [5, 18], [5, 20], [5, 21], [5, 22], [5, 23], [5, 24], [5, 26], [5, 28], [5, 29], [5, 31], [5, 33], [5, 34], [5, 35], [6, 7], [6, 8], [6, 9], [6, 12], [6, 13], [6, 18], [6, 19], [6, 20], [6, 22], [6, 23], [6, 24], [6, 26], [6, 28], [6, 29], [6, 31], [6, 33], [6, 34], [6, 35], [7, 8], [7, 9], [7, 12], [7, 13], [7, 18], [7, 20], [7, 22], [7, 23], [7, 24], [7, 26], [7, 28], [7, 29], [7, 31], [7, 33], [7, 34], [7, 35], [8, 9], [8, 12], [8, 13], [8, 18], [8, 20], [8, 22], [8, 23], [8, 24], [8, 26], [8, 28], [8, 29], [8, 31], [8, 33], [8, 34], [8, 35], [9, 12], [9, 13], [9, 18], [9, 20], [9, 22], [9, 23], [9, 24], [9, 26], [9, 28], [9, 29], [9, 31], [9, 33], [9, 34], [9, 35], [10, 33], [12, 13], [12, 18], [12, 20], [12, 22], [12, 23], [12, 24], [12, 26], [12, 28], [12, 29], [12, 31], [12, 33], [12, 34], [12, 35], [13, 16], [13, 18], [13, 20], [13, 22], [13, 23], [13, 24], [13, 26], [13, 28], [13, 29], [13, 31], [13, 33], [13, 34], [13, 35], [17, 23], [17, 35], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 26], [18, 28], [18, 29], [18, 31], [18, 33], [18, 34], [18, 35], [20, 22], [20, 23], [20, 24], [20, 26], [20, 28], [20, 29], [20, 31], [20, 33], [20, 34], [20, 35], [21, 26], [22, 23], [22, 24], [22, 26], [22, 28], [22, 29], [22, 31], [22, 33], [22, 34], [22, 35], [23, 24], [23, 26], [23, 28], [23, 29], [23, 31], [23, 33], [23, 34], [23, 35], [24, 26], [24, 28], [24, 29], [24, 31], [24, 33], [24, 34], [24, 35], [26, 28], [26, 29], [26, 31], [26, 33], [26, 34], [26, 35], [28, 29], [28, 31], [28, 33], [28, 34], [28, 35], [29, 31], [29, 33], [29, 34], [29, 35], [31, 33], [31, 34], [31, 35], [33, 34], [33, 35], [34, 35]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s3/solution/solve.sh b/tasks/construct-rlve-imp-party-l4-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f557c2abcc753b07b2ac609275a24761fd4db556
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-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": [0, 1, 3, 5, 7, 13, 20, 24, 26, 28, 34, 35]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-imp-party-l4-s3/tests/check.py b/tasks/construct-rlve-imp-party-l4-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..97b5a037a2ba8bf4495cf87cc074d1c60b11311c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s3/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-s3/tests/instance.json b/tasks/construct-rlve-imp-party-l4-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b83356b9f44ea4591a7c4a2de65d1ada14ec410
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 12], [0, 13], [0, 18], [0, 20], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [0, 31], [0, 33], [0, 34], [0, 35], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 12], [1, 13], [1, 18], [1, 20], [1, 22], [1, 23], [1, 24], [1, 26], [1, 28], [1, 29], [1, 31], [1, 33], [1, 34], [1, 35], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 12], [2, 13], [2, 17], [2, 18], [2, 20], [2, 22], [2, 23], [2, 24], [2, 26], [2, 28], [2, 29], [2, 30], [2, 31], [2, 33], [2, 34], [2, 35], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 12], [3, 13], [3, 16], [3, 18], [3, 20], [3, 22], [3, 23], [3, 24], [3, 26], [3, 28], [3, 29], [3, 31], [3, 33], [3, 34], [3, 35], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 18], [4, 20], [4, 22], [4, 23], [4, 24], [4, 26], [4, 27], [4, 28], [4, 29], [4, 31], [4, 33], [4, 34], [4, 35], [5, 6], [5, 7], [5, 8], [5, 9], [5, 12], [5, 13], [5, 16], [5, 18], [5, 20], [5, 21], [5, 22], [5, 23], [5, 24], [5, 26], [5, 28], [5, 29], [5, 31], [5, 33], [5, 34], [5, 35], [6, 7], [6, 8], [6, 9], [6, 12], [6, 13], [6, 18], [6, 19], [6, 20], [6, 22], [6, 23], [6, 24], [6, 26], [6, 28], [6, 29], [6, 31], [6, 33], [6, 34], [6, 35], [7, 8], [7, 9], [7, 12], [7, 13], [7, 18], [7, 20], [7, 22], [7, 23], [7, 24], [7, 26], [7, 28], [7, 29], [7, 31], [7, 33], [7, 34], [7, 35], [8, 9], [8, 12], [8, 13], [8, 18], [8, 20], [8, 22], [8, 23], [8, 24], [8, 26], [8, 28], [8, 29], [8, 31], [8, 33], [8, 34], [8, 35], [9, 12], [9, 13], [9, 18], [9, 20], [9, 22], [9, 23], [9, 24], [9, 26], [9, 28], [9, 29], [9, 31], [9, 33], [9, 34], [9, 35], [10, 33], [12, 13], [12, 18], [12, 20], [12, 22], [12, 23], [12, 24], [12, 26], [12, 28], [12, 29], [12, 31], [12, 33], [12, 34], [12, 35], [13, 16], [13, 18], [13, 20], [13, 22], [13, 23], [13, 24], [13, 26], [13, 28], [13, 29], [13, 31], [13, 33], [13, 34], [13, 35], [17, 23], [17, 35], [18, 20], [18, 21], [18, 22], [18, 23], [18, 24], [18, 26], [18, 28], [18, 29], [18, 31], [18, 33], [18, 34], [18, 35], [20, 22], [20, 23], [20, 24], [20, 26], [20, 28], [20, 29], [20, 31], [20, 33], [20, 34], [20, 35], [21, 26], [22, 23], [22, 24], [22, 26], [22, 28], [22, 29], [22, 31], [22, 33], [22, 34], [22, 35], [23, 24], [23, 26], [23, 28], [23, 29], [23, 31], [23, 33], [23, 34], [23, 35], [24, 26], [24, 28], [24, 29], [24, 31], [24, 33], [24, 34], [24, 35], [26, 28], [26, 29], [26, 31], [26, 33], [26, 34], [26, 35], [28, 29], [28, 31], [28, 33], [28, 34], [28, 35], [29, 31], [29, 33], [29, 34], [29, 35], [31, 33], [31, 34], [31, 35], [33, 34], [33, 35], [34, 35]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l4-s3/tests/run.py b/tasks/construct-rlve-imp-party-l4-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-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-imp-party-l4-s3/tests/test.sh b/tasks/construct-rlve-imp-party-l4-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l4-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-integer-linear-system-l3-s3/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l3-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-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-integer-linear-system-l3-s3/environment/instance.json b/tasks/construct-rlve-integer-linear-system-l3-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1f88a6f9f50e5c8e1d424213f2ea31cbdd8eba67
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s3/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[1, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 1, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 1], [0, 1, 1, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1], [0, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 1, 1, 1, 0, 0]], "rhs": [22, 5, 21, 23, 31, 10, 24, 23, 24, 14, 15, 30, 31, 23, 16, 27, 23, 15, 21, 12], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s3/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l3-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8d2b3dee0520b24d0ae90771423b9201caadf129
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-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": [7, 8, 4, 3, 5, 4, 1, 7]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s3/tests/check.py b/tasks/construct-rlve-integer-linear-system-l3-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s3/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-s3/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l3-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1f88a6f9f50e5c8e1d424213f2ea31cbdd8eba67
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-s3/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[1, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 1, 1, 1, 1], [1, 0, 0, 0, 1, 1, 0, 1], [0, 1, 1, 1, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 1, 0, 0, 1, 0], [1, 1, 1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 1, 1, 1, 0, 1], [1, 1, 1, 0, 0, 1, 1, 1], [0, 1, 1, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 0, 1, 1], [1, 1, 0, 0, 0, 1, 1, 1], [0, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 1, 0, 0], [1, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 1, 1, 1, 0, 0]], "rhs": [22, 5, 21, 23, 31, 10, 24, 23, 24, 14, 15, 30, 31, 23, 16, 27, 23, 15, 21, 12], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l3-s3/tests/run.py b/tasks/construct-rlve-integer-linear-system-l3-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-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-integer-linear-system-l3-s3/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l3-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l3-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-largest-convex-polygon-l1-s3/environment/Dockerfile b/tasks/construct-rlve-largest-convex-polygon-l1-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-convex-polygon-l1-s3/environment/instance.json b/tasks/construct-rlve-largest-convex-polygon-l1-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c967dff51eb50f2849290627d94e6e6ac854270a
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l1-s3/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 1], [4, 0], [4, 3], [6, 1], [0, 2], [2, 6]], "k": 5, "family": "rlve_largest_convex_polygon", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-convex-polygon-l1-s3/solution/solve.sh b/tasks/construct-rlve-largest-convex-polygon-l1-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e51a48f1c4946d37565e02d368bfff25c982d455
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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'
+{"indices": [0, 4, 5, 2, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-largest-convex-polygon-l1-s3/tests/check.py b/tasks/construct-rlve-largest-convex-polygon-l1-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a09cc858f41ce5745e4e491188cd42360c65dae
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l1-s3/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-l1-s3/tests/instance.json b/tasks/construct-rlve-largest-convex-polygon-l1-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c967dff51eb50f2849290627d94e6e6ac854270a
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l1-s3/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 1], [4, 0], [4, 3], [6, 1], [0, 2], [2, 6]], "k": 5, "family": "rlve_largest_convex_polygon", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-convex-polygon-l1-s3/tests/run.py b/tasks/construct-rlve-largest-convex-polygon-l1-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-convex-polygon-l1-s3/tests/test.sh b/tasks/construct-rlve-largest-convex-polygon-l1-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-convex-polygon-l1-s4/environment/Dockerfile b/tasks/construct-rlve-largest-convex-polygon-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-convex-polygon-l1-s4/environment/instance.json b/tasks/construct-rlve-largest-convex-polygon-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bbcccc6a506a92e1ac1be414688232d4be8abbbe
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[5, 5], [3, 1], [1, 1], [4, 5], [2, 6], [6, 3]], "k": 5, "family": "rlve_largest_convex_polygon", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-convex-polygon-l1-s4/solution/solve.sh b/tasks/construct-rlve-largest-convex-polygon-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..82e3f64a527a56f0f14020043be87b8eacf7cc4c
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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'
+{"indices": [2, 4, 3, 5, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-largest-convex-polygon-l1-s4/tests/check.py b/tasks/construct-rlve-largest-convex-polygon-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a09cc858f41ce5745e4e491188cd42360c65dae
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l1-s4/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-l1-s4/tests/instance.json b/tasks/construct-rlve-largest-convex-polygon-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bbcccc6a506a92e1ac1be414688232d4be8abbbe
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[5, 5], [3, 1], [1, 1], [4, 5], [2, 6], [6, 3]], "k": 5, "family": "rlve_largest_convex_polygon", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-convex-polygon-l1-s4/tests/run.py b/tasks/construct-rlve-largest-convex-polygon-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-convex-polygon-l1-s4/tests/test.sh b/tasks/construct-rlve-largest-convex-polygon-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-convex-polygon-l5-s2/environment/Dockerfile b/tasks/construct-rlve-largest-convex-polygon-l5-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-convex-polygon-l5-s2/environment/instance.json b/tasks/construct-rlve-largest-convex-polygon-l5-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d5834735531564692ea494cbd3971aefd935b108
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l5-s2/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[6, 18], [12, 1], [12, 16], [5, 4], [4, 15], [17, 24], [25, 4], [0, 11], [0, 23], [2, 20], [20, 13], [3, 9], [13, 7], [1, 8], [16, 12], [20, 18], [5, 2], [4, 13], [3, 23], [25, 5], [17, 25], [6, 0], [2, 15], [16, 14], [18, 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-l5-s2/solution/solve.sh b/tasks/construct-rlve-largest-convex-polygon-l5-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b5ca4e8f95663e02cf3fedcf82ea69b0759579ed
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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'
+{"indices": [22, 9, 18, 2, 24, 19, 6, 1, 21, 16, 11]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-largest-convex-polygon-l5-s2/tests/check.py b/tasks/construct-rlve-largest-convex-polygon-l5-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3a09cc858f41ce5745e4e491188cd42360c65dae
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l5-s2/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-l5-s2/tests/instance.json b/tasks/construct-rlve-largest-convex-polygon-l5-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d5834735531564692ea494cbd3971aefd935b108
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l5-s2/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[6, 18], [12, 1], [12, 16], [5, 4], [4, 15], [17, 24], [25, 4], [0, 11], [0, 23], [2, 20], [20, 13], [3, 9], [13, 7], [1, 8], [16, 12], [20, 18], [5, 2], [4, 13], [3, 23], [25, 5], [17, 25], [6, 0], [2, 15], [16, 14], [18, 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-l5-s2/tests/run.py b/tasks/construct-rlve-largest-convex-polygon-l5-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-rlve-largest-convex-polygon-l5-s2/tests/test.sh b/tasks/construct-rlve-largest-convex-polygon-l5-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-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-largest-rectangle-l3-s3/environment/Dockerfile b/tasks/construct-rlve-largest-rectangle-l3-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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-largest-rectangle-l3-s3/environment/instance.json b/tasks/construct-rlve-largest-rectangle-l3-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1534bf12c740c3a5d5a97d4af136ec8587a48797
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-s3/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[-5, -15], [3, 12], [-14, 10], [-11, -10], [13, 16], [-15, -11], [-16, -2], [-5, -10], [4, -3], [-9, -11], [3, -3], [5, -8], [4, -10], [7, -4], [-1, -4], [0, -9]], "area": 26, "family": "rlve_largest_rectangle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-rectangle-l3-s3/solution/solve.sh b/tasks/construct-rlve-largest-rectangle-l3-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b98cce94cf84ea68ef497329ebb7f4f01dc2593c
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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'
+{"indices": [8, 11, 15, 14]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-largest-rectangle-l3-s3/tests/check.py b/tasks/construct-rlve-largest-rectangle-l3-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2251b2af23a481e598fa1e48d0a8249f70b6cc44
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-s3/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-l3-s3/tests/instance.json b/tasks/construct-rlve-largest-rectangle-l3-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1534bf12c740c3a5d5a97d4af136ec8587a48797
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-s3/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[-5, -15], [3, 12], [-14, 10], [-11, -10], [13, 16], [-15, -11], [-16, -2], [-5, -10], [4, -3], [-9, -11], [3, -3], [5, -8], [4, -10], [7, -4], [-1, -4], [0, -9]], "area": 26, "family": "rlve_largest_rectangle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-rectangle-l3-s3/tests/run.py b/tasks/construct-rlve-largest-rectangle-l3-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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-largest-rectangle-l3-s3/tests/test.sh b/tasks/construct-rlve-largest-rectangle-l3-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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-largest-rectangle-l3-s4/environment/Dockerfile b/tasks/construct-rlve-largest-rectangle-l3-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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-largest-rectangle-l3-s4/environment/instance.json b/tasks/construct-rlve-largest-rectangle-l3-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..76ed14a5ff7ff4f0d2161a0c6ccf4d34bbbc14e9
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-s4/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[-5, -16], [-1, -5], [3, 2], [15, -12], [8, -5], [1, -4], [-4, 6], [-12, 11], [-3, -13], [-13, 4], [5, -14], [-5, 16], [-8, 7], [9, -15], [-8, -1], [-8, 11]], "area": 65, "family": "rlve_largest_rectangle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-rectangle-l3-s4/solution/solve.sh b/tasks/construct-rlve-largest-rectangle-l3-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6a65773cec92d19f78348c0464bb42061b5123ef
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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'
+{"indices": [1, 2, 6, 14]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-largest-rectangle-l3-s4/tests/check.py b/tasks/construct-rlve-largest-rectangle-l3-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2251b2af23a481e598fa1e48d0a8249f70b6cc44
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-s4/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-l3-s4/tests/instance.json b/tasks/construct-rlve-largest-rectangle-l3-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..76ed14a5ff7ff4f0d2161a0c6ccf4d34bbbc14e9
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-s4/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[-5, -16], [-1, -5], [3, 2], [15, -12], [8, -5], [1, -4], [-4, 6], [-12, 11], [-3, -13], [-13, 4], [5, -14], [-5, 16], [-8, 7], [9, -15], [-8, -1], [-8, 11]], "area": 65, "family": "rlve_largest_rectangle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-largest-rectangle-l3-s4/tests/run.py b/tasks/construct-rlve-largest-rectangle-l3-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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-largest-rectangle-l3-s4/tests/test.sh b/tasks/construct-rlve-largest-rectangle-l3-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-largest-rectangle-l3-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-matrix-permutation-equivalence-l1-s0/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-rlve-matrix-permutation-equivalence-l1-s0/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e14141cc023eff2b84b1cd81d3cb5545bf9bc270
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["01", "00", "10"], "B": ["10", "00", "01"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bae30f9403ba73217a2da34d661343b3e3869a5a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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'
+{"a": [2, 1, 0], "b": [0, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/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-s0/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e14141cc023eff2b84b1cd81d3cb5545bf9bc270
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["01", "00", "10"], "B": ["10", "00", "01"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-rlve-matrix-permutation-equivalence-l1-s0/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-rlve-matrix-permutation-equivalence-l1-s7/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-matrix-permutation-equivalence-l1-s7/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cb010939427f65a080fbe12510abe5e52c2b1c08
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["111", "101"], "B": ["110", "111"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..50a5f8a4c6a232f318df5db2ff220f650daa1dc1
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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'
+{"a": [1, 0], "b": [2, 0, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-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-l1-s7/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cb010939427f65a080fbe12510abe5e52c2b1c08
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["111", "101"], "B": ["110", "111"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-matrix-permutation-equivalence-l1-s7/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l1-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-matrix-permutation-equivalence-l5-s1/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-rlve-matrix-permutation-equivalence-l5-s1/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..66affd9beb4b6ef29a658a1155feda0439a892b2
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["010011111101", "111111110011", "110111101101", "101010110110", "111101111111", "101111011101", "001111101011", "111111111011"], "B": ["111011100111", "010011111111", "110100101111", "001001111111", "111110111110", "111110111111", "111111111101", "101111001010"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..90d0505cdfbb3b379484a32179583d93cb7a4167
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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'
+{"a": [5, 2, 6, 0, 1, 7, 4, 3], "b": [2, 3, 7, 10, 0, 9, 11, 1, 6, 5, 4, 8]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/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-s1/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..66affd9beb4b6ef29a658a1155feda0439a892b2
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["010011111101", "111111110011", "110111101101", "101010110110", "111101111111", "101111011101", "001111101011", "111111111011"], "B": ["111011100111", "010011111111", "110100101111", "001001111111", "111110111110", "111110111111", "111111111101", "101111001010"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-rlve-matrix-permutation-equivalence-l5-s1/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-rlve-matrix-permutation-equivalence-l5-s8/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-matrix-permutation-equivalence-l5-s8/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0d2962a2c8520e406cb8a79af51a6789d1ff2ae2
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["0000100", "0000110", "0001011", "1100010", "0010011", "0000000", "1101000", "0001010", "0000000", "1011001", "0100000", "0000000", "0000000", "0000000", "0100000"], "B": ["0000010", "0010000", "0000000", "1100000", "1001101", "0101100", "0000000", "0110000", "0000000", "1000011", "0100011", "0000000", "1101000", "0000000", "0000010"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3e82abf77384b3576f29a839a14a28c116fc9a0c
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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'
+{"a": [10, 0, 5, 7, 9, 4, 8, 1, 11, 6, 3, 12, 2, 13, 14], "b": [3, 5, 4, 6, 2, 1, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/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-s8/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0d2962a2c8520e406cb8a79af51a6789d1ff2ae2
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["0000100", "0000110", "0001011", "1100010", "0010011", "0000000", "1101000", "0001010", "0000000", "1011001", "0100000", "0000000", "0000000", "0000000", "0100000"], "B": ["0000010", "0010000", "0000000", "1100000", "1001101", "0101100", "0000000", "0110000", "0000000", "1000011", "0100011", "0000000", "1101000", "0000000", "0000010"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-matrix-permutation-equivalence-l5-s8/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l5-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-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-max-achromatic-coloring-l1-s2/environment/Dockerfile b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l1-s2/environment/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca2217cc85bcda591b8d13785139a1fd19ed3d15
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 6, "k": 3, "edges": [[0, 3], [1, 4], [3, 4], [3, 5]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l1-s2/solution/solve.sh b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..507750783edb4737b84f155ecabef4d2b36c3f75
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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'
+{"colors": [0, 0, 0, 1, 2, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l1-s2/tests/check.py b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..bb676a518264e5db4fb0964e27ccffccf6980807
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l1-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("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-l1-s2/tests/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca2217cc85bcda591b8d13785139a1fd19ed3d15
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 6, "k": 3, "edges": [[0, 3], [1, 4], [3, 4], [3, 5]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l1-s2/tests/run.py b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l1-s2/tests/test.sh b/tasks/construct-rlve-max-achromatic-coloring-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l1-s5/environment/Dockerfile b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l1-s5/environment/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a31ef797a9a7b5235cc13ad913e51f4885e94632
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 6, "k": 4, "edges": [[0, 1], [0, 3], [1, 5], [2, 5], [3, 4], [3, 5], [4, 5]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l1-s5/solution/solve.sh b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b61244106d70cfb43a8b8062e3f38b6f1353bed6
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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'
+{"colors": [0, 1, 0, 2, 1, 3]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l1-s5/tests/check.py b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..bb676a518264e5db4fb0964e27ccffccf6980807
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l1-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("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-l1-s5/tests/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a31ef797a9a7b5235cc13ad913e51f4885e94632
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 6, "k": 4, "edges": [[0, 1], [0, 3], [1, 5], [2, 5], [3, 4], [3, 5], [4, 5]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l1-s5/tests/run.py b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l1-s5/tests/test.sh b/tasks/construct-rlve-max-achromatic-coloring-l1-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l5-s3/environment/Dockerfile b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l5-s3/environment/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5bdbc345afd9b2ae85edae267e9169d64903fba0
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 13, "k": 8, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [1, 2], [1, 3], [1, 6], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 12], [3, 7], [3, 8], [3, 10], [4, 5], [4, 9], [4, 11], [5, 7], [5, 8], [5, 9], [5, 11], [6, 9], [6, 10], [6, 12], [7, 10], [7, 12], [8, 11], [9, 10], [9, 11], [9, 12], [10, 12], [11, 12]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l5-s3/solution/solve.sh b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f043f47b8e5bf0f319e6137ce4b851571e762fd5
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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'
+{"colors": [0, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 1, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l5-s3/tests/check.py b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..bb676a518264e5db4fb0964e27ccffccf6980807
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/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-l5-s3/tests/instance.json b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5bdbc345afd9b2ae85edae267e9169d64903fba0
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 13, "k": 8, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [1, 2], [1, 3], [1, 6], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 12], [3, 7], [3, 8], [3, 10], [4, 5], [4, 9], [4, 11], [5, 7], [5, 8], [5, 9], [5, 11], [6, 9], [6, 10], [6, 12], [7, 10], [7, 12], [8, 11], [9, 10], [9, 11], [9, 12], [10, 12], [11, 12]], "family": "rlve_max_achromatic_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l5-s3/tests/run.py b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-max-achromatic-coloring-l5-s3/tests/test.sh b/tasks/construct-rlve-max-achromatic-coloring-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-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-maximum-clique-l2-s1/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l2-s1/environment/instance.json b/tasks/construct-rlve-maximum-clique-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..94665089faa05442037cfdc1ea59548ba76e5330
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 6, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 12], [1, 13], [2, 3], [2, 5], [2, 6], [2, 8], [2, 9], [2, 11], [2, 12], [2, 13], [3, 4], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [4, 5], [4, 6], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [6, 7], [6, 8], [6, 9], [6, 11], [6, 12], [6, 13], [7, 8], [7, 9], [7, 10], [7, 11], [7, 13], [8, 9], [8, 10], [8, 12], [8, 13], [9, 10], [9, 12], [10, 11], [10, 13], [11, 13], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s1/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f7cb780eeda770e16ce48145721bb80f7bd31076
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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'
+{"clique": [0, 1, 5, 6, 7, 9]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l2-s1/tests/check.py b/tasks/construct-rlve-maximum-clique-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-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("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-s1/tests/instance.json b/tasks/construct-rlve-maximum-clique-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..94665089faa05442037cfdc1ea59548ba76e5330
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 6, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 12], [1, 13], [2, 3], [2, 5], [2, 6], [2, 8], [2, 9], [2, 11], [2, 12], [2, 13], [3, 4], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [4, 5], [4, 6], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [6, 7], [6, 8], [6, 9], [6, 11], [6, 12], [6, 13], [7, 8], [7, 9], [7, 10], [7, 11], [7, 13], [8, 9], [8, 10], [8, 12], [8, 13], [9, 10], [9, 12], [10, 11], [10, 13], [11, 13], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s1/tests/run.py b/tasks/construct-rlve-maximum-clique-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l2-s1/tests/test.sh b/tasks/construct-rlve-maximum-clique-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l2-s6/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l2-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-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-l2-s6/environment/instance.json b/tasks/construct-rlve-maximum-clique-l2-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a2b7f5515c17a4c5d0be925aa5c8b78f76ba986
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 7, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [2, 3], [2, 4], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 13], [3, 4], [3, 5], [3, 6], [3, 10], [3, 12], [3, 13], [4, 5], [4, 6], [4, 7], [4, 8], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 10], [5, 11], [6, 7], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [7, 10], [7, 11], [7, 12], [7, 13], [8, 10], [8, 11], [8, 12], [9, 10], [9, 12], [9, 13], [10, 11], [10, 13], [11, 12], [11, 13], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s6/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l2-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..eebb666aca0229eb870a45692dc5c0416c894684
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-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": [0, 1, 2, 3, 4, 6, 10]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l2-s6/tests/check.py b/tasks/construct-rlve-maximum-clique-l2-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-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-l2-s6/tests/instance.json b/tasks/construct-rlve-maximum-clique-l2-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a2b7f5515c17a4c5d0be925aa5c8b78f76ba986
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 7, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [2, 3], [2, 4], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 13], [3, 4], [3, 5], [3, 6], [3, 10], [3, 12], [3, 13], [4, 5], [4, 6], [4, 7], [4, 8], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 10], [5, 11], [6, 7], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [7, 10], [7, 11], [7, 12], [7, 13], [8, 10], [8, 11], [8, 12], [9, 10], [9, 12], [9, 13], [10, 11], [10, 13], [11, 12], [11, 13], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s6/tests/run.py b/tasks/construct-rlve-maximum-clique-l2-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-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-l2-s6/tests/test.sh b/tasks/construct-rlve-maximum-clique-l2-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-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-s8/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l2-s8/environment/instance.json b/tasks/construct-rlve-maximum-clique-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..19a12ccffdc21db6795f5ef0a7d5fb118a6957eb
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 6, "edges": [[0, 1], [0, 3], [0, 4], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 2], [1, 4], [1, 5], [1, 6], [1, 13], [2, 3], [2, 5], [2, 7], [2, 8], [2, 9], [2, 12], [3, 4], [3, 5], [3, 6], [3, 7], [3, 9], [3, 12], [3, 13], [4, 6], [4, 8], [4, 10], [4, 11], [5, 6], [5, 7], [5, 9], [5, 11], [5, 12], [6, 7], [6, 8], [6, 11], [6, 13], [7, 9], [7, 12], [7, 13], [8, 9], [9, 12], [9, 13], [10, 12], [11, 12], [11, 13], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s8/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8878d1b517a654639976eefdb104ab32e9730cf3
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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'
+{"clique": [2, 3, 5, 7, 9, 12]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l2-s8/tests/check.py b/tasks/construct-rlve-maximum-clique-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s8/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-s8/tests/instance.json b/tasks/construct-rlve-maximum-clique-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..19a12ccffdc21db6795f5ef0a7d5fb118a6957eb
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 14, "k": 6, "edges": [[0, 1], [0, 3], [0, 4], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 2], [1, 4], [1, 5], [1, 6], [1, 13], [2, 3], [2, 5], [2, 7], [2, 8], [2, 9], [2, 12], [3, 4], [3, 5], [3, 6], [3, 7], [3, 9], [3, 12], [3, 13], [4, 6], [4, 8], [4, 10], [4, 11], [5, 6], [5, 7], [5, 9], [5, 11], [5, 12], [6, 7], [6, 8], [6, 11], [6, 13], [7, 9], [7, 12], [7, 13], [8, 9], [9, 12], [9, 13], [10, 12], [11, 12], [11, 13], [12, 13]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l2-s8/tests/run.py b/tasks/construct-rlve-maximum-clique-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l2-s8/tests/test.sh b/tasks/construct-rlve-maximum-clique-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l6-s7/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l6-s7/environment/instance.json b/tasks/construct-rlve-maximum-clique-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d4225ab6757cb4026f365f9c3368e610ca524a7a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 11, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 32], [0, 33], [0, 34], [0, 35], [0, 37], [0, 38], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [1, 2], [1, 4], [1, 5], [1, 8], [1, 10], [1, 12], [1, 13], [1, 14], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 23], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 36], [1, 37], [1, 38], [1, 40], [1, 42], [1, 43], [1, 44], [1, 45], [1, 46], [1, 47], [1, 48], [1, 51], [1, 52], [1, 53], [1, 54], [1, 55], [2, 3], [2, 6], [2, 7], [2, 8], [2, 9], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 18], [2, 19], [2, 22], [2, 23], [2, 24], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 33], [2, 34], [2, 36], [2, 40], [2, 41], [2, 43], [2, 44], [2, 45], [2, 48], [2, 49], [2, 50], [2, 52], [2, 53], [2, 54], [3, 4], [3, 5], [3, 6], [3, 14], [3, 15], [3, 16], [3, 18], [3, 21], [3, 23], [3, 24], [3, 25], [3, 27], [3, 29], [3, 30], [3, 32], [3, 33], [3, 34], [3, 35], [3, 38], [3, 39], [3, 40], [3, 42], [3, 44], [3, 45], [3, 46], [3, 47], [3, 48], [3, 49], [3, 50], [3, 51], [3, 54], [3, 55], [4, 6], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 15], [4, 16], [4, 17], [4, 19], [4, 21], [4, 23], [4, 24], [4, 26], [4, 27], [4, 28], [4, 29], [4, 30], [4, 31], [4, 32], [4, 33], [4, 35], [4, 37], [4, 38], [4, 39], [4, 40], [4, 41], [4, 42], [4, 43], [4, 45], [4, 46], [4, 47], [4, 48], [4, 49], [4, 54], [4, 55], [5, 6], [5, 8], [5, 11], [5, 12], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [5, 22], [5, 23], [5, 24], [5, 26], [5, 27], [5, 28], [5, 30], [5, 34], [5, 36], [5, 37], [5, 38], [5, 40], [5, 42], [5, 43], [5, 45], [5, 46], [5, 47], [5, 48], [5, 51], [5, 52], [5, 54], [5, 55], [6, 7], [6, 9], [6, 11], [6, 14], [6, 17], [6, 18], [6, 19], [6, 21], [6, 22], [6, 24], [6, 25], [6, 26], [6, 28], [6, 34], [6, 35], [6, 37], [6, 38], [6, 39], [6, 40], [6, 41], [6, 42], [6, 43], [6, 44], [6, 46], [6, 48], [6, 49], [6, 50], [6, 51], [6, 52], [6, 53], [6, 54], [6, 55], [7, 8], [7, 9], [7, 13], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 26], [7, 29], [7, 30], [7, 31], [7, 32], [7, 34], [7, 37], [7, 39], [7, 42], [7, 43], [7, 44], [7, 45], [7, 46], [7, 48], [7, 49], [7, 50], [7, 51], [7, 52], [7, 53], [7, 55], [8, 9], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 19], [8, 20], [8, 21], [8, 22], [8, 23], [8, 25], [8, 28], [8, 29], [8, 30], [8, 31], [8, 32], [8, 33], [8, 34], [8, 35], [8, 37], [8, 38], [8, 39], [8, 40], [8, 43], [8, 45], [8, 46], [8, 51], [8, 52], [8, 53], [8, 54], [9, 12], [9, 13], [9, 14], [9, 15], [9, 17], [9, 19], [9, 20], [9, 21], [9, 24], [9, 26], [9, 27], [9, 28], [9, 29], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 36], [9, 37], [9, 38], [9, 42], [9, 43], [9, 44], [9, 45], [9, 46], [9, 47], [9, 49], [9, 50], [9, 52], [9, 53], [9, 54], [9, 55], [10, 11], [10, 12], [10, 13], [10, 14], [10, 16], [10, 17], [10, 20], [10, 21], [10, 25], [10, 26], [10, 27], [10, 28], [10, 29], [10, 30], [10, 31], [10, 34], [10, 35], [10, 36], [10, 37], [10, 38], [10, 39], [10, 40], [10, 42], [10, 44], [10, 45], [10, 48], [10, 50], [10, 51], [10, 52], [10, 54], [10, 55], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [11, 22], [11, 23], [11, 25], [11, 27], [11, 28], [11, 30], [11, 31], [11, 32], [11, 33], [11, 35], [11, 36], [11, 37], [11, 38], [11, 40], [11, 41], [11, 42], [11, 43], [11, 44], [11, 45], [11, 49], [11, 51], [11, 53], [11, 54], [12, 13], [12, 14], [12, 15], [12, 16], [12, 18], [12, 19], [12, 20], [12, 21], [12, 23], [12, 24], [12, 25], [12, 27], [12, 28], [12, 29], [12, 30], [12, 31], [12, 33], [12, 34], [12, 36], [12, 37], [12, 38], [12, 39], [12, 40], [12, 41], [12, 42], [12, 43], [12, 44], [12, 45], [12, 46], [12, 48], [12, 50], [12, 51], [12, 53], [12, 54], [12, 55], [13, 14], [13, 15], [13, 16], [13, 18], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 26], [13, 27], [13, 28], [13, 31], [13, 36], [13, 37], [13, 38], [13, 39], [13, 40], [13, 41], [13, 42], [13, 43], [13, 46], [13, 47], [13, 49], [13, 50], [13, 51], [13, 53], [14, 15], [14, 16], [14, 17], [14, 19], [14, 20], [14, 21], [14, 22], [14, 23], [14, 24], [14, 26], [14, 28], [14, 29], [14, 31], [14, 33], [14, 34], [14, 35], [14, 37], [14, 38], [14, 39], [14, 40], [14, 41], [14, 42], [14, 44], [14, 45], [14, 47], [14, 49], [14, 51], [14, 52], [14, 53], [14, 54], [14, 55], [15, 17], [15, 22], [15, 25], [15, 26], [15, 27], [15, 28], [15, 29], [15, 30], [15, 32], [15, 33], [15, 34], [15, 35], [15, 36], [15, 38], [15, 42], [15, 43], [15, 44], [15, 45], [15, 46], [15, 47], [15, 49], [15, 50], [15, 51], [15, 52], [15, 53], [16, 17], [16, 19], [16, 20], [16, 22], [16, 23], [16, 24], [16, 26], [16, 29], [16, 30], [16, 31], [16, 32], 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[44, 52], [45, 46], [45, 49], [45, 50], [45, 52], [45, 53], [45, 55], [46, 47], [46, 48], [46, 50], [46, 51], [46, 54], [47, 49], [47, 50], [47, 51], [47, 52], [47, 53], [47, 54], [47, 55], [48, 49], [48, 50], [48, 52], [48, 53], [48, 54], [48, 55], [49, 50], [49, 51], [49, 52], [49, 53], [49, 54], [49, 55], [50, 51], [50, 53], [50, 54], [50, 55], [51, 52], [51, 53], [51, 54], [52, 53], [52, 54], [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-s7/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7ca583e1e2e43b9dd13ad9ca357c8b840838bdbc
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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'
+{"clique": [0, 6, 9, 14, 17, 24, 28, 34, 42, 44, 49]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l6-s7/tests/check.py b/tasks/construct-rlve-maximum-clique-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s7/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-s7/tests/instance.json b/tasks/construct-rlve-maximum-clique-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d4225ab6757cb4026f365f9c3368e610ca524a7a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 11, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 32], [0, 33], [0, 34], [0, 35], [0, 37], [0, 38], [0, 41], [0, 42], [0, 43], [0, 44], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [1, 2], [1, 4], [1, 5], [1, 8], [1, 10], [1, 12], [1, 13], [1, 14], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 23], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 36], [1, 37], [1, 38], [1, 40], [1, 42], [1, 43], [1, 44], [1, 45], [1, 46], [1, 47], [1, 48], [1, 51], [1, 52], [1, 53], [1, 54], [1, 55], [2, 3], [2, 6], [2, 7], [2, 8], [2, 9], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 18], [2, 19], [2, 22], [2, 23], [2, 24], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 33], [2, 34], [2, 36], [2, 40], [2, 41], [2, 43], [2, 44], [2, 45], [2, 48], [2, 49], [2, 50], [2, 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[24, 37], [24, 38], [24, 39], [24, 41], [24, 42], [24, 44], [24, 45], [24, 46], [24, 47], [24, 48], [24, 49], [24, 50], [24, 53], [24, 54], [24, 55], [25, 26], [25, 27], [25, 28], [25, 29], [25, 31], [25, 33], [25, 35], [25, 36], [25, 37], [25, 39], [25, 40], [25, 41], [25, 42], [25, 43], [25, 44], [25, 47], [25, 48], [25, 50], [25, 52], [25, 53], [25, 55], [26, 28], [26, 29], [26, 30], [26, 31], [26, 32], [26, 33], [26, 34], [26, 35], [26, 36], [26, 37], [26, 38], [26, 39], [26, 41], [26, 42], [26, 43], [26, 44], [26, 48], [26, 49], [26, 50], [26, 51], [26, 53], [26, 54], [27, 29], [27, 31], [27, 32], [27, 33], [27, 35], [27, 36], [27, 37], [27, 40], [27, 41], [27, 42], [27, 43], [27, 46], [27, 47], [27, 48], [27, 49], [27, 50], [27, 52], [27, 55], [28, 29], [28, 30], [28, 31], [28, 32], [28, 33], [28, 34], [28, 39], [28, 40], [28, 41], [28, 42], [28, 43], [28, 44], [28, 47], [28, 49], [28, 51], [28, 55], [29, 31], [29, 33], [29, 34], [29, 36], [29, 37], [29, 38], [29, 39], [29, 40], [29, 42], [29, 44], [29, 46], [29, 50], [29, 52], [29, 53], [29, 54], [29, 55], [30, 32], [30, 33], [30, 34], [30, 35], [30, 36], [30, 37], [30, 38], [30, 42], [30, 43], [30, 44], [30, 46], [30, 47], [30, 48], [30, 49], [30, 52], [30, 53], [30, 55], [31, 32], [31, 33], [31, 35], [31, 36], [31, 37], [31, 39], [31, 41], [31, 43], [31, 45], [31, 46], [31, 47], [31, 48], [31, 49], [31, 52], [31, 54], [31, 55], [32, 33], [32, 34], [32, 35], [32, 36], [32, 37], [32, 38], [32, 39], [32, 41], [32, 43], [32, 46], [32, 48], [32, 50], [32, 51], [32, 52], [32, 54], [33, 35], [33, 36], [33, 38], [33, 39], [33, 40], [33, 41], [33, 43], [33, 44], [33, 45], [33, 46], [33, 47], [33, 48], [33, 50], [33, 51], [33, 54], [33, 55], [34, 35], [34, 36], [34, 37], [34, 39], [34, 40], [34, 41], [34, 42], [34, 43], [34, 44], [34, 45], [34, 46], [34, 48], [34, 49], [34, 50], [34, 51], [34, 52], [34, 53], [34, 54], [34, 55], [35, 36], [35, 37], [35, 38], [35, 40], [35, 41], [35, 42], [35, 44], [35, 45], [35, 48], 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[44, 52], [45, 46], [45, 49], [45, 50], [45, 52], [45, 53], [45, 55], [46, 47], [46, 48], [46, 50], [46, 51], [46, 54], [47, 49], [47, 50], [47, 51], [47, 52], [47, 53], [47, 54], [47, 55], [48, 49], [48, 50], [48, 52], [48, 53], [48, 54], [48, 55], [49, 50], [49, 51], [49, 52], [49, 53], [49, 54], [49, 55], [50, 51], [50, 53], [50, 54], [50, 55], [51, 52], [51, 53], [51, 54], [52, 53], [52, 54], [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-s7/tests/run.py b/tasks/construct-rlve-maximum-clique-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l6-s7/tests/test.sh b/tasks/construct-rlve-maximum-clique-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-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-maximum-clique-l6-s9/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l6-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-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-maximum-clique-l6-s9/environment/instance.json b/tasks/construct-rlve-maximum-clique-l6-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..58a977ce0cab6200ae2083b0b7ec52403800e126
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 9, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 12], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 30], [0, 31], [0, 32], [0, 35], [0, 37], [0, 42], [0, 43], [0, 45], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [0, 53], [0, 55], [1, 4], [1, 5], [1, 6], [1, 8], [1, 10], [1, 11], [1, 12], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 21], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 29], [1, 30], [1, 33], [1, 35], [1, 36], [1, 37], [1, 38], [1, 42], [1, 43], [1, 44], [1, 45], [1, 46], [1, 48], [1, 49], [1, 51], [1, 55], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 11], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 22], [2, 24], [2, 25], [2, 28], [2, 30], [2, 31], [2, 33], [2, 39], [2, 40], [2, 42], [2, 44], [2, 45], [2, 46], [2, 48], [2, 50], [2, 52], [2, 53], [2, 54], [3, 4], [3, 6], [3, 7], [3, 11], [3, 12], [3, 14], [3, 16], [3, 17], [3, 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"construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l6-s9/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l6-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fe8844fabe3abda722ad4bd8759befc7802a5961
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-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'
+{"clique": [0, 3, 14, 16, 17, 24, 32, 37, 52]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l6-s9/tests/check.py b/tasks/construct-rlve-maximum-clique-l6-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s9/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-s9/tests/instance.json b/tasks/construct-rlve-maximum-clique-l6-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..58a977ce0cab6200ae2083b0b7ec52403800e126
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 56, "k": 9, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 12], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 30], [0, 31], [0, 32], [0, 35], [0, 37], [0, 42], [0, 43], [0, 45], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [0, 53], [0, 55], [1, 4], [1, 5], [1, 6], [1, 8], [1, 10], [1, 11], [1, 12], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 21], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 29], [1, 30], [1, 33], [1, 35], [1, 36], [1, 37], [1, 38], [1, 42], [1, 43], [1, 44], [1, 45], [1, 46], [1, 48], [1, 49], [1, 51], [1, 55], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 11], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 22], [2, 24], [2, 25], [2, 28], [2, 30], [2, 31], [2, 33], [2, 39], [2, 40], [2, 42], [2, 44], [2, 45], [2, 46], [2, 48], [2, 50], [2, 52], [2, 53], [2, 54], [3, 4], [3, 6], [3, 7], [3, 11], [3, 12], [3, 14], [3, 16], [3, 17], [3, 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44], [24, 46], [24, 47], [24, 48], [24, 50], [24, 51], [24, 52], [24, 54], [24, 55], [25, 26], [25, 27], [25, 28], [25, 29], [25, 30], [25, 31], [25, 32], [25, 33], [25, 35], [25, 36], [25, 37], [25, 38], [25, 39], [25, 44], [25, 45], [25, 46], [25, 49], [25, 50], [25, 51], [25, 55], [26, 27], [26, 29], [26, 31], [26, 32], [26, 36], [26, 38], [26, 39], [26, 40], [26, 43], [26, 45], [26, 46], [26, 47], [26, 48], [26, 49], [26, 53], [26, 54], [26, 55], [27, 29], [27, 31], [27, 32], [27, 33], [27, 36], [27, 39], [27, 41], [27, 42], [27, 43], [27, 46], [27, 47], [27, 48], [27, 49], [27, 50], [27, 51], [27, 54], [27, 55], [28, 29], [28, 34], [28, 35], [28, 38], [28, 42], [28, 44], [28, 48], [28, 52], [29, 30], [29, 31], [29, 32], [29, 34], [29, 35], [29, 37], [29, 38], [29, 39], [29, 40], [29, 42], [29, 43], [29, 44], [29, 46], [29, 47], [29, 48], [29, 49], [29, 50], [29, 53], [29, 54], [29, 55], [30, 32], [30, 33], [30, 34], [30, 35], [30, 38], [30, 43], [30, 45], [30, 47], [30, 49], [30, 50], [30, 51], [30, 53], [30, 55], [31, 32], [31, 34], [31, 35], [31, 36], [31, 39], [31, 40], [31, 42], [31, 43], [31, 44], [31, 46], [31, 47], [31, 49], [31, 50], [31, 52], [31, 55], [32, 34], [32, 35], [32, 37], [32, 38], [32, 40], [32, 41], [32, 42], [32, 43], [32, 45], [32, 46], [32, 47], [32, 48], [32, 49], [32, 52], [32, 54], [32, 55], [33, 34], [33, 35], [33, 36], [33, 39], [33, 40], [33, 41], [33, 42], [33, 43], [33, 44], [33, 47], [33, 48], [33, 50], [33, 52], [33, 53], [33, 55], [34, 35], [34, 36], [34, 40], [34, 41], [34, 42], [34, 43], [34, 44], [34, 45], [34, 46], [34, 47], [34, 48], [34, 49], [34, 54], [34, 55], [35, 36], [35, 37], [35, 38], [35, 39], [35, 40], [35, 41], [35, 43], [35, 45], [35, 46], [35, 47], [35, 48], [35, 49], [35, 51], [35, 54], [35, 55], [36, 39], [36, 41], [36, 43], [36, 44], [36, 45], [36, 46], [36, 47], [36, 51], [36, 52], [36, 53], [36, 54], [37, 39], [37, 41], [37, 43], [37, 45], [37, 48], [37, 49], [37, 50], [37, 51], [37, 52], [37, 54], [37, 55], [38, 39], [38, 42], [38, 43], [38, 44], [38, 45], [38, 48], [38, 49], [38, 51], [38, 52], [39, 44], [39, 45], [39, 47], [39, 49], [39, 50], [39, 51], [39, 52], [39, 54], [39, 55], [40, 41], [40, 43], [40, 44], [40, 45], [40, 46], [40, 48], [40, 50], [40, 51], [40, 54], [41, 42], [41, 44], [41, 45], [41, 48], [41, 49], [41, 52], [41, 55], [42, 45], [42, 47], [42, 48], [42, 49], [42, 51], [42, 54], [42, 55], [43, 44], [43, 45], [43, 46], [43, 47], [43, 48], [43, 50], [43, 52], [43, 53], [43, 54], [43, 55], [44, 45], [44, 46], [44, 48], [44, 49], [44, 52], [44, 54], [45, 46], [45, 47], [45, 48], [45, 50], [45, 51], [45, 52], [46, 47], [46, 48], [46, 49], [46, 50], [46, 51], [46, 52], [47, 48], [47, 49], [47, 50], [47, 51], [47, 52], [47, 53], [48, 49], [48, 51], [48, 52], [48, 53], [48, 54], [48, 55], [49, 50], [49, 54], [50, 51], [50, 55], [51, 52], [51, 53], [51, 54], [52, 53], [52, 54], [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-s9/tests/run.py b/tasks/construct-rlve-maximum-clique-l6-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-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-maximum-clique-l6-s9/tests/test.sh b/tasks/construct-rlve-maximum-clique-l6-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l6-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-min-chromatic-number-l4-s3/environment/Dockerfile b/tasks/construct-rlve-min-chromatic-number-l4-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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-min-chromatic-number-l4-s3/environment/instance.json b/tasks/construct-rlve-min-chromatic-number-l4-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f268f6f59107f7088b530d48abb03173abc00046
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 18, "k": 4, "edges": [[0, 1], [0, 13], [1, 2], [1, 4], [1, 6], [1, 8], [1, 12], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [3, 4], [3, 13], [4, 6], [4, 11], [4, 16], [5, 6], [5, 8], [5, 10], [5, 11], [5, 12], [5, 14], [5, 16], [6, 8], [6, 9], [6, 15], [6, 16], [7, 14], [7, 16], [8, 11], [8, 12], [8, 15], [8, 17], [9, 14], [9, 15], [12, 17], [13, 16]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l4-s3/solution/solve.sh b/tasks/construct-rlve-min-chromatic-number-l4-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fe5df5fff0d8c93065b406a9d4c3c77b12c5289b
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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'
+{"colors": [0, 1, 0, 0, 2, 0, 3, 0, 2, 0, 1, 1, 3, 2, 1, 1, 1, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-min-chromatic-number-l4-s3/tests/check.py b/tasks/construct-rlve-min-chromatic-number-l4-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2b77793fb15e0d97174b3c28e69a86e2a26996f
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-s3/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-l4-s3/tests/instance.json b/tasks/construct-rlve-min-chromatic-number-l4-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f268f6f59107f7088b530d48abb03173abc00046
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 18, "k": 4, "edges": [[0, 1], [0, 13], [1, 2], [1, 4], [1, 6], [1, 8], [1, 12], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [3, 4], [3, 13], [4, 6], [4, 11], [4, 16], [5, 6], [5, 8], [5, 10], [5, 11], [5, 12], [5, 14], [5, 16], [6, 8], [6, 9], [6, 15], [6, 16], [7, 14], [7, 16], [8, 11], [8, 12], [8, 15], [8, 17], [9, 14], [9, 15], [12, 17], [13, 16]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l4-s3/tests/run.py b/tasks/construct-rlve-min-chromatic-number-l4-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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-min-chromatic-number-l4-s3/tests/test.sh b/tasks/construct-rlve-min-chromatic-number-l4-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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-min-chromatic-number-l4-s4/environment/Dockerfile b/tasks/construct-rlve-min-chromatic-number-l4-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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-min-chromatic-number-l4-s4/environment/instance.json b/tasks/construct-rlve-min-chromatic-number-l4-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5852e25c22d42069ece8af44933bc374a27df6c8
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 18, "k": 7, "edges": [[0, 1], [0, 2], [0, 5], [0, 6], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 4], [1, 6], [1, 8], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 16], [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, 17], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 13], [3, 15], [3, 16], [3, 17], [4, 8], [4, 11], [4, 13], [4, 15], [4, 16], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 16], [5, 17], [6, 9], [6, 11], [6, 13], [6, 16], [6, 17], [7, 8], [7, 10], [7, 11], [7, 12], [7, 16], [8, 9], [8, 13], [8, 14], [8, 17], [9, 10], [9, 12], [9, 15], [9, 17], [10, 11], [10, 13], [10, 15], [10, 16], [10, 17], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [12, 13], [12, 16], [12, 17], [13, 14], [13, 17], [14, 15], [14, 17], [15, 16], [16, 17]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l4-s4/solution/solve.sh b/tasks/construct-rlve-min-chromatic-number-l4-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7006a0fc9fcf1b4d2569d8f62ef62574fe03444d
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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'
+{"colors": [0, 1, 2, 0, 3, 1, 3, 1, 4, 5, 3, 4, 3, 5, 3, 1, 2, 6]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-min-chromatic-number-l4-s4/tests/check.py b/tasks/construct-rlve-min-chromatic-number-l4-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2b77793fb15e0d97174b3c28e69a86e2a26996f
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-s4/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-l4-s4/tests/instance.json b/tasks/construct-rlve-min-chromatic-number-l4-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5852e25c22d42069ece8af44933bc374a27df6c8
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-s4/tests/instance.json
@@ -0,0 +1 @@
+{"n": 18, "k": 7, "edges": [[0, 1], [0, 2], [0, 5], [0, 6], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 4], [1, 6], [1, 8], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 16], [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, 17], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 13], [3, 15], [3, 16], [3, 17], [4, 8], [4, 11], [4, 13], [4, 15], [4, 16], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 16], [5, 17], [6, 9], [6, 11], [6, 13], [6, 16], [6, 17], [7, 8], [7, 10], [7, 11], [7, 12], [7, 16], [8, 9], [8, 13], [8, 14], [8, 17], [9, 10], [9, 12], [9, 15], [9, 17], [10, 11], [10, 13], [10, 15], [10, 16], [10, 17], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [12, 13], [12, 16], [12, 17], [13, 14], [13, 17], [14, 15], [14, 17], [15, 16], [16, 17]], "family": "rlve_min_chromatic_number", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-chromatic-number-l4-s4/tests/run.py b/tasks/construct-rlve-min-chromatic-number-l4-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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-min-chromatic-number-l4-s4/tests/test.sh b/tasks/construct-rlve-min-chromatic-number-l4-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-min-chromatic-number-l4-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-min-harmonious-coloring-l4-s9/environment/Dockerfile b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-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-rlve-min-harmonious-coloring-l4-s9/environment/instance.json b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..96388d80ebb0144a07c6a5de2dcd70cd40cb9b60
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12, "k": 6, "edges": [[1, 4], [1, 7], [1, 10], [2, 4], [2, 8], [3, 4], [3, 6], [3, 7], [5, 8], [6, 7], [6, 9], [6, 10], [9, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s9/solution/solve.sh b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ac5a2998d97dd536430f40c827041622fdb5a8ed
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-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'
+{"colors": [0, 0, 1, 2, 3, 0, 4, 5, 2, 3, 1, 5]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/check.py b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..91282a31c765b6103e6575180adb47abddb6a506
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/check.py
@@ -0,0 +1,15 @@
+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")
+    seen = set()
+    for u, v in inst["edges"]:
+        if c[u] == c[v]:
+            raise Invalid(f"edge ({u},{v}) is monochromatic")
+        pair = (min(c[u], c[v]), max(c[u], c[v]))
+        if pair in seen:
+            raise Invalid(f"colour pair {pair} appears on two edges")
+        seen.add(pair)
+    return None, {}
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/instance.json b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..96388d80ebb0144a07c6a5de2dcd70cd40cb9b60
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12, "k": 6, "edges": [[1, 4], [1, 7], [1, 10], [2, 4], [2, 8], [3, 4], [3, 6], [3, 7], [5, 8], [6, 7], [6, 9], [6, 10], [9, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/run.py b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-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-rlve-min-harmonious-coloring-l4-s9/tests/test.sh b/tasks/construct-rlve-min-harmonious-coloring-l4-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-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-rlve-pairwise-sums-recovery-l2-s6/environment/Dockerfile b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-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-pairwise-sums-recovery-l2-s6/environment/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b6b8b06124015369cb96545018a62675f2e48c12
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 5, "sums": [7, 12, 11, 13, 8, 17, 9, 14, 13, 12], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/solution/solve.sh b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3b9a9b16a9d365bab1f96d596d79c2998c9fa7fd
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-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'
+{"numbers": [3, 4, 5, 8, 9]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/check.py b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..01b5b475e927688c0209fb93478a95f6dd1d3407
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/check.py
@@ -0,0 +1,14 @@
+from collections import Counter
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("numbers"), n, 1, None, "numbers")
+    if len(set(x)) != n:
+        raise Invalid("numbers must be distinct")
+    got = Counter(x[i] + x[j] for i in range(n) for j in range(i + 1, n))
+    if got != Counter(inst["sums"]):
+        raise Invalid("pairwise sums do not match")
+    return None, {}
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b6b8b06124015369cb96545018a62675f2e48c12
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 5, "sums": [7, 12, 11, 13, 8, 17, 9, 14, 13, 12], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/run.py b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-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-pairwise-sums-recovery-l2-s6/tests/test.sh b/tasks/construct-rlve-pairwise-sums-recovery-l2-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-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-pairwise-sums-recovery-l2-s8/environment/Dockerfile b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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-pairwise-sums-recovery-l2-s8/environment/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e275101183a70c8d300346400bd899a57ae3c919
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 5, "sums": [5, 13, 7, 15, 9, 14, 12, 6, 8, 7], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/solution/solve.sh b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c1945db2f904f8d94ea8e297719ae7e812b5da89
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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'
+{"numbers": [2, 3, 4, 5, 10]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/check.py b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..01b5b475e927688c0209fb93478a95f6dd1d3407
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/check.py
@@ -0,0 +1,14 @@
+from collections import Counter
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("numbers"), n, 1, None, "numbers")
+    if len(set(x)) != n:
+        raise Invalid("numbers must be distinct")
+    got = Counter(x[i] + x[j] for i in range(n) for j in range(i + 1, n))
+    if got != Counter(inst["sums"]):
+        raise Invalid("pairwise sums do not match")
+    return None, {}
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e275101183a70c8d300346400bd899a57ae3c919
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 5, "sums": [5, 13, 7, 15, 9, 14, 12, 6, 8, 7], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/run.py b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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-pairwise-sums-recovery-l2-s8/tests/test.sh b/tasks/construct-rlve-pairwise-sums-recovery-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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-pairwise-sums-recovery-l6-s7/environment/Dockerfile b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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-pairwise-sums-recovery-l6-s7/environment/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d2597a1c847536cc61650e79c0649d8f04561b3b
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 26, "sums": [45, 9, 70, 57, 46, 74, 44, 37, 78, 49, 48, 15, 49, 52, 75, 58, 34, 64, 14, 31, 59, 37, 43, 13, 35, 54, 47, 73, 70, 31, 69, 56, 66, 58, 44, 44, 22, 62, 43, 41, 25, 48, 21, 43, 39, 71, 37, 60, 8, 87, 60, 44, 44, 8, 59, 32, 36, 48, 22, 75, 35, 35, 38, 32, 34, 67, 46, 18, 33, 4, 62, 10, 59, 54, 19, 94, 65, 15, 50, 62, 36, 56, 88, 37, 71, 78, 76, 86, 82, 63, 50, 7, 39, 41, 23, 53, 54, 65, 51, 31, 64, 58, 79, 33, 7, 62, 61, 67, 12, 20, 53, 28, 28, 26, 43, 27, 71, 76, 26, 89, 15, 46, 57, 67, 20, 89, 37, 56, 37, 42, 46, 42, 47, 20, 52, 65, 51, 12, 32, 22, 46, 40, 21, 13, 93, 15, 73, 55, 40, 61, 39, 83, 69, 18, 26, 57, 70, 72, 49, 34, 42, 33, 60, 50, 39, 74, 78, 59, 52, 54, 49, 24, 61, 23, 41, 49, 60, 91, 30, 66, 34, 67, 84, 48, 30, 53, 27, 14, 80, 32, 56, 55, 66, 49, 50, 73, 85, 63, 35, 80, 11, 19, 64, 38, 46, 77, 23, 42, 45, 36, 73, 53, 63, 10, 43, 21, 13, 53, 48, 32, 16, 66, 47, 6, 33, 60, 19, 40, 49, 50, 16, 56, 45, 53, 31, 29, 31, 51, 29, 33, 63, 38, 5, 36, 72, 51, 30, 38, 24, 41, 77, 24, 51, 55, 24, 53, 27, 49, 40, 17, 58, 53, 87, 56, 59, 42, 38, 45, 55, 69, 9, 45, 31, 11, 67, 74, 52, 49, 32, 49, 52, 38, 34, 81, 25, 51, 26, 45, 91, 71, 16, 47, 64, 20, 9, 25, 11, 42, 27, 48, 33, 47, 28, 76, 46, 21, 55, 3, 80, 26, 29, 29, 69, 40, 76, 84, 17, 51, 44, 68, 35, 27, 54, 8, 38], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/solution/solve.sh b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b7863d832a3b67befdb1e9c29328a3f2611ffa02
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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'
+{"numbers": [1, 2, 3, 5, 6, 7, 8, 10, 13, 14, 18, 19, 21, 24, 25, 28, 30, 31, 32, 35, 39, 41, 43, 45, 46, 48]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/check.py b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..01b5b475e927688c0209fb93478a95f6dd1d3407
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/check.py
@@ -0,0 +1,14 @@
+from collections import Counter
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("numbers"), n, 1, None, "numbers")
+    if len(set(x)) != n:
+        raise Invalid("numbers must be distinct")
+    got = Counter(x[i] + x[j] for i in range(n) for j in range(i + 1, n))
+    if got != Counter(inst["sums"]):
+        raise Invalid("pairwise sums do not match")
+    return None, {}
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d2597a1c847536cc61650e79c0649d8f04561b3b
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 26, "sums": [45, 9, 70, 57, 46, 74, 44, 37, 78, 49, 48, 15, 49, 52, 75, 58, 34, 64, 14, 31, 59, 37, 43, 13, 35, 54, 47, 73, 70, 31, 69, 56, 66, 58, 44, 44, 22, 62, 43, 41, 25, 48, 21, 43, 39, 71, 37, 60, 8, 87, 60, 44, 44, 8, 59, 32, 36, 48, 22, 75, 35, 35, 38, 32, 34, 67, 46, 18, 33, 4, 62, 10, 59, 54, 19, 94, 65, 15, 50, 62, 36, 56, 88, 37, 71, 78, 76, 86, 82, 63, 50, 7, 39, 41, 23, 53, 54, 65, 51, 31, 64, 58, 79, 33, 7, 62, 61, 67, 12, 20, 53, 28, 28, 26, 43, 27, 71, 76, 26, 89, 15, 46, 57, 67, 20, 89, 37, 56, 37, 42, 46, 42, 47, 20, 52, 65, 51, 12, 32, 22, 46, 40, 21, 13, 93, 15, 73, 55, 40, 61, 39, 83, 69, 18, 26, 57, 70, 72, 49, 34, 42, 33, 60, 50, 39, 74, 78, 59, 52, 54, 49, 24, 61, 23, 41, 49, 60, 91, 30, 66, 34, 67, 84, 48, 30, 53, 27, 14, 80, 32, 56, 55, 66, 49, 50, 73, 85, 63, 35, 80, 11, 19, 64, 38, 46, 77, 23, 42, 45, 36, 73, 53, 63, 10, 43, 21, 13, 53, 48, 32, 16, 66, 47, 6, 33, 60, 19, 40, 49, 50, 16, 56, 45, 53, 31, 29, 31, 51, 29, 33, 63, 38, 5, 36, 72, 51, 30, 38, 24, 41, 77, 24, 51, 55, 24, 53, 27, 49, 40, 17, 58, 53, 87, 56, 59, 42, 38, 45, 55, 69, 9, 45, 31, 11, 67, 74, 52, 49, 32, 49, 52, 38, 34, 81, 25, 51, 26, 45, 91, 71, 16, 47, 64, 20, 9, 25, 11, 42, 27, 48, 33, 47, 28, 76, 46, 21, 55, 3, 80, 26, 29, 29, 69, 40, 76, 84, 17, 51, 44, 68, 35, 27, 54, 8, 38], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/run.py b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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-pairwise-sums-recovery-l6-s7/tests/test.sh b/tasks/construct-rlve-pairwise-sums-recovery-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-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-pairwise-sums-recovery-l6-s9/environment/Dockerfile b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-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-pairwise-sums-recovery-l6-s9/environment/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d1b37d6452fd85b947f176d50f1d0267657fabe9
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 26, "sums": [47, 46, 34, 60, 78, 51, 19, 50, 58, 27, 48, 28, 18, 42, 19, 27, 16, 9, 54, 10, 66, 35, 50, 64, 15, 41, 19, 18, 57, 62, 54, 65, 18, 37, 54, 39, 29, 32, 13, 29, 33, 25, 17, 43, 76, 21, 76, 47, 61, 26, 56, 81, 24, 39, 20, 47, 57, 45, 63, 24, 61, 49, 15, 24, 58, 36, 49, 31, 45, 37, 63, 16, 63, 21, 40, 34, 59, 13, 53, 31, 43, 19, 38, 13, 34, 41, 59, 21, 65, 27, 58, 77, 52, 63, 61, 84, 72, 22, 52, 59, 88, 45, 63, 66, 53, 20, 29, 26, 66, 22, 45, 28, 55, 12, 55, 32, 22, 34, 92, 52, 72, 74, 59, 40, 46, 17, 35, 65, 23, 29, 62, 10, 94, 41, 20, 46, 58, 68, 43, 36, 61, 69, 41, 54, 35, 44, 38, 42, 43, 42, 62, 21, 26, 38, 33, 39, 101, 75, 38, 70, 31, 23, 24, 50, 79, 58, 33, 78, 31, 25, 34, 21, 8, 62, 55, 82, 68, 33, 44, 32, 36, 30, 39, 56, 79, 17, 38, 75, 40, 49, 23, 14, 18, 60, 11, 23, 32, 91, 5, 33, 28, 60, 32, 26, 53, 7, 55, 40, 39, 36, 69, 63, 22, 48, 58, 49, 44, 31, 61, 75, 47, 24, 31, 15, 46, 29, 53, 44, 17, 37, 56, 81, 19, 50, 52, 38, 25, 53, 27, 60, 46, 65, 22, 28, 12, 30, 98, 47, 74, 27, 26, 24, 48, 51, 15, 23, 36, 72, 67, 31, 37, 52, 69, 42, 25, 89, 64, 66, 21, 45, 57, 73, 37, 29, 16, 49, 29, 95, 57, 20, 51, 37, 20, 30, 71, 75, 55, 26, 64, 25, 68, 50, 48, 62, 30, 40, 41, 44, 61, 57, 43, 60, 97, 14, 24, 50, 77, 53, 70, 67, 82, 35, 78, 33, 41, 34, 56, 59, 56, 27, 36, 47, 30, 85, 95], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/solution/solve.sh b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e0f364a61910604d8d3c70237071d3baf9eb8f1b
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-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'
+{"numbers": [1, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 29, 30, 32, 33, 43, 45, 46, 49, 52]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/check.py b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..01b5b475e927688c0209fb93478a95f6dd1d3407
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/check.py
@@ -0,0 +1,14 @@
+from collections import Counter
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("numbers"), n, 1, None, "numbers")
+    if len(set(x)) != n:
+        raise Invalid("numbers must be distinct")
+    got = Counter(x[i] + x[j] for i in range(n) for j in range(i + 1, n))
+    if got != Counter(inst["sums"]):
+        raise Invalid("pairwise sums do not match")
+    return None, {}
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/instance.json b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d1b37d6452fd85b947f176d50f1d0267657fabe9
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 26, "sums": [47, 46, 34, 60, 78, 51, 19, 50, 58, 27, 48, 28, 18, 42, 19, 27, 16, 9, 54, 10, 66, 35, 50, 64, 15, 41, 19, 18, 57, 62, 54, 65, 18, 37, 54, 39, 29, 32, 13, 29, 33, 25, 17, 43, 76, 21, 76, 47, 61, 26, 56, 81, 24, 39, 20, 47, 57, 45, 63, 24, 61, 49, 15, 24, 58, 36, 49, 31, 45, 37, 63, 16, 63, 21, 40, 34, 59, 13, 53, 31, 43, 19, 38, 13, 34, 41, 59, 21, 65, 27, 58, 77, 52, 63, 61, 84, 72, 22, 52, 59, 88, 45, 63, 66, 53, 20, 29, 26, 66, 22, 45, 28, 55, 12, 55, 32, 22, 34, 92, 52, 72, 74, 59, 40, 46, 17, 35, 65, 23, 29, 62, 10, 94, 41, 20, 46, 58, 68, 43, 36, 61, 69, 41, 54, 35, 44, 38, 42, 43, 42, 62, 21, 26, 38, 33, 39, 101, 75, 38, 70, 31, 23, 24, 50, 79, 58, 33, 78, 31, 25, 34, 21, 8, 62, 55, 82, 68, 33, 44, 32, 36, 30, 39, 56, 79, 17, 38, 75, 40, 49, 23, 14, 18, 60, 11, 23, 32, 91, 5, 33, 28, 60, 32, 26, 53, 7, 55, 40, 39, 36, 69, 63, 22, 48, 58, 49, 44, 31, 61, 75, 47, 24, 31, 15, 46, 29, 53, 44, 17, 37, 56, 81, 19, 50, 52, 38, 25, 53, 27, 60, 46, 65, 22, 28, 12, 30, 98, 47, 74, 27, 26, 24, 48, 51, 15, 23, 36, 72, 67, 31, 37, 52, 69, 42, 25, 89, 64, 66, 21, 45, 57, 73, 37, 29, 16, 49, 29, 95, 57, 20, 51, 37, 20, 30, 71, 75, 55, 26, 64, 25, 68, 50, 48, 62, 30, 40, 41, 44, 61, 57, 43, 60, 97, 14, 24, 50, 77, 53, 70, 67, 82, 35, 78, 33, 41, 34, 56, 59, 56, 27, 36, 47, 30, 85, 95], "family": "rlve_pairwise_sums_recovery", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/run.py b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-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-pairwise-sums-recovery-l6-s9/tests/test.sh b/tasks/construct-rlve-pairwise-sums-recovery-l6-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-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-pan-solar-panels-l3-s3/environment/Dockerfile b/tasks/construct-rlve-pan-solar-panels-l3-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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-pan-solar-panels-l3-s3/environment/instance.json b/tasks/construct-rlve-pan-solar-panels-l3-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8df1f6fe29139db303b28fe25df80cab5d3f0efb
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-s3/environment/instance.json
@@ -0,0 +1 @@
+{"A": 61659, "B": 83716, "C": 39815, "D": 51897, "target": 41858, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l3-s3/solution/solve.sh b/tasks/construct-rlve-pan-solar-panels-l3-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8d94e5604870a048289ec3accc818dbfd10f492c
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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": 83716, "Y": 41858}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pan-solar-panels-l3-s3/tests/check.py b/tasks/construct-rlve-pan-solar-panels-l3-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bb2e7cc0b0280ab877755cc5d97b510680f7aa3
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-s3/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-l3-s3/tests/instance.json b/tasks/construct-rlve-pan-solar-panels-l3-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8df1f6fe29139db303b28fe25df80cab5d3f0efb
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-s3/tests/instance.json
@@ -0,0 +1 @@
+{"A": 61659, "B": 83716, "C": 39815, "D": 51897, "target": 41858, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l3-s3/tests/run.py b/tasks/construct-rlve-pan-solar-panels-l3-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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-pan-solar-panels-l3-s3/tests/test.sh b/tasks/construct-rlve-pan-solar-panels-l3-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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-pan-solar-panels-l3-s4/environment/Dockerfile b/tasks/construct-rlve-pan-solar-panels-l3-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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-pan-solar-panels-l3-s4/environment/instance.json b/tasks/construct-rlve-pan-solar-panels-l3-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cca1fc49c7aec132555bafebb47cf890218ef3eb
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-s4/environment/instance.json
@@ -0,0 +1 @@
+{"A": 3768, "B": 35631, "C": 47859, "D": 72030, "target": 35631, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l3-s4/solution/solve.sh b/tasks/construct-rlve-pan-solar-panels-l3-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..93a6852f4c45c8e116d9a74be0aea67a0890ed41
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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": 35631, "Y": 71262}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-pan-solar-panels-l3-s4/tests/check.py b/tasks/construct-rlve-pan-solar-panels-l3-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bb2e7cc0b0280ab877755cc5d97b510680f7aa3
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-s4/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-l3-s4/tests/instance.json b/tasks/construct-rlve-pan-solar-panels-l3-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cca1fc49c7aec132555bafebb47cf890218ef3eb
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-s4/tests/instance.json
@@ -0,0 +1 @@
+{"A": 3768, "B": 35631, "C": 47859, "D": 72030, "target": 35631, "family": "rlve_pan_solar_panels", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-pan-solar-panels-l3-s4/tests/run.py b/tasks/construct-rlve-pan-solar-panels-l3-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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-pan-solar-panels-l3-s4/tests/test.sh b/tasks/construct-rlve-pan-solar-panels-l3-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-pan-solar-panels-l3-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-polynomial-global-minimum-l2-s9/environment/Dockerfile b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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-polynomial-global-minimum-l2-s9/environment/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bced3a97b978494d094d3cc8b89fb57053c12ab1
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [18, 28, 26, 8, 1], "fmin": "8.55166289846733219174765454317744194832562008", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l2-s9/solution/solve.sh b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4b35666c54e52d0fdfdd2961c8b59f4c2e180939
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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'
+{"x0": -0.7865883372377703}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l2-s9/tests/check.py b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3be068f4391ad0838c29a4f7d521b8072cf39991
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/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-l2-s9/tests/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bced3a97b978494d094d3cc8b89fb57053c12ab1
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [18, 28, 26, 8, 1], "fmin": "8.55166289846733219174765454317744194832562008", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l2-s9/tests/run.py b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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-polynomial-global-minimum-l2-s9/tests/test.sh b/tasks/construct-rlve-polynomial-global-minimum-l2-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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-polynomial-global-minimum-l6-s1/environment/Dockerfile b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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-polynomial-global-minimum-l6-s1/environment/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f0cdcc11bddba8d27f5b152f536db18487093e87
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [4101, -24576, 67698, -112980, 127737, -103372, 62140, -28776, 10925, -3762, 1266, -388, 92, -14, 1], "fmin": "59.0039109627281987932410883940007931597765564", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s1/solution/solve.sh b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c7e7006193ed2ea534342a82c1696023286064c9
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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'
+{"x0": 0.756373857798139}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s1/tests/check.py b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3be068f4391ad0838c29a4f7d521b8072cf39991
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/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-l6-s1/tests/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..f0cdcc11bddba8d27f5b152f536db18487093e87
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [4101, -24576, 67698, -112980, 127737, -103372, 62140, -28776, 10925, -3762, 1266, -388, 92, -14, 1], "fmin": "59.0039109627281987932410883940007931597765564", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s1/tests/run.py b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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-polynomial-global-minimum-l6-s1/tests/test.sh b/tasks/construct-rlve-polynomial-global-minimum-l6-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-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-polynomial-global-minimum-l6-s6/environment/Dockerfile b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-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-polynomial-global-minimum-l6-s6/environment/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e02ea8c718f68bbe6858e64d685c1a8edf4ca133
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [9, 4, 400, -344, 3274, -2616, 8093, -5392, 7042, -3574, 2135, -704, 184, -28, 2], "fmin": "8.99004459031947540668898065482177119741379617", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s6/solution/solve.sh b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..37e6235244440d47aca260bdf8d45044f165fba3
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-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'
+{"x0": -0.004966169808665889}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s6/tests/check.py b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3be068f4391ad0838c29a4f7d521b8072cf39991
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/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-l6-s6/tests/instance.json b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e02ea8c718f68bbe6858e64d685c1a8edf4ca133
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [9, 4, 400, -344, 3274, -2616, 8093, -5392, 7042, -3574, 2135, -704, 184, -28, 2], "fmin": "8.99004459031947540668898065482177119741379617", "family": "rlve_polynomial_global_minimum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s6/tests/run.py b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-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-polynomial-global-minimum-l6-s6/tests/test.sh b/tasks/construct-rlve-polynomial-global-minimum-l6-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-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-polynomial-integer-roots-l1-s3/environment/Dockerfile b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l1-s3/environment/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..42e8e8809e1779145145281686524c8706364397
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [2, -1, -2, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l1-s3/solution/solve.sh b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..70ef4ab6e40d5fc34392d47d4cc4651d0162c419
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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'
+{"roots": [-1, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l1-s3/tests/check.py b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d30553cb884c5e03c8afe73ef652efc483ab791
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/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-l1-s3/tests/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..42e8e8809e1779145145281686524c8706364397
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [2, -1, -2, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l1-s3/tests/run.py b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l1-s3/tests/test.sh b/tasks/construct-rlve-polynomial-integer-roots-l1-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l1-s4/environment/Dockerfile b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l1-s4/environment/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..848f97853ce14b3cf7b0d21cb0259f0822a87cc5
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [-18, -3, 4, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l1-s4/solution/solve.sh b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ee2d9d17ee8696d32d91594a8ce6b084a7dcc99a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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'
+{"roots": [-3, -3, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l1-s4/tests/check.py b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d30553cb884c5e03c8afe73ef652efc483ab791
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/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-l1-s4/tests/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..848f97853ce14b3cf7b0d21cb0259f0822a87cc5
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [-18, -3, 4, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l1-s4/tests/run.py b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l1-s4/tests/test.sh b/tasks/construct-rlve-polynomial-integer-roots-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l5-s5/environment/Dockerfile b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l5-s5/environment/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ee3a33b0f8db2c95329a7a173e9901413050b91e
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [-63685440000000, 99845784000000, -30833805600000, -9324970740000, 3798035394000, 367781615600, -162116078040, -8700978866, 3348027901, 122630940, -37541800, -966728, 233898, 3860, -760, -6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l5-s5/solution/solve.sh b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a0afdda4d3d85a606fdc742327a0f6849dec96cd
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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'
+{"roots": [-15, -12, -10, -9, -9, -8, -5, 1, 2, 4, 5, 10, 10, 13, 14, 15]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l5-s5/tests/check.py b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2d30553cb884c5e03c8afe73ef652efc483ab791
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/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-l5-s5/tests/instance.json b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ee3a33b0f8db2c95329a7a173e9901413050b91e
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [-63685440000000, 99845784000000, -30833805600000, -9324970740000, 3798035394000, 367781615600, -162116078040, -8700978866, 3348027901, 122630940, -37541800, -966728, 233898, 3860, -760, -6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l5-s5/tests/run.py b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-integer-roots-l5-s5/tests/test.sh b/tasks/construct-rlve-polynomial-integer-roots-l5-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-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-polynomial-interpolation-l2-s2/environment/Dockerfile b/tasks/construct-rlve-polynomial-interpolation-l2-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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-rlve-polynomial-interpolation-l2-s2/environment/instance.json b/tasks/construct-rlve-polynomial-interpolation-l2-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..32e104e9227336387c4cf83844e930752e492e45
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s2/environment/instance.json
@@ -0,0 +1 @@
+{"X": [-1, 0, -3, -2, 1], "Y": [5, -4, 407, 88, -5], "family": "rlve_polynomial_interpolation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s2/solution/solve.sh b/tasks/construct-rlve-polynomial-interpolation-l2-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6f9baf3bb6c9e69cbd2abb8e7170515fc3001a12
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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'
+{"coeffs": [-4, -2, 0, -3, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s2/tests/check.py b/tasks/construct-rlve-polynomial-interpolation-l2-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..f05264e3fd4584db7cb3768800e4a2497564b4f5
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s2/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-l2-s2/tests/instance.json b/tasks/construct-rlve-polynomial-interpolation-l2-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..32e104e9227336387c4cf83844e930752e492e45
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s2/tests/instance.json
@@ -0,0 +1 @@
+{"X": [-1, 0, -3, -2, 1], "Y": [5, -4, 407, 88, -5], "family": "rlve_polynomial_interpolation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s2/tests/run.py b/tasks/construct-rlve-polynomial-interpolation-l2-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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-rlve-polynomial-interpolation-l2-s2/tests/test.sh b/tasks/construct-rlve-polynomial-interpolation-l2-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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-rlve-polynomial-interpolation-l2-s5/environment/Dockerfile b/tasks/construct-rlve-polynomial-interpolation-l2-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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-rlve-polynomial-interpolation-l2-s5/environment/instance.json b/tasks/construct-rlve-polynomial-interpolation-l2-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7a4c577a280e367877f1da42f75dd4545fd312b2
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s5/environment/instance.json
@@ -0,0 +1 @@
+{"X": [4, 3, 1, -3, 2], "Y": [1012, 344, 4, 116, 76], "family": "rlve_polynomial_interpolation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s5/solution/solve.sh b/tasks/construct-rlve-polynomial-interpolation-l2-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3d9ed5b7ae0a0db492120c269fa6a266e5908659
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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'
+{"coeffs": [-4, 2, -1, 4, 3]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s5/tests/check.py b/tasks/construct-rlve-polynomial-interpolation-l2-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..f05264e3fd4584db7cb3768800e4a2497564b4f5
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s5/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-l2-s5/tests/instance.json b/tasks/construct-rlve-polynomial-interpolation-l2-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7a4c577a280e367877f1da42f75dd4545fd312b2
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s5/tests/instance.json
@@ -0,0 +1 @@
+{"X": [4, 3, 1, -3, 2], "Y": [1012, 344, 4, 116, 76], "family": "rlve_polynomial_interpolation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s5/tests/run.py b/tasks/construct-rlve-polynomial-interpolation-l2-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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-rlve-polynomial-interpolation-l2-s5/tests/test.sh b/tasks/construct-rlve-polynomial-interpolation-l2-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-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-rlve-prefix-product-permutation-l2-s0/environment/Dockerfile b/tasks/construct-rlve-prefix-product-permutation-l2-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-rlve-prefix-product-permutation-l2-s0/environment/instance.json b/tasks/construct-rlve-prefix-product-permutation-l2-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..67af7071d921c8ba862989f6b2f2b5c545e156a5
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 83, "family": "rlve_prefix_product_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s0/solution/solve.sh b/tasks/construct-rlve-prefix-product-permutation-l2-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f09b3535e4b1e563d01c17da98c2c2da3dd38ee7
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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'
+{"perm": [1, 2, 43, 29, 22, 51, 15, 13, 53, 38, 26, 69, 8, 33, 7, 73, 27, 45, 61, 36, 55, 5, 35, 66, 46, 11, 17, 41, 4, 64, 37, 76, 14, 79, 23, 20, 31, 10, 60, 67, 28, 82, 3, 57, 18, 25, 75, 54, 65, 62, 6, 71, 9, 48, 21, 81, 44, 68, 74, 39, 19, 50, 80, 30, 49, 24, 40, 58, 12, 78, 52, 77, 16, 59, 47, 32, 72, 70, 34, 63, 56, 42, 83]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/check.py b/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3d93850acd79cc0f8fff05cdbb0c63aabc484815
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-s0/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(), 1
+    for v in p:
+        acc = acc * v % n
+        if acc in seen:
+            raise Invalid(f"prefix product residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/instance.json b/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..67af7071d921c8ba862989f6b2f2b5c545e156a5
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 83, "family": "rlve_prefix_product_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/run.py b/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-rlve-prefix-product-permutation-l2-s0/tests/test.sh b/tasks/construct-rlve-prefix-product-permutation-l2-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-rlve-prefix-product-permutation-l2-s7/environment/Dockerfile b/tasks/construct-rlve-prefix-product-permutation-l2-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-prefix-product-permutation-l2-s7/environment/instance.json b/tasks/construct-rlve-prefix-product-permutation-l2-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca2ac9852accf3fd8c35a2d8b423b253d68e4257
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 71, "family": "rlve_prefix_product_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s7/solution/solve.sh b/tasks/construct-rlve-prefix-product-permutation-l2-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..151a5dda5ea071ad25f240b360ff3a005a282543
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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'
+{"perm": [1, 2, 37, 25, 19, 58, 13, 62, 10, 9, 65, 14, 7, 12, 67, 20, 41, 47, 5, 16, 33, 45, 43, 35, 4, 55, 42, 51, 34, 50, 46, 56, 21, 29, 24, 70, 3, 49, 44, 52, 17, 27, 23, 39, 22, 31, 18, 69, 38, 30, 28, 40, 57, 68, 26, 32, 53, 6, 61, 66, 59, 8, 64, 63, 11, 60, 15, 54, 48, 36, 71]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/check.py b/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3d93850acd79cc0f8fff05cdbb0c63aabc484815
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-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(), 1
+    for v in p:
+        acc = acc * v % n
+        if acc in seen:
+            raise Invalid(f"prefix product residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/instance.json b/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca2ac9852accf3fd8c35a2d8b423b253d68e4257
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 71, "family": "rlve_prefix_product_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/run.py b/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-prefix-product-permutation-l2-s7/tests/test.sh b/tasks/construct-rlve-prefix-product-permutation-l2-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-prefix-product-permutation-l6-s8/environment/Dockerfile b/tasks/construct-rlve-prefix-product-permutation-l6-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-rlve-prefix-product-permutation-l6-s8/environment/instance.json b/tasks/construct-rlve-prefix-product-permutation-l6-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d9352455711232780c22267dbeeba4dbcee94118
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l6-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 12713, "family": "rlve_prefix_product_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s8/solution/solve.sh b/tasks/construct-rlve-prefix-product-permutation-l6-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5d6a931199545e384362013ad141314719fe6ace
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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'
+{"perm": [1, 2, 6358, 4239, 9536, 7629, 2120, 10898, 11125, 9889, 3815, 4624, 7417, 979, 11806, 11019, 5563, 4488, 4945, 6023, 1908, 7871, 8669, 2212, 3709, 11697, 490, 3297, 12260, 9207, 5510, 4102, 2782, 1542, 8601, 4723, 2473, 1719, 3012, 327, 7311, 8373, 3936, 6801, 4335, 12149, 7463, 542, 1855, 5190, 5849, 9972, 6602, 9116, 1649, 11096, 12487, 6246, 4604, 8620, 9112, 8129, 8408, 6862, 7748, 10367, 7128, 760, 4301, 738, 2362, 9491, 1237, 9231, 860, 12375, 7863, 7926, 164, 10622, 3656, 9575, 4187, 11795, 8325, 3441, 3401, 11545, 2168, 10000, 6075, 3773, 3732, 1368, 6628, 3748, 928, 2098, 8952, 8990, 2925, 8812, 11343, 865, 9658, 1575, 10915, 10813, 825, 3500, 11905, 9049, 6244, 12489, 9480, 8071, 8659, 8585, 10667, 642, 10913, 1577, 4065, 11267, 10561, 9968, 9788, 3905, 10231, 10743, 5184, 10579, 9921, 9942, 6737, 8288, 2151, 8631, 6726, 6952, 7538, 4419, 4746, 8180, 619, 9470, 4616, 10206, 6787, 7680, 6188, 2190, 3932, 11800, 10320, 8449, 6439, 9556, 11668, 7277, 8185, 2133, 4788, 79, 2094, 7937, 5898, 12105, 4163, 3010, 1721, 10558, 1701, 2573, 5773, 3488, 7441, 2874, 11357, 9518, 3038, 7095, 1887, 6948, 8223, 10515, 7041, 8499, 9671, 2288, 8231, 11050, 6821, 9157, 7406, 7694, 10833, 969, 10852, 1662, 1463, 254, 10763, 12213, 5672, 4218, 433, 8722, 11186, 10950, 788, 12473, 5458, 7402, 5407, 1361, 413, 2403, 8107, 11553, 5953, 2302, 4525, 6329, 9479, 12601, 6245, 12658, 11097, 10882, 4036, 11118, 4330, 874, 4293, 7737, 5334, 7779, 6678, 11331, 5457, 12503, 789, 7430, 2033, 6124, 5634, 3398, 5281, 8170, 11341, 8814, 11251, 202, 1953, 9623, 5116, 11972, 5372, 7511, 8949, 3849, 5290, 3143, 4961, 1824, 11328, 3334, 3369, 3451, 10501, 9008, 1076, 5496, 4316, 2220, 9720, 3948, 9833, 8932, 10126, 9909, 2210, 8671, 8730, 1250, 10447, 1197, 310, 8491, 11092, 700, 8665, 11933, 11460, 6810, 3394, 7235, 10197, 1149, 9451, 8237, 7452, 2938, 8323, 11797, 12257, 5550, 11517, 289, 4225, 9035, 3220, 2438, 11135, 9001, 12191, 1926, 3639, 8928, 4093, 3605, 1067, 5590, 8751, 9702, 40, 5405, 7404, 9159, 3969, 2920, 9306, 3017, 6053, 5238, 2082, 1095, 7862, 12639, 861, 3841, 11636, 9823, 851, 2691, 1287, 6156, 2887, 3243, 8101, 7100, 3721, 5079, 7794, 1899, 5679, 8690, 11116, 4038, 7876, 7009, 3548, 4764, 944, 1847, 9831, 3950, 4112, 7994, 5258, 12200, 3521, 410, 4250, 7561, 4836, 2665, 7501, 11171, 4116, 5540, 11882, 9793, 3411, 1586, 4579, 12057, 10060, 5230, 10204, 4618, 5417, 3527, 485, 9753, 11783, 1410, 7188, 11790, 732, 7800, 6484, 6184, 5382, 7001, 6107, 9403, 9193, 374, 8466, 11353, 217, 10313, 10718, 7445, 11950, 2318, 11832, 8891, 6751, 2145, 6237, 9949, 9086, 689, 10058, 12059, 2704, 6965, 681, 8496, 207, 3994, 1202, 7395, 4054, 4132, 5777, 3534, 2977, 11878, 7508, 4650, 2263, 7086, 3165, 11036, 4740, 3427, 6301, 5385, 3123, 9206, 12686, 3298, 5549, 12408, 11798, 3934, 8375, 11997, 11916, 5218, 8522, 2817, 6794, 6235, 2147, 7374, 3869, 3186, 9024, 9865, 3890, 3293, 9696, 6664, 5666, 8149, 2729, 2089, 6252, 9187, 395, 2963, 10072, 7728, 1017, 27, 9419, 8157, 9174, 2786, 8056, 6884, 2641, 4989, 10442, 11058, 5671, 12511, 10764, 9858, 5626, 9391, 6458, 1004, 977, 7419, 4812, 6768, 8915, 3520, 12343, 5259, 9043, 9296, 3756, 5096, 4475, 4198, 1925, 12398, 9002, 5401, 1572, 5477, 2481, 6730, 7269, 9434, 12021, 645, 8024, 4706, 1685, 7411, 1726, 12030, 5251, 48, 10861, 10841, 6895, 5786, 9105, 675, 8515, 10792, 7467, 9853, 11217, 10599, 8331, 11981, 4917, 2466, 10823, 1502, 11420, 11309, 4955, 8243, 7462, 12669, 4336, 5001, 10722, 8737, 6982, 2695, 5224, 3684, 599, 1615, 6512, 7360, 4246, 3053, 11903, 3502, 6707, 7764, 4333, 6803, 5967, 5567, 12087, 7577, 9762, 8799, 8054, 2788, 3618, 7757, 5099, 9030, 575, 11101, 4726, 10641, 4119, 4323, 10083, 7944, 7826, 2619, 4162, 12547, 5899, 7866, 6129, 6596, 9132, 9882, 5759, 4534, 145, 3246, 2113, 2908, 4518, 8694, 7967, 4537, 7576, 12126, 5568, 4589, 4501, 10800, 6096, 8396, 7320, 5867, 1820, 2356, 10821, 2468, 2047, 120, 1803, 693, 534, 4692, 9152, 11594, 4376, 3096, 11208, 9277, 6377, 8684, 2703, 12287, 10059, 12327, 4580, 10264, 1985, 7348, 7817, 768, 11010, 9617, 1509, 954, 3027, 6348, 8976, 8830, 7398, 3609, 548, 4201, 10288, 3137, 6320, 5749, 431, 4220, 1921, 5250, 12175, 1727, 4912, 3628, 426, 2658, 1346, 10911, 644, 12182, 9435, 9019, 1444, 10963, 1622, 292, 4051, 8833, 9907, 10128, 1861, 11055, 2540, 4892, 10254, 4412, 950, 11069, 2840, 2943, 10702, 6722, 11915, 12253, 8376, 5164, 10295, 7389, 3505, 8406, 8131, 6980, 8739, 7363, 6829, 6715, 924, 401, 4916, 12159, 8332, 2042, 8413, 70, 10354, 9239, 8986, 5371, 12457, 5117, 1761, 6622, 6562, 2724, 8482, 6994, 3781, 2591, 8775, 11414, 1333, 5524, 3751, 7743, 5586, 68, 8415, 8571, 9127, 2317, 12298, 7446, 4897, 664, 1706, 6746, 7150, 8229, 2290, 7813, 6029, 11861, 11387, 6742, 8972, 9140, 11459, 12421, 8666, 9759, 2709, 1912, 1764, 211, 243, 5286, 4877, 1785, 5892, 3560, 7062, 9084, 9951, 5217, 12252, 11998, 6723, 1112, 10257, 5463, 9599, 2970, 9449, 1151, 9048, 12604, 3501, 12134, 3054, 7241, 4702, 10187, 4597, 1028, 6544, 10308, 10590, 6613, 5677, 1901, 109, 9216, 5157, 5243, 11716, 5077, 3723, 9792, 12332, 5541, 7516, 7507, 12273, 2978, 4446, 11820, 3376, 5579, 1073, 11779, 3119, 5688, 4975, 11123, 10900, 2891, 345, 10025, 11386, 11939, 6030, 4655, 7709, 7611, 3483, 75, 341, 8875, 10605, 1371, 104, 3058, 8354, 2831, 6958, 3278, 3698, 4949, 8384, 234, 8423, 3241, 2889, 10902, 8124, 8216, 1489, 8890, 12296, 2319, 10111, 10746, 8682, 6379, 1132, 4191, 9900, 6650, 1583, 3375, 11875, 4447, 8727, 8859, 1714, 8910, 3151, 1285, 2693, 6984, 1562, 6505, 10960, 11018, 12700, 980, 8006, 2792, 2775, 10319, 12561, 3933, 12256, 12409, 8324, 12631, 4188, 10326, 5999, 731, 12315, 7189, 8966, 97, 10618, 1780, 1409, 12318, 9754, 7250, 3118, 11871, 1074, 9010, 10044, 5051, 1935, 2676, 7950, 365, 10869, 3001, 4933, 4713, 8302, 711, 1647, 9118, 11205, 668, 9689, 7296, 9190, 11452, 4075, 3050, 1365, 11616, 1045, 5440, 9483, 9460, 4594, 1881, 198, 1864, 1482, 10030, 11393, 994, 10221, 11710, 509, 5297, 14, 910, 4710, 6040, 4079, 3661, 10944, 10365, 7750, 11529, 10385, 8035, 9799, 9648, 1321, 974, 2495, 7961, 11578, 5076, 11886, 5244, 2836, 8434, 6256, 508, 11739, 10222, 11286, 8510, 9170, 6389, 4696, 8841, 9586, 8560, 6859, 4986, 489, 12689, 3710, 2596, 8763, 8605, 9741, 1281, 4458, 3387, 8117, 818, 6172, 3275, 2630, 4773, 4522, 2327, 11005, 9373, 8235, 9453, 8905, 2803, 2238, 10528, 8456, 1098, 963, 7276, 12556, 9557, 10858, 7527, 2701, 8686, 7143, 6605, 2739, 5038, 1241, 3946, 9722, 10169, 3635, 8700, 11074, 5323, 6011, 9109, 323, 7126, 10369, 7850, 8710, 7135, 843, 937, 3706, 273, 7220, 9822, 12372, 3842, 2626, 1130, 6381, 2337, 5431, 3024, 5421, 9603, 3448, 10064, 9250, 6911, 4553, 10632, 338, 4854, 4258, 1044, 11753, 1366, 3734, 5555, 4927, 8922, 5609, 8089, 5300, 6903, 4166, 4082, 5991, 802, 2459, 8305, 7590, 11437, 5412, 3791, 7108, 4375, 12067, 9153, 5655, 2367, 2478, 2521, 4122, 5754, 10088, 1082, 6335, 889, 8525, 2391, 2501, 5075, 11718, 7962, 4369, 11263, 9848, 10909, 1348, 6085, 8969, 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10613, 1352, 1215, 6144, 1378, 5030, 10458, 6164, 3172, 8647, 9654, 11489, 3066, 993, 11742, 10031, 3960, 3909, 10536, 6741, 11938, 11862, 10026, 4809, 1300, 755, 7192, 6834, 10838, 1514, 8844, 9531, 5935, 10845, 7917, 10772, 8104, 10056, 691, 1805, 1143, 6631, 3846, 2101, 1309, 11501, 10271, 1569, 4345, 9517, 12536, 2875, 7307, 216, 12303, 8467, 9664, 961, 1100, 8982, 94, 6088, 2109, 864, 12612, 8813, 12464, 8171, 5530, 6570, 1312, 7686, 9220, 7030, 10431, 5456, 12475, 6679, 3333, 12448, 1825, 4718, 1740, 4510, 9634, 7079, 9319, 5482, 9415, 7168, 8446, 6503, 1564, 2026, 2079, 4417, 7540, 4954, 12153, 11421, 10934, 931, 398, 5528, 8173, 7627, 9538, 8803, 1735, 11484, 2226, 8563, 3289, 6832, 7194, 5535, 8792, 7777, 5336, 1472, 8509, 11708, 10223, 9718, 2222, 5958, 10434, 6127, 7868, 10545, 2717, 8939, 9242, 5148, 7897, 3695, 697, 1753, 1699, 10560, 12591, 4066, 3063, 9847, 11575, 4370, 8488, 3682, 5226, 3415, 6580, 3358, 4776, 6819, 11052, 201, 12462, 8815, 4930, 6080, 8485, 10523, 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8053, 12123, 9763, 9582, 3567, 10573, 10713, 7776, 11291, 5536, 4689, 8011, 2530, 8881, 7377, 11245, 10524, 153, 916, 460, 4341, 43, 5915, 4638, 11413, 11962, 2592, 8443, 6293, 7810, 11473, 1058, 2994, 278, 2883, 368, 8604, 11694, 2597, 7340, 8068, 5443, 8366, 9498, 2683, 1324, 8807, 1548, 9701, 12390, 5591, 5798, 7582, 3555, 331, 9796, 9041, 5261, 9779, 4244, 7362, 11988, 6981, 12145, 10723, 3982, 1991, 3980, 10725, 1249, 12430, 8672, 8858, 11818, 4448, 5744, 10079, 11185, 12507, 434, 11514, 4943, 4490, 2202, 9938, 2398, 3888, 9867, 10754, 7134, 11644, 7851, 11086, 10785, 4743, 10694, 9680, 11424, 3306, 11073, 11653, 3636, 9292, 1979, 7351, 7966, 12091, 4519, 3361, 11115, 12357, 5680, 7829, 7142, 11663, 2702, 12061, 6378, 11828, 10747, 1832, 231, 1598, 360, 4840, 10133, 4353, 8857, 8729, 12431, 2211, 12692, 7872, 9758, 11932, 12422, 701, 3883, 5319, 437, 8584, 12598, 8072, 5560, 2053, 7662, 10782, 3623, 8999, 11137, 123, 1449, 9653, 11398, 3173, 6056, 8569, 8417, 10463, 1262, 959, 9666, 3828, 6674, 983, 9055, 8548, 1110, 6725, 12577, 2152, 2749, 2823, 3348, 2436, 3222, 11480, 3786, 321, 9111, 12655, 4605, 10650, 6719, 11470, 2293, 7204, 32, 9934, 9284, 2030, 3866, 8884, 9179, 9740, 11693, 8764, 369, 4722, 12680, 1543, 381, 7176, 2073, 603, 8393, 10193, 1127, 6962, 10164, 1194, 1844, 9716, 10225, 10666, 12597, 8660, 438, 6939, 4738, 11038, 3592, 2752, 3074, 9270, 2535, 2344, 4867, 9126, 11953, 8416, 8644, 6057, 9489, 2364, 4159, 3288, 11296, 2227, 6858, 11701, 9587, 7058, 10350, 4150, 9428, 10095, 609, 169, 9706, 5811, 1109, 8634, 9056, 5293, 11418, 1504, 8328, 9810, 3212, 4993, 9130, 6598, 7056, 9589, 3107, 4998, 7554, 1828, 6435, 6318, 3139, 83, 921, 2390, 11582, 890, 2816, 12250, 5219, 6406, 7450, 8239, 522, 10791, 12166, 676, 2428, 5704, 9169, 11707, 11287, 1473, 1521, 8143, 2514, 2758, 1749, 1652, 10137, 9670, 12527, 7042, 206, 12283, 682, 10795, 7883, 11091, 12425, 311, 3681, 11261, 4371, 10522, 11247, 6081, 6993, 11966, 2725, 11558, 4768, 2543, 6356, 4, 3180, 7266, 11443, 2935, 3974, 5354, 579, 9663, 11352, 12304, 375, 5155, 9218, 7688, 9674, 2855, 7091, 7860, 1097, 11672, 10529, 2278, 7084, 2265, 10874, 6438, 12559, 10321, 6502, 11317, 7169, 6292, 8773, 2593, 7317, 10498, 6017, 11498, 6573, 4729, 6255, 11713, 2837, 4398, 6451, 8141, 1523, 2982, 7646, 6568, 5532, 3240, 11840, 235, 4979, 9028, 5101, 10462, 8643, 8570, 11954, 69, 11978, 2043, 7071, 4984, 6861, 12652, 8130, 11991, 3506, 7207, 5144, 6272, 6020, 7218, 275, 10496, 7319, 12081, 6097, 10192, 8595, 604, 2633, 9818, 3155, 5470, 10105, 1596, 233, 11842, 4950, 585, 5913, 45, 567, 7715, 5163, 11996, 12254, 3935, 12673, 7312, 11145, 1356, 3199, 3678, 9497, 8758, 5444, 3283, 2581, 4041, 3859, 9727, 11161, 5695, 7920, 8312, 2830, 11848, 3059, 1228, 1793, 8085, 10218, 4756, 4752, 1139, 1453, 4228, 2194, 5837, 5606, 1120, 649, 9620, 10068, 6433, 1830, 10749, 2041, 11980, 12160, 10600, 9809, 8543, 1505, 3440, 12630, 11796, 12410, 2939, 7667, 9407, 1644, 9877, 4283, 6265, 1183, 10469, 2829, 8356, 7921, 7746, 6864, 2745, 2929, 7589, 11601, 2460, 710, 11766, 4714, 7475, 10635, 1403, 5176, 142, 7970, 2023, 9686, 6369, 2036, 4504, 2150, 12579, 6738, 8083, 1795, 9365, 10281, 10577, 5186, 10016, 11447, 10556, 1723, 6495, 4821, 7855, 4982, 7073, 4562, 9736, 839, 896, 3989, 6972, 9245, 7066, 6139, 2077, 2028, 9286, 6416, 11433, 1025, 9329, 7602, 2860, 1500, 10825, 5436, 4532, 5761, 5179, 1276, 7305, 2877, 7461, 12151, 4956, 7618, 521, 8518, 7451, 12413, 9452, 11678, 9374, 2770, 11049, 12524, 2289, 11943, 7151, 18, 7771, 3997, 10514, 12530, 6949, 1976, 7523, 6868, 10155, 1488, 11835, 8125, 631, 1916, 10678, 4425, 10566, 5343, 8908, 1716, 10974, 1391, 3082, 6342, 5701, 2756, 2516, 11568, 9806, 623, 4022, 9355, 7941, 1033, 10389, 10412, 223, 6387, 9172, 8159, 2132, 12554, 7278, 4465, 6955, 618, 12571, 4747, 626, 5140, 3853, 4684, 7626, 11303, 5529, 11340, 12465, 5282, 8852, 6426, 11526, 9352, 1602, 5803, 1093, 2084, 2131, 8187, 9173, 12223, 9420, 3021, 5641, 4444, 2980, 1525, 2728, 12235, 5667, 5727, 3516, 7483, 2513, 8506, 1522, 8430, 6452, 3330, 2243, 11128, 387, 659, 2452, 7888, 6979, 11990, 8407, 12653, 9113, 7146, 630, 8215, 11836, 10903, 3254, 967, 10835, 2527, 817, 11688, 3388, 3578, 3381, 2322, 6468, 59, 4096, 2066, 11552, 12496, 2404, 10055, 11371, 10773, 7099, 12364, 3244, 147, 2510, 392, 7299, 1479, 7549, 2422, 8899, 12, 5299, 11609, 5610, 6499, 10217, 8350, 1794, 8286, 6739, 10538, 6566, 7648, 6799, 3938, 1303, 6178, 4667, 5559, 8658, 12599, 9481, 5442, 8760, 7341, 5206, 444, 10453, 3169, 6874, 6684, 856, 5007, 10374, 6883, 12220, 2787, 12122, 8800, 7481, 3518, 8917, 6536, 4641, 7157, 3615, 11034, 3167, 10455, 6899, 6669, 3643, 2375, 9514, 9039, 9798, 11725, 10386, 1712, 8861, 4540, 5090, 6888, 2071, 7178, 3925, 4705, 12180, 646, 3564, 1518, 6325, 1011, 3875, 10343, 5865, 7322, 5473, 815, 2529, 8789, 4690, 536, 11031, 2791, 11804, 981, 6676, 7781, 948, 4414, 5241, 5159, 10889, 1389, 10976, 5257, 12345, 4113, 36, 10243, 1613, 601, 2075, 6141, 4279, 6461, 3530, 7122, 6919, 7675, 11476, 3486, 5775, 4134, 1678, 449, 9289, 1929, 4009, 2022, 8295, 143, 4536, 12090, 8695, 7352, 7958, 4368, 11577, 11719, 2496, 4367, 7964, 7353, 2713, 6642, 7327, 9224, 9166, 364, 11772, 2677, 1156, 4236, 10173, 7825, 12109, 10084, 1032, 8194, 9356, 1460, 5897, 12549, 2095, 10937, 6924, 2567, 5108, 3459, 3251, 9919, 10581, 163, 12637, 7864, 5901, 5584, 7745, 8311, 8357, 5696, 10771, 11373, 10846, 1609, 5359, 2175, 6151, 9993, 6466, 2324, 2305, 2688, 1331, 11416, 5295, 511, 5948, 2056, 3273, 6174, 3694, 11273, 5149, 6219, 4440, 4861, 7623, 5829, 10076, 6978, 8133, 2453, 10984, 9568, 11090, 8493, 10796, 5062, 5153, 377, 10051, 7008, 12354, 4039, 2583, 9757, 8668, 12693, 1909, 10544, 11279, 6128, 12103, 5900, 7925, 12638, 12376, 1096, 8458, 7092, 9863, 9026, 4981, 8274, 4822, 5093, 11085, 8709, 11645, 10370, 4142, 3590, 11040, 7069, 2045, 2470, 11104, 7358, 6514, 7428, 791, 10931, 9683, 1567, 10273, 7833, 10274, 6653, 7141, 8688, 5681, 2618, 12108, 7945, 10174, 708, 2462, 5491, 4908, 5268, 767, 12052, 7349, 1981, 6028, 11941, 2291, 11472, 8771, 6294, 7223, 4895, 7448, 6408, 10987, 687, 9088, 6483, 12313, 733, 557, 10250, 2206, 1898, 12360, 5080, 2447, 2901, 3613, 7159, 1103, 3794, 3899, 1466, 6636, 9713, 947, 8003, 6677, 12477, 5335, 11290, 8793, 10714, 7163, 1200, 3996, 8226, 19, 6693, 5499, 9016, 872, 4332, 12131, 6708, 5174, 1405, 563, 4473, 5098, 12119, 3619, 9571, 265, 10892, 9350, 11528, 11728, 10366, 12650, 6863, 8310, 7922, 5585, 11957, 3752, 7026, 847, 1593, 5333, 12479, 4294, 3688, 4859, 4442, 5643, 4305, 5855, 1016, 12227, 10073, 498, 2274, 2378, 9502, 4175, 3586, 10400, 11220, 9607, 4181, 5162, 8378, 568, 1994, 3821, 6806, 7610, 11858, 4656, 2342, 2537, 10445, 1252, 2571, 1703, 3100, 9750, 2645, 6284, 6227, 2309, 10832, 12519, 7407, 2616, 5683, 2286, 9673, 8462, 9219, 11336, 1313, 2258, 5818, 6931, 6187, 12565, 6788, 9975, 1056, 11475, 7981, 6920, 1209, 10654, 1206, 10554, 11449, 9406, 8321, 2940, 2670, 940, 10781, 8655, 2054, 5950, 1769, 2352, 3337, 1964, 10676, 1918, 4834, 7563, 5613, 8996, 6798, 8079, 6567, 8427, 2983, 11543, 3403, 2505, 10213, 1136, 998, 830, 8993, 354, 4922, 10269, 11503, 10330, 2312, 2119, 12709, 9537, 11302, 8174, 4685, 5828, 7892, 4862, 1631, 8958, 520, 8241, 4957, 597, 3686, 4296, 2254, 3482, 11857, 7710, 6807, 10147, 4783, 9257, 3206, 1949, 2859, 8255, 9330, 3091, 257, 744, 10955, 10466, 2333, 3435, 9447, 2972, 11436, 11600, 8306, 2930, 3894, 1605, 6909, 9252, 3554, 8748, 5799, 10161, 2707, 9761, 12125, 12088, 4538, 8863, 6517, 5507, 4312, 6444, 5741, 3472, 1441, 4819, 6497, 5612, 7652, 4835, 12339, 4251, 3498, 827, 7473, 4716, 1827, 8533, 4999, 4338, 720, 2421, 8094, 1480, 1866, 2734, 6312, 7287, 9395, 6006, 4953, 11311, 4418, 12574, 6953, 4467, 11440, 6733, 2602, 1971, 131, 2137, 4434, 2700, 11665, 10859, 50, 6867, 8220, 1977, 9294, 9045, 3104, 3512, 7506, 11880, 5542, 2991, 2548, 8948, 12455, 5373, 4649, 12272, 11879, 7517, 3513, 1692, 10228, 11170, 12336, 2666, 2763, 798, 464, 4194, 6310, 2736, 3315, 10019, 573, 9032, 1456, 9301, 9343, 2654, 390, 2512, 8145, 3517, 8052, 8801, 9540, 6661, 336, 10634, 8300, 4715, 7557, 828, 1000, 9880, 9134, 9852, 12164, 10793, 684, 541, 12668, 12150, 8244, 2878, 1738, 4720, 371, 516, 3673, 3972, 2937, 12412, 8238, 8519, 6407, 7806, 4896, 11949, 12299, 10719, 8896, 2873, 12538, 3489, 3551, 10302, 2533, 9272, 9316, 249, 4546, 3864, 2032, 12471, 790, 7839, 6515, 8865, 263, 9573, 3658, 4169, 1298, 4811, 12205, 978, 12702, 4625, 1107, 5813, 6493, 1725, 12177, 1686, 6826, 2615, 7693, 12520, 9158, 12386, 5406, 12501, 5459, 6702, 3608, 12042, 8831, 4053, 12279, 1203, 1640, 1064, 6705, 3504, 11993, 10296, 10306, 6546, 3088, 2608, 11121, 4977, 237, 4937, 1426, 11244, 8786, 8882, 3868, 12245, 2148, 4506, 3808, 9914, 6656, 3228, 6071, 5390, 2613, 6828, 11987, 8740, 4245, 12137, 6513, 7841, 11105, 4801, 10541, 2712, 7957, 7965, 8696, 1980, 7816, 12053, 1986, 5872, 3728, 742, 259, 5205, 8067, 8761, 2598, 5693, 11163, 5932, 5782, 6530, 405, 5715, 6413, 452, 9593, 9223, 7954, 6643, 5349, 10103, 5472, 8015, 5866, 12080, 8397, 10497, 8441, 2594, 3712, 526, 11144, 8372, 12674, 328, 5312, 215, 11355, 2876, 8246, 1277, 1117, 8925, 1180, 1478, 8096, 393, 9189, 11759, 9690, 1087, 3113, 2681, 9500, 2380, 10776, 9394, 7544, 6313, 10377, 1085, 9692, 7076, 6946, 1889, 4464, 8184, 12555, 11669, 964, 3233, 4646, 3956, 4350, 9433, 12184, 6731, 11442, 8474, 3181, 6936, 9183, 5595, 6755, 2283, 1383, 241, 213, 5314, 6014, 3454, 2457, 804, 3117, 11781, 9755, 2585, 10856, 9559, 4327, 2611, 5392, 4701, 11901, 3055, 11142, 528, 10235, 10196, 12417, 3395, 1395, 3301, 5517, 6332, 10380, 9282, 9936, 2204, 10252, 4894, 7808, 6295, 9821, 11638, 274, 8400, 6021, 4947, 3700, 10918, 3352, 2069, 6890, 11178, 6197, 5143, 8404, 3507, 31, 8614, 2294, 11457, 9142, 2106, 9413, 5484, 6384, 3238, 5534, 11293, 6833, 11381, 756, 8965, 11789, 12316, 1411, 4543, 1376, 6146, 4290, 9476, 5520, 1423, 3924, 8027, 2072, 8598, 382, 834, 5200, 9725, 3861, 6291, 8445, 11318, 9416, 457, 308, 1199, 7774, 10715, 8980, 1102, 7789, 3614, 8047, 4642, 4058, 10663, 1695, 17, 8228, 11944, 6747, 588, 629, 8127, 9114, 6604, 11662, 8687, 7830, 6654, 9916, 10906, 9338, 842, 11643, 8711, 10755, 6813, 4792, 4971, 759, 12648, 10368, 11647, 324, 3965, 6918, 7983, 3531, 5453, 5961, 3570, 2947, 3328, 6454, 10042, 9012, 1905, 6522, 6877, 4374, 11596, 3792, 1105, 4627, 6217, 5151, 5064, 3720, 12363, 8102, 10774, 2382, 1886, 12533, 3039, 9862, 7859, 8459, 2856, 505, 3325, 3164, 12269, 2264, 8453, 2279, 6590, 247, 9318, 11322, 9635, 6945, 7282, 9693, 4561, 8272, 4983, 8411, 2044, 7845, 11041, 6138, 8264, 9246, 6353, 9083, 11920, 3561, 1123, 10349, 8558, 9588, 8537, 6599, 6791, 6161, 9236, 9066, 6050, 479, 4567, 6989, 10092, 1656, 501, 205, 8498, 12528, 10516, 6101, 823, 10815, 357, 4026, 4887, 10098, 5024, 10430, 11334, 9221, 9595, 846, 7741, 3753, 11045, 10116, 5377, 1553, 4357, 4796, 1945, 6584, 6121, 6372, 4513, 9960, 10286, 4203, 3547, 12353, 7877, 10052, 2128, 9710, 2813, 6067, 6106, 12309, 5383, 6303, 8913, 6770, 2231, 3780, 11965, 8483, 6082, 8871, 10091, 7047, 4568, 9200, 11025, 1561, 11811, 2694, 12144, 8738, 11989, 8132, 7889, 10077, 5746, 6270, 5146, 9244, 8266, 3990, 2637, 5739, 6446, 6394, 680, 12285, 2705, 10163, 8592, 1128, 2628, 3277, 11846, 2832, 617, 8182, 4466, 7537, 12575, 6727, 1975, 8222, 12531, 1888, 7281, 7077, 9636, 10141, 175, 9228, 4737, 8582, 439, 9182, 7264, 3182, 6782, 5380, 6186, 7682, 5819, 546, 3611, 2903, 9505, 2566, 7934, 10938, 10552, 1208, 7674, 7982, 7123, 3966, 5134, 2555, 8819, 11112, 4552, 11623, 9251, 7585, 1606, 9984, 10628, 3008, 4165, 11607, 5301, 6223, 6668, 8042, 10456, 5032, 5785, 12170, 10842, 11159, 9729, 11177, 7211, 2070, 8029, 5091, 4824, 2640, 12219, 8057, 10375, 6315, 10877, 10520, 4373, 7110, 6523, 6683, 8062, 3170, 6166, 11080, 5942, 10154, 8219, 7524, 51, 2744, 8309, 7747, 12651, 8409, 4985, 11700, 8561, 2228, 2564, 9507, 10768, 6133, 9359, 2371, 4699, 5394, 636, 10896, 2122, 2009, 10728, 5369, 8988, 8954, 6509, 1836, 2197, 6616, 2525, 10837, 11380, 7193, 11294, 3290, 6714, 11986, 7364, 2614, 7409, 1687, 10929, 793, 9156, 12522, 11051, 11254, 4777, 167, 611, 4850, 4791, 7132, 10756, 3393, 12419, 11461, 10146, 7609, 7711, 3822, 5966, 12129, 4334, 12671, 3937, 8078, 7649, 8997, 3625, 6234, 12248, 2818, 6160, 7054, 6600, 9974, 7679, 12566, 10207, 3406, 1551, 5379, 6934, 3183, 1340, 1871, 1558, 1789, 6760, 10415, 1634, 5845, 2562, 2230, 6997, 8914, 12203, 4813, 10660, 5055, 10947, 1161, 221, 10414, 6776, 1790, 10492, 1433, 2282, 7261, 5596, 9146, 2144, 12294, 8892, 5911, 587, 7149, 11945, 1707, 9803, 8971, 11937, 11388, 10537, 8082, 8287, 12580, 9943, 1668, 2601, 7534, 11441, 7268, 12185, 2482, 1974, 6951, 12576, 8632, 1111, 11914, 11999, 10703, 11469, 8617, 10651, 2388, 923, 11985, 6830, 3291, 3892, 2932, 3319, 5173, 7763, 12132, 3503, 7391, 1065, 3607, 7400, 5460, 9262, 2216, 4276, 1218, 6442, 4314, 5498, 7769, 20, 10808, 6195, 11180, 10733, 4901, 775, 855, 8061, 6875, 6524, 2241, 3332, 11330, 12476, 7780, 8004, 982, 8637, 3829, 3538, 1177, 3642, 8041, 6900, 6224, 3648, 5665, 12237, 9697, 335, 7478, 9541, 4070, 4147, 3227, 7369, 9915, 7140, 7831, 10275, 1582, 11823, 9901, 5712, 6610, 10709, 9486, 5348, 7326, 7955, 2714, 91, 8943, 2811, 9712, 7784, 1467, 4231, 5723, 3845, 11366, 1144, 3747, 12620, 1369, 10607, 3304, 11426, 6561, 11969, 1762, 1914, 633, 4320, 2524, 6837, 2198, 5676, 11893, 10591, 10708, 6647, 5713, 407, 3313, 2738, 11661, 7144, 9115, 12662, 9973, 6790, 7055, 8538, 9131, 12101, 6130, 5699, 6344, 10681, 246, 7082, 2280, 1435, 4848, 613, 6120, 7017, 1946, 5862, 3357, 11257, 3416, 1673, 5648, 4452, 10639, 4728, 8437, 11499, 1311, 11338, 5531, 8426, 7647, 8080, 10539, 4803, 2723, 11968, 6623, 11427, 348, 9829, 1849, 9896, 5923, 5662, 3480, 2256, 1315, 9544, 5843, 1636, 3087, 7386, 10307, 11896, 1029, 9441, 4816, 9022, 3188, 11411, 4640, 8049, 8918, 2558, 11229, 6230, 404, 7334, 5783, 5034, 151, 10526, 2240, 6682, 6876, 7111, 1906, 6025, 1536, 5506, 7573, 8864, 7427, 7840, 7359, 12138, 1616, 1835, 6840, 8955, 10418, 10959, 11809, 1563, 11316, 8447, 10322, 10216, 8087, 5611, 7565, 4820, 8276, 1724, 7413, 5814, 6048, 9068, 6430, 5018, 10407, 1485, 6183, 12312, 7801, 9089, 5920, 468, 10569, 423, 2767, 9871, 9955, 10968, 3193, 3665, 113, 227, 58, 8112, 2323, 7910, 9994, 10625, 483, 3529, 7985, 4280, 1003, 12208, 9392, 10778, 10041, 7115, 3329, 8140, 8431, 4399, 11533, 11239, 6393, 6968, 5740, 7570, 4313, 6696, 1219, 9555, 12558, 8450, 10875, 6317, 8531, 1829, 8336, 10069, 5017, 6489, 9069, 3878, 11525, 8167, 8853, 5545, 4271, 3943, 4906, 5493, 2895, 9562, 11432, 8259, 9287, 451, 7331, 5716, 3803, 9566, 10986, 7805, 7449, 8520, 5220, 9980, 5170, 5429, 2339, 5834, 1839, 6279, 4185, 9577, 679, 6967, 6447, 11240, 11196, 4695, 11705, 9171, 8189, 224, 3237, 7197, 5485, 2336, 11632, 1131, 11827, 8683, 12062, 9278, 3270, 9632, 4512, 7015, 6122, 2035, 8292, 9687, 670, 3740, 3391, 10758, 3468, 5651, 3633, 10171, 4238, 12712, 3, 8477, 2544, 9082, 7064, 9247, 1957, 9324, 8975, 12045, 3028, 4423, 10680, 6593, 5700, 8203, 3083, 9445, 3437, 653, 4032, 888, 11584, 1083, 10379, 7230, 5518, 9478, 12491, 4526, 3544, 1010, 8020, 1519, 1475, 6268, 5748, 12036, 3138, 8530, 6436, 10876, 6881, 10376, 7286, 7545, 2735, 7495, 4195, 5266, 4910, 1729, 3149, 8912, 6999, 5384, 12264, 3428, 4456, 1283, 3153, 9820, 7222, 7809, 8772, 8444, 7170, 3862, 4548, 1190, 8837, 3646, 6226, 7698, 2646, 4379, 10886, 4184, 6398, 1840, 4265, 157, 3160, 11496, 6019, 8402, 5145, 6975, 5747, 6322, 1476, 1182, 8316, 4284, 4575, 9386, 5600, 2674, 1937, 3323, 507, 11712, 8435, 4730, 9186, 12232, 2090, 2721, 4805, 10392, 4603, 12657, 12488, 12602, 9050, 9522, 1747, 2760, 2844, 9948, 12292, 2146, 12247, 6795, 3626, 4914, 403, 6532, 11230, 2308, 7697, 6285, 3647, 6667, 6901, 5302, 10991, 4439, 7895, 5150, 7104, 4628, 2499, 2393, 4268, 1399, 11152, 906, 1756, 2297, 3760, 5875, 10880, 11099, 577, 5356, 4875, 5288, 3851, 5142, 7209, 11179, 6690, 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5235, 3176, 1415, 10981, 10535, 11390, 3961, 11168, 10230, 12587, 9789, 102, 1373, 252, 1465, 7786, 3795, 10159, 5801, 1604, 7587, 2931, 6712, 3292, 12240, 9866, 8714, 2399, 3738, 672, 5318, 8663, 702, 2809, 8945, 11524, 6428, 9070, 10342, 8018, 1012, 3130, 11200, 1338, 3185, 12244, 7375, 8883, 8609, 2031, 7432, 4547, 6290, 7171, 9726, 8361, 4042, 3987, 898, 11002, 4683, 8176, 5141, 6199, 5289, 12453, 8950, 2100, 11365, 6632, 5724, 2625, 11635, 12373, 862, 2111, 3248, 2417, 2411, 10184, 3928, 5339, 8848, 4107, 3537, 6673, 8638, 9667, 11225, 882, 420, 5965, 6805, 7712, 1995, 5272, 9843, 10292, 4623, 12704, 9890, 9369, 3070, 3261, 1039, 9913, 7371, 4507, 11000, 900, 9565, 6411, 5717, 5946, 513, 9196, 4665, 6180, 10158, 3898, 7787, 1104, 7107, 11597, 5413, 11536, 9075, 320, 8623, 11481, 2881, 280, 2590, 11964, 6995, 2232, 3653, 9997, 1439, 3474, 3731, 12623, 6076, 9905, 8835, 1192, 10166, 5203, 261, 8867, 10616, 99, 3726, 5874, 6207, 2298, 11083, 5095, 12196, 9297, 11044, 7025, 7742, 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5194, 3671, 518, 8960, 1672, 6579, 11258, 5227, 3373, 1585, 12330, 9794, 333, 9699, 1550, 6785, 10208, 2504, 7643, 11544, 12628, 3442, 5280, 12467, 5635, 1394, 7234, 12418, 6811, 10757, 6365, 3741, 3577, 8116, 11689, 4459, 5114, 9625, 10109, 2321, 8114, 3579, 2865, 1808, 5578, 11874, 11821, 1584, 3413, 5228, 10062, 3450, 12446, 3335, 2354, 1822, 4963, 1188, 4550, 11114, 8692, 4520, 4775, 11256, 6581, 5863, 10345, 11550, 2068, 7213, 10919, 4431, 2435, 8627, 2824, 8902, 9646, 9801, 1709, 1036, 4481, 9946, 2846, 1963, 7657, 2353, 3368, 12447, 11329, 6680, 2242, 8139, 6453, 7116, 2948, 3163, 7088, 506, 6258, 1938, 5427, 5172, 6710, 2933, 11445, 10018, 7493, 2737, 6607, 408, 3523, 1265, 5047, 4395, 11072, 8702, 11425, 6625, 10608, 5516, 7232, 1396, 5548, 12259, 12687, 491, 4559, 9695, 12239, 3891, 6713, 6831, 11295, 8564, 4160, 2621, 11061, 2580, 8364, 5445, 532, 695, 3697, 11845, 6959, 2629, 11685, 6173, 7900, 2057, 9631, 6375, 9279, 5122, 9744, 807, 11565, 301, 4479, 1038, 3811, 3071, 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12065, 4377, 2648, 10761, 256, 7600, 9331, 2607, 7385, 6547, 1637, 10657, 9444, 6341, 8204, 1392, 5637, 5771, 2575, 1493, 3110, 9269, 8577, 2753, 2431, 3260, 3812, 9370, 2915, 992, 11395, 11490, 9846, 11265, 4067, 1318, 1227, 8353, 11849, 105, 11141, 7240, 11902, 12135, 4247, 1364, 11755, 4076, 8888, 1491, 2577, 4215, 189, 10428, 5026, 4254, 9861, 7094, 12534, 9519, 2020, 4011, 1292, 1783, 4879, 11149, 10691, 4422, 6347, 12046, 955, 5420, 11629, 5432, 5640, 8155, 9421, 477, 6052, 12381, 9307, 11166, 3963, 326, 12676, 1720, 12545, 4164, 6905, 10629, 10586, 5710, 9903, 6078, 4932, 11769, 10870, 4127, 2491, 1431, 10494, 277, 8768, 1059, 2547, 7514, 5543, 8855, 4355, 1555, 5823, 1539, 11542, 7645, 8428, 1524, 8152, 4445, 11877, 12274, 3535, 4109, 1023, 11435, 7592, 9448, 11909, 9600, 10036, 11561, 9614, 5015, 10071, 12229, 396, 933, 5466, 10131, 4842, 4048, 784, 10007, 5137, 591, 3917, 3134, 11494, 3162, 3327, 7117, 3571, 10611, 10701, 12001, 2841, 2669, 7666, 8322, 12411, 7453, 3973, 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11048, 8233, 9375, 9870, 6477, 424, 3630, 797, 7499, 2667, 2843, 6240, 1748, 8504, 2515, 8201, 5702, 2430, 3073, 8578, 3593, 2822, 8629, 2153, 126, 2928, 8308, 6865, 52, 6114, 5926, 5037, 11660, 6606, 3314, 7494, 6311, 7546, 1867, 11108, 5808, 2088, 12234, 8150, 1526, 11557, 8481, 11967, 6563, 4804, 6250, 2091, 9061, 8938, 11277, 10546, 90, 6641, 7956, 7354, 10542, 1911, 11930, 9760, 7579, 10162, 6964, 12286, 12060, 8685, 11664, 7528, 4435, 1269, 9399, 5223, 12143, 6983, 11812, 1286, 12369, 852, 1330, 7907, 2306, 11232, 972, 1323, 8756, 9499, 7292, 3114, 9747, 1155, 7949, 11773, 1936, 6260, 5601, 3704, 939, 7665, 2941, 2842, 2762, 7500, 12337, 4837, 5708, 10588, 10310, 4610, 1345, 12025, 427, 657, 389, 7486, 9344, 9266, 1090, 3466, 10760, 3094, 4378, 6283, 7699, 9751, 487, 4988, 12218, 6885, 4825, 5738, 6970, 3991, 1531, 9817, 8391, 605, 4772, 11684, 3276, 6960, 1129, 11634, 3843, 5725, 5669, 11060, 3286, 4161, 12107, 7827, 5682, 7692, 7408, 6827, 7365, 5391, 7244, 4328, 11120, 7384, 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8351, 1229, 10491, 6759, 6777, 1559, 11027, 5891, 11923, 4878, 3033, 1293, 1408, 11785, 10619, 4780, 5792, 2164, 9525, 1306, 2017, 9053, 985, 2351, 7659, 5951, 11555, 1528, 210, 11928, 1913, 6621, 11970, 5118, 2250, 11455, 2296, 6209, 907, 1698, 11270, 698, 11094, 1651, 8503, 2759, 6241, 9523, 2166, 11547, 10240, 10998, 4509, 11325, 4719, 7459, 2879, 11483, 11299, 8804, 2181, 10261, 4829, 3148, 6306, 4911, 12029, 12176, 7412, 6494, 8277, 10557, 12544, 3011, 12677, 2474, 10973, 8207, 8909, 11816, 8860, 8033, 10387, 1035, 3343, 9802, 6745, 11946, 665, 3099, 7702, 2572, 12542, 10559, 11269, 1754, 908, 16, 7153, 10664, 10227, 7504, 3514, 5729, 11155, 10928, 6825, 7410, 12178, 4707, 9925, 9099, 4670, 9549, 448, 7976, 4135, 9124, 4869, 5647, 6578, 3417, 8961, 5691, 2600, 6735, 9944, 4483, 192, 5895, 1462, 12515, 10853, 706, 10176, 2272, 500, 7045, 10093, 9430, 10136, 8502, 1750, 11095, 12660, 9117, 11764, 712, 9876, 8319, 9408, 4014, 1063, 7393, 1204, 10656, 3086, 6548, 5844, 6774, 10416, 8957, 7621, 4863, 4007, 1931, 9094, 3146, 4831, 4223, 291, 12016, 10964, 11065, 56, 229, 1834, 6511, 12139, 600, 7990, 10244, 4873, 5358, 7915, 10847, 9983, 6908, 7586, 3895, 5802, 8164, 9353, 4024, 359, 8678, 232, 8386, 10106, 5332, 7739, 848, 1816, 9, 2827, 10471, 4578, 12329, 3412, 3374, 11822, 6651, 10276, 315, 3715, 4064, 12593, 10914, 12609, 9659, 5476, 12188, 5402, 4344, 11360, 10272, 7835, 9684, 2025, 11315, 6504, 11810, 6985, 11026, 1788, 6778, 1872, 5822, 2987, 4356, 7021, 5378, 6784, 3407, 9700, 8753, 8808, 2486, 5213, 380, 8600, 12681, 2783, 11541, 2985, 5824, 5505, 6519, 6026, 1983, 10266, 9816, 2635, 3992, 209, 1766, 11556, 2727, 8151, 2981, 8429, 8142, 8507, 1474, 6324, 8021, 3565, 9584, 8843, 11378, 10839, 10863, 3596, 953, 12048, 9618, 651, 3439, 8327, 8544, 11419, 12155, 10824, 8253, 2861, 553, 2117, 2314, 4996, 3109, 3077, 2576, 3047, 8889, 11834, 8217, 10156, 6182, 6486, 10408, 10029, 11744, 1865, 7548, 8095, 7300, 1181, 6267, 6323, 1520, 8508, 11288, 5337, 3930, 2192, 4230, 6635, 7785, 3900, 253, 12514, 1663, 5896, 7939, 9357, 6135, 9300, 7489, 9033, 4227, 8345, 1140, 2868, 9652, 8649, 124, 2155, 11016, 10962, 12018, 9020, 4818, 7567, 3473, 3776, 9998, 2170, 4847, 6588, 2281, 6757, 10493, 2997, 2492, 1007, 4206, 11243, 7379, 4938, 3923, 7180, 5521, 5883, 9426, 4152, 10489, 1231, 10980, 3912, 3177, 5088, 4542, 7187, 12317, 11784, 1781, 1294, 562, 7761, 5175, 8298, 10636, 10689, 11151, 6212, 4269, 5547, 3300, 7233, 3396, 5636, 3081, 8205, 10975, 7997, 10890, 267, 9382, 6036, 240, 7259, 2284, 5685, 3495, 5029, 11403, 6145, 7185, 4544, 251, 3902, 103, 11851, 10606, 6627, 12621, 3733, 11615, 11754, 3051, 4248, 412, 12499, 5408, 9840, 179, 3198, 8370, 11146, 2444, 1214, 11406, 10614, 8869, 6084, 11572, 10910, 12024, 2659, 4611, 1943, 4798, 1870, 6780, 3184, 3871, 11201, 1877, 5881, 5523, 11960, 11415, 7906, 2689, 853, 777, 5974, 2179, 8806, 8755, 2684, 973, 11722, 9649, 1226, 3061, 4068, 9543, 6551, 2257, 7685, 11337, 6571, 11500, 11363, 2102, 2016, 1774, 9526, 6177, 8076, 3939, 754, 11383, 4810, 7421, 4170, 11212, 561, 1407, 1782, 3034, 4012, 9410, 6091, 6155, 12368, 2692, 11813, 3152, 6298, 4457, 11691, 9742, 5124, 1116, 7304, 8247, 5180, 5983, 5448, 4242, 9781, 9398, 2698, 4436, 2160, 5046, 3310, 3524, 958, 8641, 10464, 10957, 10420, 5513, 3574, 781, 295, 5906, 2570, 7704, 10446, 12429, 8731, 10726, 2011, 5995, 4099, 10423, 4904, 3945, 11658, 5039, 4735, 9230, 12642, 9492, 4091, 8930, 9835, 10979, 1417, 10490, 1792, 8352, 3060, 1319, 9650, 2870, 2425, 9580, 9765, 9554, 6441, 6697, 4277, 6143, 11405, 1353, 2445, 5082, 2386, 10653, 7673, 6921, 10553, 7671, 10655, 1639, 7394, 12280, 3995, 7773, 7164, 309, 12427, 10448, 1843, 8590, 10165, 3769, 8836, 6288, 4549, 3364, 4964, 988, 2331, 10468, 8315, 6266, 1477, 7301, 8926, 3641, 6671, 3539, 9931, 11175, 9731, 5071, 9313, 88, 10548, 10971, 2476, 2369, 9361, 10648, 4607, 220, 6763, 10948, 11188, 9989, 4235, 7948, 2678, 9748, 3102, 9047, 11907, 9450, 12415, 10198, 4516, 2910, 3746, 6630, 11367, 1806, 2867, 1452, 8346, 4753, 997, 7640, 10214, 10324, 4190, 11826, 6380, 11633, 2627, 6961, 8593, 10194, 10237, 10348, 7060, 3562, 648, 8340, 5607, 8924, 7303, 1278, 5125, 4410, 10256, 11913, 6724, 8633, 8549, 5812, 7415, 4626, 7106, 3793, 7788, 7160, 8981, 11349, 962, 11671, 8457, 7861, 12377, 2083, 8162, 5804, 3465, 2651, 9267, 3112, 7294, 9691, 7284, 10378, 6334, 11585, 10089, 8873, 343, 2893, 5495, 12442, 9009, 11778, 11872, 5580, 4005, 4865, 2346, 5589, 12392, 3606, 6704, 7392, 1641, 4015, 9080, 2546, 2993, 8769, 11474, 7677, 9976, 6110, 5572, 4029, 10014, 5188, 1857, 3158, 159, 5439, 11752, 11617, 4259, 2187, 10477, 9912, 3810, 3262, 4480, 3342, 1710, 10388, 8193, 7942, 10085, 9440, 6543, 11897, 4598, 9328, 8257, 11434, 2974, 4110, 3952, 10119, 9005, 26, 12226, 7729, 5856, 4155, 3129, 3874, 8019, 6326, 3545, 4205, 1429, 2493, 976, 12207, 6459, 4281, 9879, 7471, 829, 7639, 1137, 4754, 10220, 11741, 11394, 3067, 2916, 4680, 2330, 1186, 4965, 2350, 1771, 9054, 8636, 6675, 8005, 11805, 12701, 7418, 12206, 1005, 2494, 11721, 1322, 2685, 11233, 10851, 12517, 10834, 8121, 3255, 3232, 7275, 11670, 1099, 11350, 9665, 8640, 1263, 3525, 5419, 3026, 12047, 1510, 3597, 11068, 12004, 4413, 8002, 7782, 9714, 1846, 12350, 4765, 10039, 10780, 7664, 2671, 3705, 11641, 844, 9597, 5465, 2961, 397, 11306, 10935, 2097, 12618, 3749, 5526, 400, 11984, 6716, 2389, 8527, 84, 4391, 306, 459, 8782, 154, 2396, 9940, 9923, 4709, 11735, 15, 1697, 1755, 6210, 11153, 5731, 10022, 11430, 9564, 3805, 11001, 3856, 3988, 8268, 840, 9340, 11132, 6065, 2815, 8524, 11583, 6336, 4033, 1969, 2604, 10396, 419, 3825, 11226, 4499, 4591, 1813, 9826, 9474, 4292, 12481, 4331, 7766, 9017, 9437, 5757, 9884, 4361, 9657, 12611, 11344, 2110, 3840, 12374, 12640, 9232, 5104, 5006, 8060, 6685, 776, 1329, 2690, 12370, 9824, 1815, 1592, 7740, 7027, 9596, 936, 11642, 7136, 9339, 895, 8269, 9737, 442, 5208, 5199, 7174, 383, 2923, 8992, 7638, 999, 7472, 7558, 3499, 12606, 10814, 7038, 6102, 2125, 2407, 6171, 11687, 8118, 2528, 8013, 5474, 9661, 581, 9214, 111, 3667, 11564, 3266, 9745, 3116, 7252, 2458, 11603, 5992, 717, 463, 7498, 2764, 3631, 5653, 9155, 6823, 10930, 7838, 7429, 12472, 12504, 10951, 10803, 10006, 2956, 4049, 294, 1256, 3575, 3743, 5973, 1328, 854, 6686, 4902, 10425, 4486, 5565, 5969, 11009, 12051, 7818, 5269, 417, 10398, 3588, 4144, 4300, 12647, 7129, 4972, 8964, 7191, 11382, 1301, 3940, 10124, 8934, 5721, 4233, 9991, 6153, 6093, 10954, 7598, 258, 7344, 3729, 3476, 2361, 12645, 4302, 10673, 4383, 556, 7799, 12314, 11791, 6000, 5886, 5352, 3976, 5735, 4584, 4309, 9210, 5326, 2420, 7551, 4339, 462, 800, 5993, 2013, 9772, 9875, 1646, 11765, 8303, 2461, 7823, 10175, 1660, 10854, 2587, 2808, 3882, 8664, 12423, 11093, 1752, 11271, 3696, 3280, 533, 12071, 1804, 11369, 10057, 12289, 9087, 7803, 10988, 540, 7465, 10794, 8495, 12284, 6966, 6395, 9578, 2427, 8514, 12167, 9106, 5317, 3885, 3739, 6367, 9688, 11761, 11206, 3098, 1705, 11947, 4898, 5367, 10730, 2451, 8135, 388, 2656, 428, 10012, 4031, 6338, 3438, 1507, 9619, 8339, 1121, 3563, 8023, 12181, 12022, 10912, 12595, 10668, 10247, 1894, 10359, 10895, 6848, 5395, 4319, 6619, 1915, 8214, 8126, 7147, 589, 5139, 8178, 4748, 4021, 8197, 9807, 10602, 9469, 12570, 8181, 6956, 2833, 3583, 6119, 6586, 4849, 6816, 168, 8553, 10096, 4889, 4771, 2632, 8392, 8596, 2074, 7989, 1614, 12140, 3685, 7616, 4958, 9097, 9927, 4661, 3916, 2953, 5138, 628, 7148, 6748, 5912, 8382, 4951, 6008, 9213, 812, 9662, 8469, 5355, 6203, 11100, 12116, 9031, 7491, 10020, 5733, 3978, 1993, 7714, 8379, 46, 5253, 4472, 7760, 1406, 1295, 11213, 1892, 10249, 7798, 734, 4384, 2116, 1498, 2862, 5248, 1923, 4200, 12040, 3610, 6929, 5820, 1874, 1854, 12667, 7464, 685, 10989, 5304, 11030, 8009, 4691, 12070, 694, 3281, 5446, 5985, 10234, 7238, 11143, 7314, 3713, 317, 10790, 8517, 8240, 7619, 8959, 3419, 3672, 7456, 372, 9195, 3800, 5947, 7903, 5296, 11738, 11711, 6257, 3324, 7089, 2857, 1951, 204, 7044, 1657, 2273, 7726, 10074, 5831, 4659, 9929, 3541, 4558, 3296, 12688, 11698, 4987, 2643, 9752, 12320, 3528, 6463, 10626, 9986, 4566, 7049, 6051, 3019, 9422, 8825, 2850, 3691, 9529, 8846, 5341, 10568, 6480, 5921, 9898, 4193, 7497, 799, 718, 4340, 8781, 917, 307, 7166, 9417, 29, 3509, 9592, 7330, 6414, 9288, 7975, 1679, 9550, 5629, 10452, 8065, 5207, 837, 9738, 9181, 6938, 8583, 8661, 5320, 11513, 8721, 12508, 4219, 12034, 5750, 10011, 656, 2657, 12026, 3629, 2766, 6478, 10570, 5964, 3824, 883, 10397, 765, 5270, 1997, 2402, 12498, 1362, 4249, 12341, 3522, 3312, 6608, 5714, 7333, 6531, 6231, 4915, 11983, 925, 5527, 11305, 932, 2962, 12230, 9188, 7298, 8097, 2511, 7485, 2655, 658, 8136, 11129, 9304, 2922, 833, 7175, 8599, 1544, 5214, 10050, 7879, 5154, 8465, 12305, 9194, 515, 7457, 4721, 8603, 8765, 2884, 10868, 11771, 7951, 9167, 5706, 4839, 8677, 1599, 4025, 7036, 10816, 4921, 7636, 8994, 5615, 4614, 9472, 9828, 6559, 11428, 10024, 11864, 2892, 1079, 8874, 11854, 76, 4853, 11620, 10633, 7477, 6662, 9698, 3409, 9795, 8746, 3556, 5311, 7310, 12675, 3013, 3964, 7125, 11648, 9110, 8622, 3787, 9076, 10789, 524, 3714, 1580, 10277, 9495, 3680, 8490, 12426, 1198, 7165, 458, 918, 4392, 9777, 5263, 4478, 3264, 11566, 2518, 5480, 9321, 5905, 1255, 782, 4050, 12015, 1623, 4224, 12405, 11518, 2268, 11465, 3985, 4044, 10505, 2806, 2589, 3783, 2882, 8767, 2995, 10495, 8399, 7219, 11639, 3707, 2214, 9264, 9346, 9381, 1387, 10891, 7754, 9572, 7425, 8866, 3766, 5204, 7343, 743, 7599, 3092, 10762, 12513, 1464, 3901, 1374, 4545, 7434, 9317, 7081, 6591, 10682, 5285, 11926, 212, 7258, 1384, 6037, 4936, 7381, 4978, 8422, 11841, 8385, 1597, 8679, 1833, 1618, 57, 6470, 114, 3236, 6386, 8190, 10413, 6762, 1162, 4608, 10312, 12302, 11354, 7308, 5313, 7257, 242, 11927, 1765, 1529, 3993, 12282, 8497, 7043, 502, 1952, 12461, 11252, 11053, 1863, 11746, 1882, 5021, 5309, 3558, 5894, 1665, 4484, 10427, 3044, 4216, 5674, 2200, 4492, 5767, 10828, 5620, 9677, 3197, 1358, 9841, 5274, 9227, 6942, 10142, 11014, 2157, 10994, 9705, 8552, 610, 6817, 4778, 10621, 12636, 7927, 10582, 4530, 5438, 1047, 3159, 6276, 4266, 2395, 915, 8783, 10525, 6527, 5035, 5928, 2509, 8099, 3245, 12096, 4535, 7969, 8296, 5177, 5763, 5989, 4084, 10564, 4427, 5978, 2773, 2794, 2136, 7531, 1972, 2484, 8810, 2927, 2747, 2154, 1448, 8650, 11138, 1802, 12073, 2048, 4130, 4056, 4644, 3235, 226, 6471, 3666, 810, 9215, 11890, 1902, 1800, 11140, 3057, 11850, 1372, 3903, 9790, 3725, 3763, 10617, 11787, 8967, 6087, 11347, 8983, 8942, 6640, 2715, 10547, 1170, 9314, 9274, 4390, 920, 8528, 3140, 9059, 2093, 12551, 4789, 4852, 340, 11855, 3484, 11478, 3224, 10353, 11977, 8414, 11955, 5587, 2348, 4967, 5853, 4307, 4586, 3603, 4095, 8111, 6469, 228, 1619, 11066, 3599, 6113, 2743, 6866, 7525, 10860, 12173, 5252, 566, 8380, 5914, 8779, 4342, 5404, 12388, 9703, 10996, 10242, 7992, 4114, 11173, 9933, 8613, 7205, 3508, 455, 9418, 12225, 1018, 9006, 10503, 4046, 4844, 10807, 6692, 7770, 8227, 7152, 1696, 909, 11736, 5298, 8091, 8900, 2826, 1590, 1817, 10595, 5086, 3179, 8476, 6357, 12713]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/check.py b/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..3d93850acd79cc0f8fff05cdbb0c63aabc484815
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l6-s8/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(), 1
+    for v in p:
+        acc = acc * v % n
+        if acc in seen:
+            raise Invalid(f"prefix product residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/instance.json b/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d9352455711232780c22267dbeeba4dbcee94118
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 12713, "family": "rlve_prefix_product_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/run.py b/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-rlve-prefix-product-permutation-l6-s8/tests/test.sh b/tasks/construct-rlve-prefix-product-permutation-l6-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-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-rlve-prefix-sum-permutation-l2-s1/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l2-s1/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6d8b8507b2c038474c3a0fd0f35614856b9bdb17
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 94, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s1/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f9be310eff7ace9be481bb2dd7c1786d33b3c257
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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'
+{"perm": [94, 1, 92, 3, 90, 5, 88, 7, 86, 9, 84, 11, 82, 13, 80, 15, 78, 17, 76, 19, 74, 21, 72, 23, 70, 25, 68, 27, 66, 29, 64, 31, 62, 33, 60, 35, 58, 37, 56, 39, 54, 41, 52, 43, 50, 45, 48, 47, 46, 49, 44, 51, 42, 53, 40, 55, 38, 57, 36, 59, 34, 61, 32, 63, 30, 65, 28, 67, 26, 69, 24, 71, 22, 73, 20, 75, 18, 77, 16, 79, 14, 81, 12, 83, 10, 85, 8, 87, 6, 89, 4, 91, 2, 93]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s1/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/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-s1/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6d8b8507b2c038474c3a0fd0f35614856b9bdb17
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 94, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s1/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l2-s1/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l2-s8/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l2-s8/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..12babb100381cf5047a33d5b92f679ed1fe5303e
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 38, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s8/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6ed19d23ed2b36d10268747a124b41e2c3212266
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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'
+{"perm": [38, 1, 36, 3, 34, 5, 32, 7, 30, 9, 28, 11, 26, 13, 24, 15, 22, 17, 20, 19, 18, 21, 16, 23, 14, 25, 12, 27, 10, 29, 8, 31, 6, 33, 4, 35, 2, 37]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s8/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/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-s8/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..12babb100381cf5047a33d5b92f679ed1fe5303e
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 38, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l2-s8/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l2-s8/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l6-s0/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l6-s0/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ea6d338aed5729025ba71c7f0b484249b47f9004
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 10770, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s0/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d2f34a14366ff623c8e7e06c49799c3ab798b631
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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'
+{"perm": [10770, 1, 10768, 3, 10766, 5, 10764, 7, 10762, 9, 10760, 11, 10758, 13, 10756, 15, 10754, 17, 10752, 19, 10750, 21, 10748, 23, 10746, 25, 10744, 27, 10742, 29, 10740, 31, 10738, 33, 10736, 35, 10734, 37, 10732, 39, 10730, 41, 10728, 43, 10726, 45, 10724, 47, 10722, 49, 10720, 51, 10718, 53, 10716, 55, 10714, 57, 10712, 59, 10710, 61, 10708, 63, 10706, 65, 10704, 67, 10702, 69, 10700, 71, 10698, 73, 10696, 75, 10694, 77, 10692, 79, 10690, 81, 10688, 83, 10686, 85, 10684, 87, 10682, 89, 10680, 91, 10678, 93, 10676, 95, 10674, 97, 10672, 99, 10670, 101, 10668, 103, 10666, 105, 10664, 107, 10662, 109, 10660, 111, 10658, 113, 10656, 115, 10654, 117, 10652, 119, 10650, 121, 10648, 123, 10646, 125, 10644, 127, 10642, 129, 10640, 131, 10638, 133, 10636, 135, 10634, 137, 10632, 139, 10630, 141, 10628, 143, 10626, 145, 10624, 147, 10622, 149, 10620, 151, 10618, 153, 10616, 155, 10614, 157, 10612, 159, 10610, 161, 10608, 163, 10606, 165, 10604, 167, 10602, 169, 10600, 171, 10598, 173, 10596, 175, 10594, 177, 10592, 179, 10590, 181, 10588, 183, 10586, 185, 10584, 187, 10582, 189, 10580, 191, 10578, 193, 10576, 195, 10574, 197, 10572, 199, 10570, 201, 10568, 203, 10566, 205, 10564, 207, 10562, 209, 10560, 211, 10558, 213, 10556, 215, 10554, 217, 10552, 219, 10550, 221, 10548, 223, 10546, 225, 10544, 227, 10542, 229, 10540, 231, 10538, 233, 10536, 235, 10534, 237, 10532, 239, 10530, 241, 10528, 243, 10526, 245, 10524, 247, 10522, 249, 10520, 251, 10518, 253, 10516, 255, 10514, 257, 10512, 259, 10510, 261, 10508, 263, 10506, 265, 10504, 267, 10502, 269, 10500, 271, 10498, 273, 10496, 275, 10494, 277, 10492, 279, 10490, 281, 10488, 283, 10486, 285, 10484, 287, 10482, 289, 10480, 291, 10478, 293, 10476, 295, 10474, 297, 10472, 299, 10470, 301, 10468, 303, 10466, 305, 10464, 307, 10462, 309, 10460, 311, 10458, 313, 10456, 315, 10454, 317, 10452, 319, 10450, 321, 10448, 323, 10446, 325, 10444, 327, 10442, 329, 10440, 331, 10438, 333, 10436, 335, 10434, 337, 10432, 339, 10430, 341, 10428, 343, 10426, 345, 10424, 347, 10422, 349, 10420, 351, 10418, 353, 10416, 355, 10414, 357, 10412, 359, 10410, 361, 10408, 363, 10406, 365, 10404, 367, 10402, 369, 10400, 371, 10398, 373, 10396, 375, 10394, 377, 10392, 379, 10390, 381, 10388, 383, 10386, 385, 10384, 387, 10382, 389, 10380, 391, 10378, 393, 10376, 395, 10374, 397, 10372, 399, 10370, 401, 10368, 403, 10366, 405, 10364, 407, 10362, 409, 10360, 411, 10358, 413, 10356, 415, 10354, 417, 10352, 419, 10350, 421, 10348, 423, 10346, 425, 10344, 427, 10342, 429, 10340, 431, 10338, 433, 10336, 435, 10334, 437, 10332, 439, 10330, 441, 10328, 443, 10326, 445, 10324, 447, 10322, 449, 10320, 451, 10318, 453, 10316, 455, 10314, 457, 10312, 459, 10310, 461, 10308, 463, 10306, 465, 10304, 467, 10302, 469, 10300, 471, 10298, 473, 10296, 475, 10294, 477, 10292, 479, 10290, 481, 10288, 483, 10286, 485, 10284, 487, 10282, 489, 10280, 491, 10278, 493, 10276, 495, 10274, 497, 10272, 499, 10270, 501, 10268, 503, 10266, 505, 10264, 507, 10262, 509, 10260, 511, 10258, 513, 10256, 515, 10254, 517, 10252, 519, 10250, 521, 10248, 523, 10246, 525, 10244, 527, 10242, 529, 10240, 531, 10238, 533, 10236, 535, 10234, 537, 10232, 539, 10230, 541, 10228, 543, 10226, 545, 10224, 547, 10222, 549, 10220, 551, 10218, 553, 10216, 555, 10214, 557, 10212, 559, 10210, 561, 10208, 563, 10206, 565, 10204, 567, 10202, 569, 10200, 571, 10198, 573, 10196, 575, 10194, 577, 10192, 579, 10190, 581, 10188, 583, 10186, 585, 10184, 587, 10182, 589, 10180, 591, 10178, 593, 10176, 595, 10174, 597, 10172, 599, 10170, 601, 10168, 603, 10166, 605, 10164, 607, 10162, 609, 10160, 611, 10158, 613, 10156, 615, 10154, 617, 10152, 619, 10150, 621, 10148, 623, 10146, 625, 10144, 627, 10142, 629, 10140, 631, 10138, 633, 10136, 635, 10134, 637, 10132, 639, 10130, 641, 10128, 643, 10126, 645, 10124, 647, 10122, 649, 10120, 651, 10118, 653, 10116, 655, 10114, 657, 10112, 659, 10110, 661, 10108, 663, 10106, 665, 10104, 667, 10102, 669, 10100, 671, 10098, 673, 10096, 675, 10094, 677, 10092, 679, 10090, 681, 10088, 683, 10086, 685, 10084, 687, 10082, 689, 10080, 691, 10078, 693, 10076, 695, 10074, 697, 10072, 699, 10070, 701, 10068, 703, 10066, 705, 10064, 707, 10062, 709, 10060, 711, 10058, 713, 10056, 715, 10054, 717, 10052, 719, 10050, 721, 10048, 723, 10046, 725, 10044, 727, 10042, 729, 10040, 731, 10038, 733, 10036, 735, 10034, 737, 10032, 739, 10030, 741, 10028, 743, 10026, 745, 10024, 747, 10022, 749, 10020, 751, 10018, 753, 10016, 755, 10014, 757, 10012, 759, 10010, 761, 10008, 763, 10006, 765, 10004, 767, 10002, 769, 10000, 771, 9998, 773, 9996, 775, 9994, 777, 9992, 779, 9990, 781, 9988, 783, 9986, 785, 9984, 787, 9982, 789, 9980, 791, 9978, 793, 9976, 795, 9974, 797, 9972, 799, 9970, 801, 9968, 803, 9966, 805, 9964, 807, 9962, 809, 9960, 811, 9958, 813, 9956, 815, 9954, 817, 9952, 819, 9950, 821, 9948, 823, 9946, 825, 9944, 827, 9942, 829, 9940, 831, 9938, 833, 9936, 835, 9934, 837, 9932, 839, 9930, 841, 9928, 843, 9926, 845, 9924, 847, 9922, 849, 9920, 851, 9918, 853, 9916, 855, 9914, 857, 9912, 859, 9910, 861, 9908, 863, 9906, 865, 9904, 867, 9902, 869, 9900, 871, 9898, 873, 9896, 875, 9894, 877, 9892, 879, 9890, 881, 9888, 883, 9886, 885, 9884, 887, 9882, 889, 9880, 891, 9878, 893, 9876, 895, 9874, 897, 9872, 899, 9870, 901, 9868, 903, 9866, 905, 9864, 907, 9862, 909, 9860, 911, 9858, 913, 9856, 915, 9854, 917, 9852, 919, 9850, 921, 9848, 923, 9846, 925, 9844, 927, 9842, 929, 9840, 931, 9838, 933, 9836, 935, 9834, 937, 9832, 939, 9830, 941, 9828, 943, 9826, 945, 9824, 947, 9822, 949, 9820, 951, 9818, 953, 9816, 955, 9814, 957, 9812, 959, 9810, 961, 9808, 963, 9806, 965, 9804, 967, 9802, 969, 9800, 971, 9798, 973, 9796, 975, 9794, 977, 9792, 979, 9790, 981, 9788, 983, 9786, 985, 9784, 987, 9782, 989, 9780, 991, 9778, 993, 9776, 995, 9774, 997, 9772, 999, 9770, 1001, 9768, 1003, 9766, 1005, 9764, 1007, 9762, 1009, 9760, 1011, 9758, 1013, 9756, 1015, 9754, 1017, 9752, 1019, 9750, 1021, 9748, 1023, 9746, 1025, 9744, 1027, 9742, 1029, 9740, 1031, 9738, 1033, 9736, 1035, 9734, 1037, 9732, 1039, 9730, 1041, 9728, 1043, 9726, 1045, 9724, 1047, 9722, 1049, 9720, 1051, 9718, 1053, 9716, 1055, 9714, 1057, 9712, 1059, 9710, 1061, 9708, 1063, 9706, 1065, 9704, 1067, 9702, 1069, 9700, 1071, 9698, 1073, 9696, 1075, 9694, 1077, 9692, 1079, 9690, 1081, 9688, 1083, 9686, 1085, 9684, 1087, 9682, 1089, 9680, 1091, 9678, 1093, 9676, 1095, 9674, 1097, 9672, 1099, 9670, 1101, 9668, 1103, 9666, 1105, 9664, 1107, 9662, 1109, 9660, 1111, 9658, 1113, 9656, 1115, 9654, 1117, 9652, 1119, 9650, 1121, 9648, 1123, 9646, 1125, 9644, 1127, 9642, 1129, 9640, 1131, 9638, 1133, 9636, 1135, 9634, 1137, 9632, 1139, 9630, 1141, 9628, 1143, 9626, 1145, 9624, 1147, 9622, 1149, 9620, 1151, 9618, 1153, 9616, 1155, 9614, 1157, 9612, 1159, 9610, 1161, 9608, 1163, 9606, 1165, 9604, 1167, 9602, 1169, 9600, 1171, 9598, 1173, 9596, 1175, 9594, 1177, 9592, 1179, 9590, 1181, 9588, 1183, 9586, 1185, 9584, 1187, 9582, 1189, 9580, 1191, 9578, 1193, 9576, 1195, 9574, 1197, 9572, 1199, 9570, 1201, 9568, 1203, 9566, 1205, 9564, 1207, 9562, 1209, 9560, 1211, 9558, 1213, 9556, 1215, 9554, 1217, 9552, 1219, 9550, 1221, 9548, 1223, 9546, 1225, 9544, 1227, 9542, 1229, 9540, 1231, 9538, 1233, 9536, 1235, 9534, 1237, 9532, 1239, 9530, 1241, 9528, 1243, 9526, 1245, 9524, 1247, 9522, 1249, 9520, 1251, 9518, 1253, 9516, 1255, 9514, 1257, 9512, 1259, 9510, 1261, 9508, 1263, 9506, 1265, 9504, 1267, 9502, 1269, 9500, 1271, 9498, 1273, 9496, 1275, 9494, 1277, 9492, 1279, 9490, 1281, 9488, 1283, 9486, 1285, 9484, 1287, 9482, 1289, 9480, 1291, 9478, 1293, 9476, 1295, 9474, 1297, 9472, 1299, 9470, 1301, 9468, 1303, 9466, 1305, 9464, 1307, 9462, 1309, 9460, 1311, 9458, 1313, 9456, 1315, 9454, 1317, 9452, 1319, 9450, 1321, 9448, 1323, 9446, 1325, 9444, 1327, 9442, 1329, 9440, 1331, 9438, 1333, 9436, 1335, 9434, 1337, 9432, 1339, 9430, 1341, 9428, 1343, 9426, 1345, 9424, 1347, 9422, 1349, 9420, 1351, 9418, 1353, 9416, 1355, 9414, 1357, 9412, 1359, 9410, 1361, 9408, 1363, 9406, 1365, 9404, 1367, 9402, 1369, 9400, 1371, 9398, 1373, 9396, 1375, 9394, 1377, 9392, 1379, 9390, 1381, 9388, 1383, 9386, 1385, 9384, 1387, 9382, 1389, 9380, 1391, 9378, 1393, 9376, 1395, 9374, 1397, 9372, 1399, 9370, 1401, 9368, 1403, 9366, 1405, 9364, 1407, 9362, 1409, 9360, 1411, 9358, 1413, 9356, 1415, 9354, 1417, 9352, 1419, 9350, 1421, 9348, 1423, 9346, 1425, 9344, 1427, 9342, 1429, 9340, 1431, 9338, 1433, 9336, 1435, 9334, 1437, 9332, 1439, 9330, 1441, 9328, 1443, 9326, 1445, 9324, 1447, 9322, 1449, 9320, 1451, 9318, 1453, 9316, 1455, 9314, 1457, 9312, 1459, 9310, 1461, 9308, 1463, 9306, 1465, 9304, 1467, 9302, 1469, 9300, 1471, 9298, 1473, 9296, 1475, 9294, 1477, 9292, 1479, 9290, 1481, 9288, 1483, 9286, 1485, 9284, 1487, 9282, 1489, 9280, 1491, 9278, 1493, 9276, 1495, 9274, 1497, 9272, 1499, 9270, 1501, 9268, 1503, 9266, 1505, 9264, 1507, 9262, 1509, 9260, 1511, 9258, 1513, 9256, 1515, 9254, 1517, 9252, 1519, 9250, 1521, 9248, 1523, 9246, 1525, 9244, 1527, 9242, 1529, 9240, 1531, 9238, 1533, 9236, 1535, 9234, 1537, 9232, 1539, 9230, 1541, 9228, 1543, 9226, 1545, 9224, 1547, 9222, 1549, 9220, 1551, 9218, 1553, 9216, 1555, 9214, 1557, 9212, 1559, 9210, 1561, 9208, 1563, 9206, 1565, 9204, 1567, 9202, 1569, 9200, 1571, 9198, 1573, 9196, 1575, 9194, 1577, 9192, 1579, 9190, 1581, 9188, 1583, 9186, 1585, 9184, 1587, 9182, 1589, 9180, 1591, 9178, 1593, 9176, 1595, 9174, 1597, 9172, 1599, 9170, 1601, 9168, 1603, 9166, 1605, 9164, 1607, 9162, 1609, 9160, 1611, 9158, 1613, 9156, 1615, 9154, 1617, 9152, 1619, 9150, 1621, 9148, 1623, 9146, 1625, 9144, 1627, 9142, 1629, 9140, 1631, 9138, 1633, 9136, 1635, 9134, 1637, 9132, 1639, 9130, 1641, 9128, 1643, 9126, 1645, 9124, 1647, 9122, 1649, 9120, 1651, 9118, 1653, 9116, 1655, 9114, 1657, 9112, 1659, 9110, 1661, 9108, 1663, 9106, 1665, 9104, 1667, 9102, 1669, 9100, 1671, 9098, 1673, 9096, 1675, 9094, 1677, 9092, 1679, 9090, 1681, 9088, 1683, 9086, 1685, 9084, 1687, 9082, 1689, 9080, 1691, 9078, 1693, 9076, 1695, 9074, 1697, 9072, 1699, 9070, 1701, 9068, 1703, 9066, 1705, 9064, 1707, 9062, 1709, 9060, 1711, 9058, 1713, 9056, 1715, 9054, 1717, 9052, 1719, 9050, 1721, 9048, 1723, 9046, 1725, 9044, 1727, 9042, 1729, 9040, 1731, 9038, 1733, 9036, 1735, 9034, 1737, 9032, 1739, 9030, 1741, 9028, 1743, 9026, 1745, 9024, 1747, 9022, 1749, 9020, 1751, 9018, 1753, 9016, 1755, 9014, 1757, 9012, 1759, 9010, 1761, 9008, 1763, 9006, 1765, 9004, 1767, 9002, 1769, 9000, 1771, 8998, 1773, 8996, 1775, 8994, 1777, 8992, 1779, 8990, 1781, 8988, 1783, 8986, 1785, 8984, 1787, 8982, 1789, 8980, 1791, 8978, 1793, 8976, 1795, 8974, 1797, 8972, 1799, 8970, 1801, 8968, 1803, 8966, 1805, 8964, 1807, 8962, 1809, 8960, 1811, 8958, 1813, 8956, 1815, 8954, 1817, 8952, 1819, 8950, 1821, 8948, 1823, 8946, 1825, 8944, 1827, 8942, 1829, 8940, 1831, 8938, 1833, 8936, 1835, 8934, 1837, 8932, 1839, 8930, 1841, 8928, 1843, 8926, 1845, 8924, 1847, 8922, 1849, 8920, 1851, 8918, 1853, 8916, 1855, 8914, 1857, 8912, 1859, 8910, 1861, 8908, 1863, 8906, 1865, 8904, 1867, 8902, 1869, 8900, 1871, 8898, 1873, 8896, 1875, 8894, 1877, 8892, 1879, 8890, 1881, 8888, 1883, 8886, 1885, 8884, 1887, 8882, 1889, 8880, 1891, 8878, 1893, 8876, 1895, 8874, 1897, 8872, 1899, 8870, 1901, 8868, 1903, 8866, 1905, 8864, 1907, 8862, 1909, 8860, 1911, 8858, 1913, 8856, 1915, 8854, 1917, 8852, 1919, 8850, 1921, 8848, 1923, 8846, 1925, 8844, 1927, 8842, 1929, 8840, 1931, 8838, 1933, 8836, 1935, 8834, 1937, 8832, 1939, 8830, 1941, 8828, 1943, 8826, 1945, 8824, 1947, 8822, 1949, 8820, 1951, 8818, 1953, 8816, 1955, 8814, 1957, 8812, 1959, 8810, 1961, 8808, 1963, 8806, 1965, 8804, 1967, 8802, 1969, 8800, 1971, 8798, 1973, 8796, 1975, 8794, 1977, 8792, 1979, 8790, 1981, 8788, 1983, 8786, 1985, 8784, 1987, 8782, 1989, 8780, 1991, 8778, 1993, 8776, 1995, 8774, 1997, 8772, 1999, 8770, 2001, 8768, 2003, 8766, 2005, 8764, 2007, 8762, 2009, 8760, 2011, 8758, 2013, 8756, 2015, 8754, 2017, 8752, 2019, 8750, 2021, 8748, 2023, 8746, 2025, 8744, 2027, 8742, 2029, 8740, 2031, 8738, 2033, 8736, 2035, 8734, 2037, 8732, 2039, 8730, 2041, 8728, 2043, 8726, 2045, 8724, 2047, 8722, 2049, 8720, 2051, 8718, 2053, 8716, 2055, 8714, 2057, 8712, 2059, 8710, 2061, 8708, 2063, 8706, 2065, 8704, 2067, 8702, 2069, 8700, 2071, 8698, 2073, 8696, 2075, 8694, 2077, 8692, 2079, 8690, 2081, 8688, 2083, 8686, 2085, 8684, 2087, 8682, 2089, 8680, 2091, 8678, 2093, 8676, 2095, 8674, 2097, 8672, 2099, 8670, 2101, 8668, 2103, 8666, 2105, 8664, 2107, 8662, 2109, 8660, 2111, 8658, 2113, 8656, 2115, 8654, 2117, 8652, 2119, 8650, 2121, 8648, 2123, 8646, 2125, 8644, 2127, 8642, 2129, 8640, 2131, 8638, 2133, 8636, 2135, 8634, 2137, 8632, 2139, 8630, 2141, 8628, 2143, 8626, 2145, 8624, 2147, 8622, 2149, 8620, 2151, 8618, 2153, 8616, 2155, 8614, 2157, 8612, 2159, 8610, 2161, 8608, 2163, 8606, 2165, 8604, 2167, 8602, 2169, 8600, 2171, 8598, 2173, 8596, 2175, 8594, 2177, 8592, 2179, 8590, 2181, 8588, 2183, 8586, 2185, 8584, 2187, 8582, 2189, 8580, 2191, 8578, 2193, 8576, 2195, 8574, 2197, 8572, 2199, 8570, 2201, 8568, 2203, 8566, 2205, 8564, 2207, 8562, 2209, 8560, 2211, 8558, 2213, 8556, 2215, 8554, 2217, 8552, 2219, 8550, 2221, 8548, 2223, 8546, 2225, 8544, 2227, 8542, 2229, 8540, 2231, 8538, 2233, 8536, 2235, 8534, 2237, 8532, 2239, 8530, 2241, 8528, 2243, 8526, 2245, 8524, 2247, 8522, 2249, 8520, 2251, 8518, 2253, 8516, 2255, 8514, 2257, 8512, 2259, 8510, 2261, 8508, 2263, 8506, 2265, 8504, 2267, 8502, 2269, 8500, 2271, 8498, 2273, 8496, 2275, 8494, 2277, 8492, 2279, 8490, 2281, 8488, 2283, 8486, 2285, 8484, 2287, 8482, 2289, 8480, 2291, 8478, 2293, 8476, 2295, 8474, 2297, 8472, 2299, 8470, 2301, 8468, 2303, 8466, 2305, 8464, 2307, 8462, 2309, 8460, 2311, 8458, 2313, 8456, 2315, 8454, 2317, 8452, 2319, 8450, 2321, 8448, 2323, 8446, 2325, 8444, 2327, 8442, 2329, 8440, 2331, 8438, 2333, 8436, 2335, 8434, 2337, 8432, 2339, 8430, 2341, 8428, 2343, 8426, 2345, 8424, 2347, 8422, 2349, 8420, 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9655, 1114, 9657, 1112, 9659, 1110, 9661, 1108, 9663, 1106, 9665, 1104, 9667, 1102, 9669, 1100, 9671, 1098, 9673, 1096, 9675, 1094, 9677, 1092, 9679, 1090, 9681, 1088, 9683, 1086, 9685, 1084, 9687, 1082, 9689, 1080, 9691, 1078, 9693, 1076, 9695, 1074, 9697, 1072, 9699, 1070, 9701, 1068, 9703, 1066, 9705, 1064, 9707, 1062, 9709, 1060, 9711, 1058, 9713, 1056, 9715, 1054, 9717, 1052, 9719, 1050, 9721, 1048, 9723, 1046, 9725, 1044, 9727, 1042, 9729, 1040, 9731, 1038, 9733, 1036, 9735, 1034, 9737, 1032, 9739, 1030, 9741, 1028, 9743, 1026, 9745, 1024, 9747, 1022, 9749, 1020, 9751, 1018, 9753, 1016, 9755, 1014, 9757, 1012, 9759, 1010, 9761, 1008, 9763, 1006, 9765, 1004, 9767, 1002, 9769, 1000, 9771, 998, 9773, 996, 9775, 994, 9777, 992, 9779, 990, 9781, 988, 9783, 986, 9785, 984, 9787, 982, 9789, 980, 9791, 978, 9793, 976, 9795, 974, 9797, 972, 9799, 970, 9801, 968, 9803, 966, 9805, 964, 9807, 962, 9809, 960, 9811, 958, 9813, 956, 9815, 954, 9817, 952, 9819, 950, 9821, 948, 9823, 946, 9825, 944, 9827, 942, 9829, 940, 9831, 938, 9833, 936, 9835, 934, 9837, 932, 9839, 930, 9841, 928, 9843, 926, 9845, 924, 9847, 922, 9849, 920, 9851, 918, 9853, 916, 9855, 914, 9857, 912, 9859, 910, 9861, 908, 9863, 906, 9865, 904, 9867, 902, 9869, 900, 9871, 898, 9873, 896, 9875, 894, 9877, 892, 9879, 890, 9881, 888, 9883, 886, 9885, 884, 9887, 882, 9889, 880, 9891, 878, 9893, 876, 9895, 874, 9897, 872, 9899, 870, 9901, 868, 9903, 866, 9905, 864, 9907, 862, 9909, 860, 9911, 858, 9913, 856, 9915, 854, 9917, 852, 9919, 850, 9921, 848, 9923, 846, 9925, 844, 9927, 842, 9929, 840, 9931, 838, 9933, 836, 9935, 834, 9937, 832, 9939, 830, 9941, 828, 9943, 826, 9945, 824, 9947, 822, 9949, 820, 9951, 818, 9953, 816, 9955, 814, 9957, 812, 9959, 810, 9961, 808, 9963, 806, 9965, 804, 9967, 802, 9969, 800, 9971, 798, 9973, 796, 9975, 794, 9977, 792, 9979, 790, 9981, 788, 9983, 786, 9985, 784, 9987, 782, 9989, 780, 9991, 778, 9993, 776, 9995, 774, 9997, 772, 9999, 770, 10001, 768, 10003, 766, 10005, 764, 10007, 762, 10009, 760, 10011, 758, 10013, 756, 10015, 754, 10017, 752, 10019, 750, 10021, 748, 10023, 746, 10025, 744, 10027, 742, 10029, 740, 10031, 738, 10033, 736, 10035, 734, 10037, 732, 10039, 730, 10041, 728, 10043, 726, 10045, 724, 10047, 722, 10049, 720, 10051, 718, 10053, 716, 10055, 714, 10057, 712, 10059, 710, 10061, 708, 10063, 706, 10065, 704, 10067, 702, 10069, 700, 10071, 698, 10073, 696, 10075, 694, 10077, 692, 10079, 690, 10081, 688, 10083, 686, 10085, 684, 10087, 682, 10089, 680, 10091, 678, 10093, 676, 10095, 674, 10097, 672, 10099, 670, 10101, 668, 10103, 666, 10105, 664, 10107, 662, 10109, 660, 10111, 658, 10113, 656, 10115, 654, 10117, 652, 10119, 650, 10121, 648, 10123, 646, 10125, 644, 10127, 642, 10129, 640, 10131, 638, 10133, 636, 10135, 634, 10137, 632, 10139, 630, 10141, 628, 10143, 626, 10145, 624, 10147, 622, 10149, 620, 10151, 618, 10153, 616, 10155, 614, 10157, 612, 10159, 610, 10161, 608, 10163, 606, 10165, 604, 10167, 602, 10169, 600, 10171, 598, 10173, 596, 10175, 594, 10177, 592, 10179, 590, 10181, 588, 10183, 586, 10185, 584, 10187, 582, 10189, 580, 10191, 578, 10193, 576, 10195, 574, 10197, 572, 10199, 570, 10201, 568, 10203, 566, 10205, 564, 10207, 562, 10209, 560, 10211, 558, 10213, 556, 10215, 554, 10217, 552, 10219, 550, 10221, 548, 10223, 546, 10225, 544, 10227, 542, 10229, 540, 10231, 538, 10233, 536, 10235, 534, 10237, 532, 10239, 530, 10241, 528, 10243, 526, 10245, 524, 10247, 522, 10249, 520, 10251, 518, 10253, 516, 10255, 514, 10257, 512, 10259, 510, 10261, 508, 10263, 506, 10265, 504, 10267, 502, 10269, 500, 10271, 498, 10273, 496, 10275, 494, 10277, 492, 10279, 490, 10281, 488, 10283, 486, 10285, 484, 10287, 482, 10289, 480, 10291, 478, 10293, 476, 10295, 474, 10297, 472, 10299, 470, 10301, 468, 10303, 466, 10305, 464, 10307, 462, 10309, 460, 10311, 458, 10313, 456, 10315, 454, 10317, 452, 10319, 450, 10321, 448, 10323, 446, 10325, 444, 10327, 442, 10329, 440, 10331, 438, 10333, 436, 10335, 434, 10337, 432, 10339, 430, 10341, 428, 10343, 426, 10345, 424, 10347, 422, 10349, 420, 10351, 418, 10353, 416, 10355, 414, 10357, 412, 10359, 410, 10361, 408, 10363, 406, 10365, 404, 10367, 402, 10369, 400, 10371, 398, 10373, 396, 10375, 394, 10377, 392, 10379, 390, 10381, 388, 10383, 386, 10385, 384, 10387, 382, 10389, 380, 10391, 378, 10393, 376, 10395, 374, 10397, 372, 10399, 370, 10401, 368, 10403, 366, 10405, 364, 10407, 362, 10409, 360, 10411, 358, 10413, 356, 10415, 354, 10417, 352, 10419, 350, 10421, 348, 10423, 346, 10425, 344, 10427, 342, 10429, 340, 10431, 338, 10433, 336, 10435, 334, 10437, 332, 10439, 330, 10441, 328, 10443, 326, 10445, 324, 10447, 322, 10449, 320, 10451, 318, 10453, 316, 10455, 314, 10457, 312, 10459, 310, 10461, 308, 10463, 306, 10465, 304, 10467, 302, 10469, 300, 10471, 298, 10473, 296, 10475, 294, 10477, 292, 10479, 290, 10481, 288, 10483, 286, 10485, 284, 10487, 282, 10489, 280, 10491, 278, 10493, 276, 10495, 274, 10497, 272, 10499, 270, 10501, 268, 10503, 266, 10505, 264, 10507, 262, 10509, 260, 10511, 258, 10513, 256, 10515, 254, 10517, 252, 10519, 250, 10521, 248, 10523, 246, 10525, 244, 10527, 242, 10529, 240, 10531, 238, 10533, 236, 10535, 234, 10537, 232, 10539, 230, 10541, 228, 10543, 226, 10545, 224, 10547, 222, 10549, 220, 10551, 218, 10553, 216, 10555, 214, 10557, 212, 10559, 210, 10561, 208, 10563, 206, 10565, 204, 10567, 202, 10569, 200, 10571, 198, 10573, 196, 10575, 194, 10577, 192, 10579, 190, 10581, 188, 10583, 186, 10585, 184, 10587, 182, 10589, 180, 10591, 178, 10593, 176, 10595, 174, 10597, 172, 10599, 170, 10601, 168, 10603, 166, 10605, 164, 10607, 162, 10609, 160, 10611, 158, 10613, 156, 10615, 154, 10617, 152, 10619, 150, 10621, 148, 10623, 146, 10625, 144, 10627, 142, 10629, 140, 10631, 138, 10633, 136, 10635, 134, 10637, 132, 10639, 130, 10641, 128, 10643, 126, 10645, 124, 10647, 122, 10649, 120, 10651, 118, 10653, 116, 10655, 114, 10657, 112, 10659, 110, 10661, 108, 10663, 106, 10665, 104, 10667, 102, 10669, 100, 10671, 98, 10673, 96, 10675, 94, 10677, 92, 10679, 90, 10681, 88, 10683, 86, 10685, 84, 10687, 82, 10689, 80, 10691, 78, 10693, 76, 10695, 74, 10697, 72, 10699, 70, 10701, 68, 10703, 66, 10705, 64, 10707, 62, 10709, 60, 10711, 58, 10713, 56, 10715, 54, 10717, 52, 10719, 50, 10721, 48, 10723, 46, 10725, 44, 10727, 42, 10729, 40, 10731, 38, 10733, 36, 10735, 34, 10737, 32, 10739, 30, 10741, 28, 10743, 26, 10745, 24, 10747, 22, 10749, 20, 10751, 18, 10753, 16, 10755, 14, 10757, 12, 10759, 10, 10761, 8, 10763, 6, 10765, 4, 10767, 2, 10769]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s0/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/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-s0/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ea6d338aed5729025ba71c7f0b484249b47f9004
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 10770, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s0/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l6-s0/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l6-s7/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l6-s7/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d97054ac60de89ea98e865b98909d1f3012c0da9
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 16524, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s7/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..25505760116536baf37217b14876fdfc9d21506c
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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'
+{"perm": [16524, 1, 16522, 3, 16520, 5, 16518, 7, 16516, 9, 16514, 11, 16512, 13, 16510, 15, 16508, 17, 16506, 19, 16504, 21, 16502, 23, 16500, 25, 16498, 27, 16496, 29, 16494, 31, 16492, 33, 16490, 35, 16488, 37, 16486, 39, 16484, 41, 16482, 43, 16480, 45, 16478, 47, 16476, 49, 16474, 51, 16472, 53, 16470, 55, 16468, 57, 16466, 59, 16464, 61, 16462, 63, 16460, 65, 16458, 67, 16456, 69, 16454, 71, 16452, 73, 16450, 75, 16448, 77, 16446, 79, 16444, 81, 16442, 83, 16440, 85, 16438, 87, 16436, 89, 16434, 91, 16432, 93, 16430, 95, 16428, 97, 16426, 99, 16424, 101, 16422, 103, 16420, 105, 16418, 107, 16416, 109, 16414, 111, 16412, 113, 16410, 115, 16408, 117, 16406, 119, 16404, 121, 16402, 123, 16400, 125, 16398, 127, 16396, 129, 16394, 131, 16392, 133, 16390, 135, 16388, 137, 16386, 139, 16384, 141, 16382, 143, 16380, 145, 16378, 147, 16376, 149, 16374, 151, 16372, 153, 16370, 155, 16368, 157, 16366, 159, 16364, 161, 16362, 163, 16360, 165, 16358, 167, 16356, 169, 16354, 171, 16352, 173, 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+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s7/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-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-l6-s7/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d97054ac60de89ea98e865b98909d1f3012c0da9
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 16524, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l6-s7/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prefix-sum-permutation-l6-s7/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-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-prime-graph-coloring-l3-s7/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-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-prime-graph-coloring-l3-s7/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8acc96bb582cc69227f10ef487931081cc922212
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 67, "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-s7/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..60b9b4c7bd2d5158edac5e64c1f4ec2d0747347b
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-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": [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]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s7/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s7/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-s7/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8acc96bb582cc69227f10ef487931081cc922212
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 67, "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-s7/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-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-prime-graph-coloring-l3-s7/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-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-prime-graph-coloring-l3-s9/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-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-prime-graph-coloring-l3-s9/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c726f4a124f45e756c9683e9d02424f3c6841252
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 42, "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-s9/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4946f8a82c105ea778690b8a6c756573a30867e6
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-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'
+{"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]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l3-s9/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s9/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-s9/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c726f4a124f45e756c9683e9d02424f3c6841252
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 42, "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-s9/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-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-prime-graph-coloring-l3-s9/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-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-recursive-sequence-sum-l4-s2/environment/Dockerfile b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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-rlve-recursive-sequence-sum-l4-s2/environment/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..043be261caa74e29d10fde98a3ca92a275f9c859
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/environment/instance.json
@@ -0,0 +1 @@
+{"F0": 128, "A": 7, "B": 7023, "S": 15110584069633972810, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l4-s2/solution/solve.sh b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..374e6bd87a2db462d1082e00d7ff952a97e5b0a5
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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'
+{"indices": [3, 5, 6, 11, 14, 15, 17, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l4-s2/tests/check.py b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..feda076c3f95e5e12198151dee30e1b8223924bc
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/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-l4-s2/tests/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..043be261caa74e29d10fde98a3ca92a275f9c859
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/tests/instance.json
@@ -0,0 +1 @@
+{"F0": 128, "A": 7, "B": 7023, "S": 15110584069633972810, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l4-s2/tests/run.py b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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-rlve-recursive-sequence-sum-l4-s2/tests/test.sh b/tasks/construct-rlve-recursive-sequence-sum-l4-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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-rlve-recursive-sequence-sum-l4-s5/environment/Dockerfile b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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-recursive-sequence-sum-l4-s5/environment/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6285decc4e4af1cbbe391c43dfcd786e0e7272d0
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/environment/instance.json
@@ -0,0 +1 @@
+{"F0": 54, "A": 1, "B": 1695, "S": 131001, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l4-s5/solution/solve.sh b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f072346ad11c5b04d30828b46e1b5c1649586d80
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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'
+{"indices": [1, 2, 3, 5, 9, 11, 13, 16, 17]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l4-s5/tests/check.py b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..feda076c3f95e5e12198151dee30e1b8223924bc
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/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-l4-s5/tests/instance.json b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6285decc4e4af1cbbe391c43dfcd786e0e7272d0
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/tests/instance.json
@@ -0,0 +1 @@
+{"F0": 54, "A": 1, "B": 1695, "S": 131001, "family": "rlve_recursive_sequence_sum", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-recursive-sequence-sum-l4-s5/tests/run.py b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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-recursive-sequence-sum-l4-s5/tests/test.sh b/tasks/construct-rlve-recursive-sequence-sum-l4-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-recursive-sequence-sum-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-round-robin-scores-l1-s0/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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-rlve-round-robin-scores-l1-s0/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fad9f58c594120868cd1b41040083c78b0e75eec
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"W": [3, 2, 4, 5], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s0/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..70ec4fb3142940741b6326d0442294b436204c31
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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'
+{"A": ["0111", "1001", "1200", "1120"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s0/tests/check.py b/tasks/construct-rlve-round-robin-scores-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s0/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-s0/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fad9f58c594120868cd1b41040083c78b0e75eec
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"W": [3, 2, 4, 5], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s0/tests/run.py b/tasks/construct-rlve-round-robin-scores-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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-rlve-round-robin-scores-l1-s0/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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-rlve-round-robin-scores-l1-s9/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l1-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-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-l1-s9/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..62080f897d5624c0cefdd2a2a1d1a8a41e89cded
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s9/environment/instance.json
@@ -0,0 +1 @@
+{"W": [9, 2, 2, 2], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s9/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l1-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fd3fe13dce04d8977e79bdd4a4bee79e4befc4bb
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-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": ["0222", "0011", "0101", "0110"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s9/tests/check.py b/tasks/construct-rlve-round-robin-scores-l1-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-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-l1-s9/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l1-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..62080f897d5624c0cefdd2a2a1d1a8a41e89cded
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-s9/tests/instance.json
@@ -0,0 +1 @@
+{"W": [9, 2, 2, 2], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l1-s9/tests/run.py b/tasks/construct-rlve-round-robin-scores-l1-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-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-l1-s9/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l1-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l1-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-s1/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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-rlve-round-robin-scores-l5-s1/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b255b856bf2dca3a757c89c233d81f7564ece47b
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"W": [17, 14, 18, 31, 27, 18, 18, 22, 19, 17, 21, 19, 30, 19, 20, 22, 27, 27], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s1/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3122e600952eb2e86034c5927ff503f9d844b60f
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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'
+{"A": ["011101112120011110", "101012101121000001", "110110211101111210", "121021112222021102", "211002010110212222", "102100011101011212", "110122002201010001", "121111201210012101", "011021010201100212", "111011000012221010", "002012212101201010", "211021121010011110", "221202221002012200", "121011112021101001", "121101202111010111", "120100210221021011", "121201221111221100", "212000110222211120"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s1/tests/check.py b/tasks/construct-rlve-round-robin-scores-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-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-l5-s1/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b255b856bf2dca3a757c89c233d81f7564ece47b
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"W": [17, 14, 18, 31, 27, 18, 18, 22, 19, 17, 21, 19, 30, 19, 20, 22, 27, 27], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s1/tests/run.py b/tasks/construct-rlve-round-robin-scores-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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-rlve-round-robin-scores-l5-s1/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-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-rlve-round-robin-scores-l5-s6/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l5-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-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-round-robin-scores-l5-s6/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..baca887a61a5e1498b3bf550eb3b5746a0c11e30
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s6/environment/instance.json
@@ -0,0 +1 @@
+{"W": [24, 23, 19, 22, 13, 24, 13, 18, 21, 18, 17, 19, 19, 18, 17, 22, 15, 20], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s6/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l5-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7d6a192adc78d91cf9f59b98ae6b7fae24f32967
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-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'
+{"A": ["012120112111211111", "102111211111112111", "000111121112111111", "111021212111111011", "011001111110011111", "211110110122121111", "101011011101110111", "110111100111012121", "011012120221111010", "111111110011111121", "111110210101111111", "110120111110111211", "011121121111010111", "111110111111102111", "101111201111200110", "111211112110111012", "111111101011111101", "111111112111112010"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s6/tests/check.py b/tasks/construct-rlve-round-robin-scores-l5-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s6/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-s6/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l5-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..baca887a61a5e1498b3bf550eb3b5746a0c11e30
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-s6/tests/instance.json
@@ -0,0 +1 @@
+{"W": [24, 23, 19, 22, 13, 24, 13, 18, 21, 18, 17, 19, 19, 18, 17, 22, 15, 20], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l5-s6/tests/run.py b/tasks/construct-rlve-round-robin-scores-l5-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-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-round-robin-scores-l5-s6/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l5-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l5-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-shortest-path-count-l2-s3/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l2-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l2-s3/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0af5d3bd2d2189e6510d4164fbf8aa8e85ecaaa1
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s3/environment/instance.json
@@ -0,0 +1 @@
+{"K": 393, "n_max": 57, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s3/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l2-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bcd727181299a9032d03073ac08f9acd9583c525
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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'
+{"n": 27, "adj": ["NNYYNNNNNNNNNNNNNNYNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNNNNNNNNNNNNNNN", "YNNNYYNNNNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNYNNNNN", "NNNNYYNNYYNNNNNNNNNNNYNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNN", "NNNNNNNNNNNNYYNNYYNNNNNNNYN", "NNNNNNNNNNNNYYNNYYNNNNNNNYN", "NNNNNNNNNNNNNNYYNNNNNNNNNNY", "NNNNNNNNNNNNNNYYNNNNNNNNNNY", "YNNNNNNNNNNNNNNNNNNYNNNNNNN", "NNNNNNNNNNNNNNNNNNYNYNNNNNN", "NNNNNNNNNNNNNNNNNNNYNYNNNNN", "NNNNNNYYNNNNNNNNNNNNYNYNNNN", "NNNNNNNNNNNNNNNNNNNNNYNYNNN", "NNNNNNNNNNNNNNNNNNNNNNYNYNN", "NNNNNNNNNNNNNNNNNNNNNNNYNYN", "NNNNNNNNNNNNNNYYNNNNNNNNYNY", "NYNNNNNNNNNNNNNNYYNNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s3/tests/check.py b/tasks/construct-rlve-shortest-path-count-l2-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-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-l2-s3/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0af5d3bd2d2189e6510d4164fbf8aa8e85ecaaa1
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s3/tests/instance.json
@@ -0,0 +1 @@
+{"K": 393, "n_max": 57, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s3/tests/run.py b/tasks/construct-rlve-shortest-path-count-l2-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l2-s3/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l2-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l2-s4/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l2-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l2-s4/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b1e705961f45a9a63a1be79ae0da33c18375782b
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s4/environment/instance.json
@@ -0,0 +1 @@
+{"K": 58, "n_max": 39, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s4/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l2-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0795265c8c2533017e1f37d5fc396d9dc373ce2c
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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'
+{"n": 18, "adj": ["NNYYNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNYNNNN", "YNNNYYNNNNNNNYNNNN", "NNYYNNYYNNNNNNNNNN", "NNYYNNYYNNNNNNNNNN", "NNNNYYNNYYNNNNNYNN", "NNNNYYNNYYNNNNNYNN", "NNNNNNYYNNYYNNNNYN", "NNNNNNYYNNYYNNNNYN", "NNNNNNNNYYNNNNNNNY", "NNNNNNNNYYNNNNNNNY", "NNNNNNNNNNNNNYNNNN", "NNYYNNNNNNNNYNYNNN", "NNNNNNNNNNNNNYNYNN", "NNNNNNYYNNNNNNYNYN", "NNNNNNNNYYNNNNNYNY", "NYNNNNNNNNYYNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s4/tests/check.py b/tasks/construct-rlve-shortest-path-count-l2-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s4/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-s4/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l2-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b1e705961f45a9a63a1be79ae0da33c18375782b
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l2-s4/tests/instance.json
@@ -0,0 +1 @@
+{"K": 58, "n_max": 39, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l2-s4/tests/run.py b/tasks/construct-rlve-shortest-path-count-l2-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l2-s4/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l2-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l6-s5/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l6-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l6-s5/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l6-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..69c684f1aceebf80d902566f82661fca07c28fa9
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s5/environment/instance.json
@@ -0,0 +1 @@
+{"K": 163750090544363596, "n_max": 351, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s5/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l6-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..43eb6815edf66387c4ddd8fb3261911d621cc9f3
--- /dev/null
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+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
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"NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNY", "NYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s5/tests/check.py b/tasks/construct-rlve-shortest-path-count-l6-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s5/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-s5/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l6-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..69c684f1aceebf80d902566f82661fca07c28fa9
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l6-s5/tests/instance.json
@@ -0,0 +1 @@
+{"K": 163750090544363596, "n_max": 351, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l6-s5/tests/run.py b/tasks/construct-rlve-shortest-path-count-l6-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-shortest-path-count-l6-s5/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l6-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-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-smallest-enclosing-circle-l1-s8/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-rlve-smallest-enclosing-circle-l1-s8/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5d4a092da7e260c8fd3e776bbbba20e121e3de6f
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 0], [2, 0], [4, 6], [6, 3]], "r_opt": 3.3579026495837594, "r2_num": 1105, "r2_den": 98, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c8f72c68cda4ede0a098e65c8b6272a38d9b7f62
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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'
+{"x": 2.642857142857143, "y": 2.9285714285714284, "r": 3.3579026505837595}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-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-l1-s8/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5d4a092da7e260c8fd3e776bbbba20e121e3de6f
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[1, 0], [2, 0], [4, 6], [6, 3]], "r_opt": 3.3579026495837594, "r2_num": 1105, "r2_den": 98, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-rlve-smallest-enclosing-circle-l1-s8/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l1-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-rlve-smallest-enclosing-circle-l5-s0/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-smallest-enclosing-circle-l5-s0/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ea267201ea3bb7919744c66576b8d6c24c6153f3
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 57], [4, 36], [4, 42], [5, 69], [10, 60], [10, 75], [13, 86], [14, 32], [16, 53], [18, 66], [19, 103], [19, 113], [20, 29], [20, 116], [25, 96], [28, 92], [29, 8], [32, 9], [34, 51], [36, 87], [37, 116], [37, 120], [41, 1], [45, 11], [45, 68], [48, 72], [50, 81], [52, 97], [52, 117], [53, 42], [56, 50], [59, 64], [59, 93], [60, 112], [61, 33], [62, 101], [64, 45], [66, 71], [71, 71], [71, 83], [72, 45], [74, 21], [76, 50], [78, 57], [79, 36], [80, 24], [81, 10], [82, 67], [87, 21], [90, 37], [98, 104], [103, 26], [103, 49], [106, 97], [108, 89], [111, 34], [111, 66], [112, 13], [116, 94], [117, 65]], "r_opt": 69.05251624669444, "r2_num": 19073, "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-l5-s0/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..775f42d1bc27575f97c5d339f1c70ad9dad3c7c5
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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'
+{"x": 66.0, "y": 64.5, "r": 69.05251624769444}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-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-l5-s0/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ea267201ea3bb7919744c66576b8d6c24c6153f3
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 57], [4, 36], [4, 42], [5, 69], [10, 60], [10, 75], [13, 86], [14, 32], [16, 53], [18, 66], [19, 103], [19, 113], [20, 29], [20, 116], [25, 96], [28, 92], [29, 8], [32, 9], [34, 51], [36, 87], [37, 116], [37, 120], [41, 1], [45, 11], [45, 68], [48, 72], [50, 81], [52, 97], [52, 117], [53, 42], [56, 50], [59, 64], [59, 93], [60, 112], [61, 33], [62, 101], [64, 45], [66, 71], [71, 71], [71, 83], [72, 45], [74, 21], [76, 50], [78, 57], [79, 36], [80, 24], [81, 10], [82, 67], [87, 21], [90, 37], [98, 104], [103, 26], [103, 49], [106, 97], [108, 89], [111, 34], [111, 66], [112, 13], [116, 94], [117, 65]], "r_opt": 69.05251624669444, "r2_num": 19073, "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-l5-s0/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-smallest-enclosing-circle-l5-s0/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-rlve-smallest-enclosing-circle-l5-s7/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-smallest-enclosing-circle-l5-s7/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9a2eea268ab795309c436f0c95a960e43a29ac87
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[6, 85], [8, 19], [11, 62], [11, 103], [12, 113], [15, 74], [15, 97], [20, 47], [20, 106], [23, 103], [24, 46], [25, 97], [26, 90], [27, 9], [31, 75], [32, 1], [32, 88], [34, 105], [35, 14], [36, 81], [38, 59], [39, 8], [43, 95], [47, 44], [50, 62], [51, 94], [52, 111], [52, 117], [54, 1], [60, 64], [67, 27], [69, 56], [70, 26], [70, 52], [72, 74], [75, 25], [76, 25], [77, 110], [78, 2], [79, 20], [81, 61], [83, 32], [84, 105], [85, 98], [88, 85], [91, 65], [94, 14], [94, 112], [98, 0], [99, 67], [101, 31], [103, 73], [110, 84], [110, 117], [113, 27], [115, 101], [117, 0], [117, 41], [118, 31], [118, 114]], "r_opt": 77.13930245665392, "r2_num": 1737524597233, "r2_den": 291997778, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5e79bae320fc9e88ca2b87aea93683f5b3481d2a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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'
+{"x": 65.52871803360092, "y": 57.45588843830175, "r": 77.13930245765393}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/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-s7/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9a2eea268ab795309c436f0c95a960e43a29ac87
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[6, 85], [8, 19], [11, 62], [11, 103], [12, 113], [15, 74], [15, 97], [20, 47], [20, 106], [23, 103], [24, 46], [25, 97], [26, 90], [27, 9], [31, 75], [32, 1], [32, 88], [34, 105], [35, 14], [36, 81], [38, 59], [39, 8], [43, 95], [47, 44], [50, 62], [51, 94], [52, 111], [52, 117], [54, 1], [60, 64], [67, 27], [69, 56], [70, 26], [70, 52], [72, 74], [75, 25], [76, 25], [77, 110], [78, 2], [79, 20], [81, 61], [83, 32], [84, 105], [85, 98], [88, 85], [91, 65], [94, 14], [94, 112], [98, 0], [99, 67], [101, 31], [103, 73], [110, 84], [110, 117], [113, 27], [115, 101], [117, 0], [117, 41], [118, 31], [118, 114]], "r_opt": 77.13930245665392, "r2_num": 1737524597233, "r2_den": 291997778, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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-smallest-enclosing-circle-l5-s7/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l5-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-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/optimize-ae-p1-ff-kakeya-d3-p31/environment/Dockerfile b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/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-p1-ff-kakeya-d3-p31/environment/instance.json b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc2bb78de5a95127ced7a6ec7020199cb896553e
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/environment/instance.json
@@ -0,0 +1 @@
+{"p": 31, "d": 3, "direction": "minimize", "family": "ae_p1_ff_kakeya", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p1-ff-kakeya-d3-p31/solution/solve.sh b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9f0cf1e870e7c26054d53a69eac2b5a65f3d3701
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/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": [[0, 0, 0], [0, 0, 1], [0, 0, 2], [0, 0, 3], [0, 0, 4], [0, 0, 5], [0, 0, 6], [0, 0, 7], [0, 0, 8], [0, 0, 9], [0, 0, 10], [0, 0, 11], [0, 0, 12], [0, 0, 13], [0, 0, 14], [0, 0, 15], [0, 0, 16], [0, 0, 17], [0, 0, 18], [0, 0, 19], [0, 0, 20], [0, 0, 21], [0, 0, 22], [0, 0, 23], [0, 0, 24], [0, 0, 25], [0, 0, 26], [0, 0, 27], [0, 0, 28], [0, 0, 29], [0, 0, 30], [0, 1, 1], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 1, 6], [0, 1, 9], [0, 1, 12], [0, 1, 14], [0, 1, 15], [0, 1, 16], [0, 1, 18], [0, 1, 20], [0, 1, 21], [0, 1, 24], [0, 1, 25], [0, 1, 26], [0, 1, 27], [0, 1, 29], [0, 1, 30], [0, 2, 0], [0, 2, 2], [0, 2, 3], [0, 2, 4], [0, 2, 5], [0, 2, 6], [0, 2, 7], [0, 2, 8], [0, 2, 10], [0, 2, 11], [0, 2, 13], [0, 2, 17], [0, 2, 18], [0, 2, 19], [0, 2, 20], [0, 2, 22], [0, 2, 24], [0, 2, 28], [0, 2, 29], [0, 2, 30], [0, 3, 3], [0, 3, 4], [0, 3, 5], [0, 3, 6], [0, 3, 8], [0, 3, 9], [0, 3, 11], [0, 3, 12], [0, 3, 13], [0, 3, 16], [0, 3, 19], [0, 3, 24], [0, 3, 25], [0, 3, 26], [0, 3, 28], [0, 3, 30], [0, 4, 1], [0, 4, 2], [0, 4, 3], [0, 4, 5], [0, 4, 6], [0, 4, 7], [0, 4, 9], [0, 4, 11], [0, 4, 12], [0, 4, 13], [0, 4, 14], [0, 4, 15], [0, 4, 16], [0, 4, 17], [0, 4, 19], [0, 4, 20], [0, 4, 21], [0, 4, 24], [0, 4, 25], [0, 4, 27], [0, 4, 30], [0, 5, 0], [0, 5, 3], [0, 5, 6], [0, 5, 8], [0, 5, 11], [0, 5, 12], [0, 5, 13], [0, 5, 14], [0, 5, 15], [0, 5, 17], [0, 5, 21], [0, 5, 22], [0, 5, 23], [0, 5, 24], [0, 5, 25], [0, 5, 26], [0, 5, 27], [0, 5, 29], [0, 5, 30], [0, 6, 1], [0, 6, 2], [0, 6, 3], [0, 6, 4], [0, 6, 5], [0, 6, 7], [0, 6, 8], [0, 6, 10], [0, 6, 11], [0, 6, 12], [0, 6, 14], [0, 6, 15], [0, 6, 16], [0, 6, 18], [0, 6, 23], [0, 6, 24], [0, 6, 25], [0, 6, 27], [0, 6, 29], [0, 7, 1], [0, 7, 6], [0, 7, 7], [0, 7, 8], [0, 7, 10], [0, 7, 12], [0, 7, 13], [0, 7, 15], [0, 7, 16], [0, 7, 17], [0, 7, 18], [0, 7, 19], [0, 7, 21], [0, 7, 22], [0, 7, 24], [0, 7, 25], [0, 7, 26], [0, 7, 27], [0, 7, 29], [0, 8, 1], [0, 8, 2], [0, 8, 3], [0, 8, 4], [0, 8, 6], [0, 8, 7], [0, 8, 9], [0, 8, 10], [0, 8, 11], [0, 8, 14], [0, 8, 16], [0, 8, 17], [0, 8, 22], [0, 8, 23], [0, 8, 24], [0, 8, 25], [0, 8, 26], [0, 8, 28], [0, 8, 29], [0, 9, 1], [0, 9, 4], [0, 9, 9], [0, 9, 10], [0, 9, 11], [0, 9, 13], [0, 9, 15], [0, 9, 19], [0, 9, 20], [0, 9, 21], [0, 9, 22], [0, 9, 24], [0, 9, 25], [0, 9, 27], [0, 9, 28], [0, 9, 29], [0, 10, 0], [0, 10, 2], [0, 10, 4], [0, 10, 8], [0, 10, 9], [0, 10, 10], [0, 10, 11], [0, 10, 12], [0, 10, 13], [0, 10, 14], [0, 10, 16], [0, 10, 17], [0, 10, 18], [0, 10, 19], [0, 10, 20], [0, 10, 21], [0, 10, 24], [0, 10, 27], [0, 10, 29], [0, 10, 30], [0, 11, 0], [0, 11, 1], [0, 11, 2], [0, 11, 4], [0, 11, 5], [0, 11, 7], [0, 11, 8], [0, 11, 9], [0, 11, 12], [0, 11, 13], [0, 11, 15], [0, 11, 17], [0, 11, 19], [0, 11, 20], [0, 11, 21], [0, 11, 22], [0, 11, 24], [0, 11, 26], [0, 11, 30], [0, 12, 0], [0, 12, 1], [0, 12, 2], [0, 12, 5], [0, 12, 7], [0, 12, 8], [0, 12, 10], [0, 12, 13], [0, 12, 14], [0, 12, 15], [0, 12, 17], [0, 12, 18], [0, 12, 19], [0, 12, 21], [0, 12, 22], [0, 12, 23], [0, 12, 24], [0, 12, 25], [0, 12, 26], [0, 12, 28], [0, 12, 29], [0, 13, 0], [0, 13, 3], [0, 13, 8], [0, 13, 9], [0, 13, 10], [0, 13, 11], [0, 13, 12], [0, 13, 14], [0, 13, 15], [0, 13, 16], [0, 13, 18], [0, 13, 19], [0, 13, 20], [0, 13, 21], [0, 13, 23], [0, 13, 24], [0, 13, 26], [0, 13, 27], [0, 13, 28], [0, 14, 0], [0, 14, 4], [0, 14, 5], [0, 14, 6], [0, 14, 7], [0, 14, 9], [0, 14, 11], [0, 14, 15], [0, 14, 16], [0, 14, 17], [0, 14, 18], [0, 14, 19], [0, 14, 20], [0, 14, 21], [0, 14, 22], [0, 14, 23], [0, 14, 24], [0, 14, 25], [0, 14, 28], [0, 15, 3], [0, 15, 4], [0, 15, 5], [0, 15, 6], [0, 15, 8], [0, 15, 10], [0, 15, 13], [0, 15, 14], [0, 15, 15], [0, 15, 16], [0, 15, 17], [0, 15, 18], [0, 15, 19], [0, 15, 20], [0, 15, 21], [0, 15, 22], [0, 15, 23], [0, 15, 24], [0, 15, 26], [0, 15, 27], [0, 15, 30], [0, 16, 0], [0, 16, 2], [0, 16, 4], [0, 16, 5], [0, 16, 6], [0, 16, 7], [0, 16, 9], [0, 16, 11], [0, 16, 14], [0, 16, 15], [0, 16, 16], [0, 16, 17], 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[0, 20, 21], [0, 20, 24], [0, 20, 29], [0, 20, 30], [0, 21, 1], [0, 21, 4], [0, 21, 7], [0, 21, 9], [0, 21, 10], [0, 21, 11], [0, 21, 13], [0, 21, 15], [0, 21, 16], [0, 21, 19], [0, 21, 20], [0, 21, 21], [0, 21, 22], [0, 21, 23], [0, 21, 24], [0, 21, 25], [0, 21, 27], [0, 21, 28], [0, 21, 29], [0, 21, 30], [0, 22, 0], [0, 22, 1], [0, 22, 2], [0, 22, 3], [0, 22, 4], [0, 22, 6], [0, 22, 7], [0, 22, 8], [0, 22, 9], [0, 22, 10], [0, 22, 11], [0, 22, 12], [0, 22, 14], [0, 22, 17], [0, 22, 22], [0, 22, 23], [0, 22, 24], [0, 22, 26], [0, 22, 27], [0, 22, 28], [0, 23, 1], [0, 23, 6], [0, 23, 7], [0, 23, 8], [0, 23, 10], [0, 23, 11], [0, 23, 12], [0, 23, 13], [0, 23, 16], [0, 23, 17], [0, 23, 18], [0, 23, 19], [0, 23, 21], [0, 23, 22], [0, 23, 24], [0, 23, 25], [0, 23, 26], [0, 23, 28], [0, 23, 29], [0, 24, 2], [0, 24, 3], [0, 24, 4], [0, 24, 5], [0, 24, 7], [0, 24, 8], [0, 24, 10], [0, 24, 11], [0, 24, 12], [0, 24, 13], [0, 24, 14], [0, 24, 15], [0, 24, 18], [0, 24, 23], [0, 24, 24], [0, 24, 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[28, 21, 10], [28, 21, 13], [28, 21, 16], [28, 21, 18], [28, 21, 20], [28, 21, 23], [28, 21, 26], [28, 22, 0], [28, 22, 5], [28, 22, 11], [28, 22, 14], [28, 22, 17], [28, 22, 18], [28, 22, 19], [28, 22, 22], [28, 22, 25], [28, 23, 18], [28, 24, 7], [28, 24, 8], [28, 24, 13], [28, 24, 16], [28, 24, 20], [28, 24, 23], [28, 24, 28], [28, 24, 29], [28, 25, 7], [28, 25, 8], [28, 25, 9], [28, 25, 14], [28, 25, 22], [28, 25, 27], [28, 25, 28], [28, 25, 29], [28, 26, 6], [28, 26, 8], [28, 26, 10], [28, 26, 15], [28, 26, 18], [28, 26, 21], [28, 26, 26], [28, 26, 28], [28, 26, 30], [28, 27, 0], [28, 27, 5], [28, 27, 7], [28, 27, 9], [28, 27, 10], [28, 27, 26], [28, 27, 27], [28, 27, 29], [28, 28, 6], [28, 28, 8], [28, 28, 11], [28, 28, 12], [28, 28, 24], [28, 28, 25], [28, 28, 28], [28, 28, 30], [28, 29, 2], [28, 29, 3], [28, 29, 7], [28, 29, 11], [28, 29, 12], [28, 29, 18], [28, 29, 24], [28, 29, 25], [28, 29, 29], [28, 30, 1], [28, 30, 2], [28, 30, 3], [28, 30, 4], [28, 30, 10], [28, 30, 14], [28, 30, 22], [28, 30, 26], [29, 0, 0], [29, 0, 3], [29, 0, 6], [29, 0, 7], [29, 0, 13], [29, 0, 18], [29, 0, 19], [29, 0, 24], [29, 0, 30], [29, 1, 1], [29, 1, 2], [29, 1, 4], [29, 1, 5], [29, 1, 9], [29, 1, 18], [29, 1, 19], [29, 1, 28], [29, 2, 1], [29, 2, 3], [29, 2, 5], [29, 2, 8], [29, 2, 11], [29, 2, 17], [29, 2, 20], [29, 2, 26], [29, 2, 29], [29, 3, 2], [29, 3, 3], [29, 3, 4], [29, 3, 7], [29, 3, 10], [29, 3, 16], [29, 3, 21], [29, 3, 27], [29, 3, 30], [29, 4, 3], [29, 5, 1], [29, 5, 5], [29, 5, 8], [29, 5, 13], [29, 5, 14], [29, 5, 23], [29, 5, 24], [29, 5, 29], [29, 6, 7], [29, 6, 12], [29, 6, 13], [29, 6, 14], [29, 6, 23], [29, 6, 24], [29, 6, 25], [29, 6, 30], [29, 7, 0], [29, 7, 3], [29, 7, 6], [29, 7, 11], [29, 7, 13], [29, 7, 15], [29, 7, 22], [29, 7, 24], [29, 7, 26], [29, 8, 11], [29, 8, 12], [29, 8, 14], [29, 8, 16], [29, 8, 21], [29, 8, 23], [29, 8, 25], [29, 8, 26], [29, 9, 9], [29, 9, 10], [29, 9, 13], [29, 9, 15], [29, 9, 22], [29, 9, 24], [29, 9, 27], [29, 9, 28], [29, 10, 3], [29, 10, 9], [29, 10, 10], [29, 10, 14], [29, 10, 18], [29, 10, 19], [29, 10, 23], [29, 10, 27], [29, 10, 28], [29, 11, 7], [29, 11, 11], [29, 11, 17], [29, 11, 18], [29, 11, 19], [29, 11, 20], [29, 11, 26], [29, 11, 30], [29, 12, 8], [29, 12, 12], [29, 12, 16], [29, 12, 18], [29, 12, 19], [29, 12, 21], [29, 12, 25], [29, 12, 29], [29, 13, 0], [29, 13, 6], [29, 13, 9], [29, 13, 16], [29, 13, 17], [29, 13, 20], [29, 13, 21], [29, 13, 28], [29, 14, 10], [29, 14, 14], [29, 14, 15], [29, 14, 17], [29, 14, 20], [29, 14, 22], [29, 14, 23], [29, 14, 27], [29, 15, 3], [29, 15, 14], [29, 15, 15], [29, 15, 16], [29, 15, 18], [29, 15, 19], [29, 15, 21], [29, 15, 22], [29, 15, 23], [29, 16, 2], [29, 16, 3], [29, 16, 4], [29, 16, 12], [29, 16, 15], [29, 16, 17], [29, 16, 20], [29, 16, 22], [29, 16, 25], [29, 17, 1], [29, 17, 3], [29, 17, 5], [29, 17, 13], [29, 17, 16], [29, 17, 17], [29, 17, 20], [29, 17, 21], [29, 17, 24], [29, 18, 0], [29, 18, 2], [29, 18, 4], [29, 18, 6], [29, 18, 11], [29, 18, 18], [29, 18, 19], [29, 18, 26], [29, 19, 1], [29, 19, 3], [29, 19, 5], [29, 19, 12], [29, 19, 15], [29, 19, 18], [29, 19, 19], [29, 19, 22], [29, 19, 25], [29, 20, 2], [29, 20, 4], [29, 20, 8], [29, 20, 13], [29, 20, 16], [29, 20, 21], [29, 20, 24], [29, 20, 29], [29, 21, 3], [29, 21, 7], [29, 21, 8], [29, 21, 9], [29, 21, 17], [29, 21, 20], [29, 21, 28], [29, 21, 29], [29, 21, 30], [29, 22, 0], [29, 22, 6], [29, 22, 8], [29, 22, 9], [29, 22, 15], [29, 22, 22], [29, 22, 28], [29, 22, 29], [29, 23, 1], [29, 23, 5], [29, 23, 7], [29, 23, 10], [29, 23, 11], [29, 23, 26], [29, 23, 27], [29, 23, 30], [29, 24, 0], [29, 24, 6], [29, 24, 10], [29, 24, 12], [29, 24, 17], [29, 24, 20], [29, 24, 25], [29, 24, 27], [29, 25, 3], [29, 25, 9], [29, 25, 11], [29, 25, 12], [29, 25, 13], [29, 25, 24], [29, 25, 25], [29, 25, 26], [29, 25, 28], [29, 26, 2], [29, 26, 3], [29, 26, 4], [29, 26, 8], [29, 26, 10], [29, 26, 12], [29, 26, 25], [29, 26, 27], [29, 26, 29], [29, 27, 2], [29, 27, 3], [29, 27, 4], [29, 27, 9], [29, 27, 11], [29, 27, 14], [29, 27, 23], [29, 27, 26], [29, 27, 28], [29, 28, 0], [29, 28, 1], [29, 28, 3], [29, 28, 5], [29, 28, 6], [29, 28, 10], [29, 28, 16], [29, 28, 21], [29, 28, 27], [29, 29, 1], [29, 29, 2], [29, 29, 4], [29, 29, 5], [29, 29, 7], [29, 29, 15], [29, 29, 22], [29, 29, 30], [29, 30, 0], [29, 30, 3], [29, 30, 6], [29, 30, 7], [29, 30, 8], [29, 30, 14], [29, 30, 23], [29, 30, 29], [29, 30, 30], [30, 0, 1], [30, 0, 2], [30, 0, 5], [30, 0, 6], [30, 0, 9], [30, 0, 17], [30, 0, 19], [30, 0, 21], [30, 0, 29], [30, 1, 3], [30, 1, 4], [30, 1, 11], [30, 1, 16], [30, 1, 18], [30, 1, 20], [30, 1, 22], [30, 1, 27], [30, 2, 0], [30, 2, 3], [30, 2, 4], [30, 2, 7], [30, 2, 10], [30, 2, 17], [30, 2, 19], [30, 2, 21], [30, 2, 28], [30, 3, 1], [30, 3, 6], [30, 3, 9], [30, 3, 14], [30, 3, 18], [30, 3, 20], [30, 3, 24], [30, 3, 29], [30, 4, 2], [30, 4, 5], [30, 4, 13], [30, 4, 14], [30, 4, 15], [30, 4, 19], [30, 4, 23], [30, 4, 24], [30, 4, 25], [30, 5, 0], [30, 5, 7], [30, 5, 13], [30, 5, 14], [30, 5, 16], [30, 5, 22], [30, 5, 24], [30, 5, 25], [30, 6, 11], [30, 6, 12], [30, 6, 15], [30, 6, 17], [30, 6, 21], [30, 6, 23], [30, 6, 26], [30, 6, 27], [30, 7, 2], [30, 7, 5], [30, 7, 10], [30, 7, 12], [30, 7, 16], [30, 7, 22], [30, 7, 26], [30, 7, 28], [30, 8, 9], [30, 8, 10], [30, 8, 11], [30, 8, 13], [30, 8, 19], [30, 8, 25], [30, 8, 27], [30, 8, 28], [30, 8, 29], [30, 9, 10], [30, 9, 12], [30, 9, 14], [30, 9, 18], [30, 9, 19], [30, 9, 20], [30, 9, 24], [30, 9, 26], [30, 9, 28], [30, 10, 8], [30, 10, 11], [30, 10, 13], [30, 10, 18], [30, 10, 19], [30, 10, 20], [30, 10, 25], [30, 10, 27], [30, 10, 30], [30, 11, 1], [30, 11, 6], [30, 11, 12], [30, 11, 16], [30, 11, 17], [30, 11, 19], [30, 11, 21], [30, 11, 22], [30, 11, 26], [30, 12, 0], [30, 12, 7], [30, 12, 15], [30, 12, 17], [30, 12, 18], [30, 12, 20], [30, 12, 21], [30, 12, 23], [30, 13, 8], [30, 13, 14], [30, 13, 15], [30, 13, 16], [30, 13, 19], [30, 13, 22], [30, 13, 23], [30, 13, 24], [30, 13, 30], [30, 14, 3], [30, 14, 4], [30, 14, 9], [30, 14, 15], [30, 14, 16], [30, 14, 19], [30, 14, 22], [30, 14, 23], [30, 14, 29], [30, 15, 3], [30, 15, 4], [30, 15, 13], [30, 15, 17], [30, 15, 18], [30, 15, 20], [30, 15, 21], [30, 15, 25], [30, 16, 2], [30, 16, 5], [30, 16, 11], [30, 16, 14], [30, 16, 17], [30, 16, 19], [30, 16, 21], [30, 16, 24], [30, 16, 27], [30, 17, 1], [30, 17, 6], [30, 17, 12], [30, 17, 15], [30, 17, 18], [30, 17, 19], [30, 17, 20], [30, 17, 23], [30, 17, 26], [30, 18, 19], [30, 19, 8], [30, 19, 9], [30, 19, 14], [30, 19, 17], [30, 19, 21], [30, 19, 24], [30, 19, 29], [30, 19, 30], [30, 20, 8], [30, 20, 9], [30, 20, 10], [30, 20, 15], [30, 20, 23], [30, 20, 28], [30, 20, 29], [30, 20, 30], [30, 21, 0], [30, 21, 7], [30, 21, 9], [30, 21, 11], [30, 21, 16], [30, 21, 19], [30, 21, 22], [30, 21, 27], [30, 21, 29], [30, 22, 1], [30, 22, 6], [30, 22, 8], [30, 22, 10], [30, 22, 11], [30, 22, 27], [30, 22, 28], [30, 22, 30], [30, 23, 0], [30, 23, 7], [30, 23, 9], [30, 23, 12], [30, 23, 13], [30, 23, 25], [30, 23, 26], [30, 23, 29], [30, 24, 3], [30, 24, 4], [30, 24, 8], [30, 24, 12], [30, 24, 13], [30, 24, 19], [30, 24, 25], [30, 24, 26], [30, 24, 30], [30, 25, 2], [30, 25, 3], [30, 25, 4], [30, 25, 5], [30, 25, 11], [30, 25, 15], [30, 25, 23], [30, 25, 27], [30, 26, 1], [30, 26, 3], [30, 26, 4], [30, 26, 6], [30, 26, 10], [30, 26, 14], [30, 26, 24], [30, 26, 28], [30, 27, 1], [30, 27, 2], [30, 27, 5], [30, 27, 6], [30, 27, 13], [30, 27, 16], [30, 27, 22], [30, 27, 25], [30, 28, 0], [30, 28, 2], [30, 28, 5], [30, 28, 7], [30, 28, 8], [30, 28, 12], [30, 28, 26], [30, 28, 30], [30, 29, 0], [30, 29, 1], [30, 29, 3], [30, 29, 4], [30, 29, 6], [30, 29, 7], [30, 29, 8], [30, 29, 19], [30, 29, 30], [30, 30, 0], [30, 30, 2], [30, 30, 5], [30, 30, 7], [30, 30, 10], [30, 30, 18], [30, 30, 19], [30, 30, 20], [30, 30, 28]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/check.py b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..dac5049b59a505ff843bc5e086d0c1c303695b2a
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/check.py
@@ -0,0 +1,32 @@
+"""Finite-field Kakeya set in F_p^d: every direction contains a full line. Score = |K| (minimize).
+
+Upstream (AlphaEvolve notebook `finite_field_kakeya.ipynb`) silently deduplicated points and only checked
+d in {3, 4}; here duplicates, out-of-range or non-integer coordinates are rejected and every projective
+direction (first non-zero coordinate = 1) is checked for any d.
+"""
+import itertools
+
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    p, d = inst["p"], inst["d"]
+    pts = ans.get("points")
+    if not isinstance(pts, list) or not pts:
+        raise Invalid("points must be a non-empty list")
+    if len(pts) > p ** d:
+        raise Invalid("more points than the whole space")
+    K = np.array([int_list(x, d, 0, p - 1, "point") for x in pts], dtype=np.int64)
+    w = p ** np.arange(d - 1, -1, -1, dtype=np.int64)
+    codes = K @ w
+    if len(np.unique(codes)) != len(codes):
+        raise Invalid("duplicate points")
+    for i in range(d):  # directions v = (0,..,0,1,*,..,*) with the 1 in position i
+        for tail in itertools.product(range(p), repeat=d - 1 - i):
+            v = np.array([0] * i + [1] + list(tail), dtype=np.int64)
+            base = (K - K[:, i:i + 1] * v) % p  # canonical point of the line through x with direction v
+            if np.bincount(base @ w, minlength=p ** d).max() < p:
+                raise Invalid(f"no full line in direction {v.tolist()}")
+    return len(pts), {"size": len(pts)}
diff --git a/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/instance.json b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..444ebf62b820509d99cc5b4746d58ee6009ed19c
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/instance.json
@@ -0,0 +1 @@
+{"p": 31, "d": 3, "direction": "minimize", "best_known": 8290, "baseline": 29791, "family": "ae_p1_ff_kakeya", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/run.py b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/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-p1-ff-kakeya-d3-p31/tests/test.sh b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d3-p31/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-p35-cubes-in-cube-n11/environment/Dockerfile b/tasks/optimize-ae-p35-cubes-in-cube-n11/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ae-p35-cubes-in-cube-n11/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-p35-cubes-in-cube-n11/environment/instance.json b/tasks/optimize-ae-p35-cubes-in-cube-n11/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0cdc7132d4d482905c13055d5b1fa73587afb997
--- /dev/null
+++ b/tasks/optimize-ae-p35-cubes-in-cube-n11/environment/instance.json
@@ -0,0 +1 @@
+{"n": 11, "tol": 1e-09, "direction": "minimize", "family": "ae_p35_cubes_in_cube", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p35-cubes-in-cube-n11/solution/solve.sh b/tasks/optimize-ae-p35-cubes-in-cube-n11/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7569554dd8e1ce1e7fdc17dd3bfd664acaa0abeb
--- /dev/null
+++ b/tasks/optimize-ae-p35-cubes-in-cube-n11/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'
+{"cubes": [[-0.877779155, -0.877126384, -1.01671182, 0, 0, 0], [-0.877779155, -0.877126384, 0.877819332, 0, 0, 0], [-0.877779155, 1.01740471, -1.01671182, 0, 0, 0], [-0.877779155, 1.01740471, 0.877819332, 0, 0, 0], [1.01675167, -0.877126384, -1.01671182, 0, 0, 0], [1.01675167, -0.877126384, 0.877819332, 0, 0, 0], [1.01675167, 1.01740471, -1.01671182, 0, 0, 0], [1.01675167, 1.01740471, 0.877819332, 0, 0, 0], [0.201013926, 0.11525216, 0.877806873, 6.76458206, 89.9998576, 160.681931], [0.11336823, -0.877124005, -0.208800374, 207.520455, 359.999904, 90.0002316], [-0.87775203, 0.204448607, -0.114126641, 180.000883, 26.5856303, 270.001203]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/check.py b/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..385bbee4f715ce70a2fb41197a6955e11d4ac10a
--- /dev/null
+++ b/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/check.py
@@ -0,0 +1,51 @@
+"""Packing n unit cubes (arbitrary orientation) in the smallest axis-aligned cube (AlphaEvolve problem 35).
+
+Cube = centre + Euler angles in degrees, R = Rz(rz) Ry(ry) Rx(rx) (upstream convention). Disjoint interiors are
+checked with the separating-axis theorem over the 15 candidate axes; projections may overlap by at most
+inst["tol"] (floating-point slack). Score = largest side of the axis-aligned bounding box (minimize)."""
+import itertools
+import math
+
+import numpy as np
+
+from run import Invalid, float_matrix
+
+
+def rot(rx, ry, rz):
+    x, y, z = map(math.radians, (rx, ry, rz))
+    cx, sx, cy, sy, cz, sz = math.cos(x), math.sin(x), math.cos(y), math.sin(y), math.cos(z), math.sin(z)
+    mx = np.array([[1, 0, 0], [0, cx, -sx], [0, sx, cx]])
+    my = np.array([[cy, 0, sy], [0, 1, 0], [-sy, 0, cy]])
+    mz = np.array([[cz, -sz, 0], [sz, cz, 0], [0, 0, 1]])
+    return mz @ my @ mx
+
+
+LOCAL = np.array(list(itertools.product((-0.5, 0.5), repeat=3)))
+
+
+def check(inst, ans):
+    n, tol = inst["n"], inst["tol"]
+    rows = float_matrix(ans.get("cubes"), n, 6, "cubes")
+    cubes = []
+    for r in rows:
+        if max(abs(v) for v in r[:3]) > 1e3 or max(abs(v) for v in r[3:]) > 1e4:
+            raise Invalid("coordinates or angles out of range")
+        m = rot(*r[3:])
+        cubes.append((m, LOCAL @ m.T + np.array(r[:3])))
+    for (m1, v1), (m2, v2) in itertools.combinations(cubes, 2):
+        axes = [m1[:, i] for i in range(3)] + [m2[:, i] for i in range(3)]
+        axes += [np.cross(m1[:, i], m2[:, j]) for i in range(3) for j in range(3)]
+        separated = False
+        for a in axes:
+            na = np.linalg.norm(a)
+            if na < 1e-9:
+                continue
+            a = a / na
+            p1, p2 = v1 @ a, v2 @ a
+            if min(p1.max(), p2.max()) - max(p1.min(), p2.min()) <= tol:
+                separated = True
+                break
+        if not separated:
+            raise Invalid("two cubes overlap")
+    allv = np.vstack([v for _, v in cubes])
+    return float((allv.max(0) - allv.min(0)).max()), {}
diff --git a/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/instance.json b/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e951c2a0307014c30cbb4cb2b623f905710277cc
--- /dev/null
+++ b/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/instance.json
@@ -0,0 +1 @@
+{"n": 11, "tol": 1e-09, "direction": "minimize", "best_known": 2.894531152, "baseline": 3.0, "family": "ae_p35_cubes_in_cube", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/run.py b/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ae-p35-cubes-in-cube-n11/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-p35-cubes-in-cube-n11/tests/test.sh b/tasks/optimize-ae-p35-cubes-in-cube-n11/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ae-p35-cubes-in-cube-n11/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-ring-loading-m15/environment/Dockerfile b/tasks/optimize-ea-ring-loading-m15/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ea-ring-loading-m15/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-ring-loading-m15/environment/instance.json b/tasks/optimize-ea-ring-loading-m15/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e8ac599bbee8ba2c18fcdedf1e3a8a6102185512
--- /dev/null
+++ b/tasks/optimize-ea-ring-loading-m15/environment/instance.json
@@ -0,0 +1 @@
+{"pairs": 15, "direction": "maximize", "family": "ea_ring_loading_15", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-ring-loading-m15/solution/solve.sh b/tasks/optimize-ea-ring-loading-m15/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e1f121eb97ae027948dcce131a678b37c1040d6f
--- /dev/null
+++ b/tasks/optimize-ea-ring-loading-m15/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'
+{"pairs": [["4021070878350065/4503599627370496", "2144571633141253/36028797018963968"], ["4015980079781185/9007199254740992", "4991219174959807/9007199254740992"], ["4347848093698155/9007199254740992", "3801522565438597/9007199254740992"], ["1501199713179029/4503599627370496", "6004799828382933/9007199254740992"], ["73719639262837/281474976710656", "1072285570860771/4503599627370496"], ["45230154090605/140737488355328", "95507334264723/140737488355328"], ["415538270686595/562949953421312", "5145206110093983/36028797018963968"], ["4503599559277793/9007199254740992", "4503599559277793/9007199254740992"], ["5145206110093983/36028797018963968", "415538270686595/562949953421312"], ["95507334264723/140737488355328", "45230154090605/140737488355328"], ["1072285570860771/4503599627370496", "73719639262837/281474976710656"], ["6004799828382933/9007199254740992", "1501199713179029/4503599627370496"], ["3801522565438597/9007199254740992", "4347848093698155/9007199254740992"], ["4991219174959807/9007199254740992", "4015980079781185/9007199254740992"], ["2144571633141253/36028797018963968", "4021070878350065/4503599627370496"]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ea-ring-loading-m15/tests/check.py b/tasks/optimize-ea-ring-loading-m15/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..df8d98093f8e743e0e107cfa81dc20d09a34b880
--- /dev/null
+++ b/tasks/optimize-ea-ring-loading-m15/tests/check.py
@@ -0,0 +1,53 @@
+"""Ring loading problem with 15 pairs (EinsteinArena ring-loading-15, MIT).
+
+A(u, v) = min over z_i in {v_i, -u_i} of max_k |sum_{i<=k} z_i - sum_{i>k} z_i|  (maximize).
+Audit: upstream verifier parses exact rationals and enumerates all 2^15 adversary choices; sound.
+Re-implemented over a common denominator with Python integers (same exact value, faster)."""
+import math
+import re
+from fractions import Fraction
+
+from run import Invalid
+
+PAT = re.compile(r"^(?:0|[1-9]\d*)(?:(?:\.\d+)|(?:/[1-9]\d*))?$")
+
+
+def _rat(s):
+    if not isinstance(s, str) or not 1 <= len(s) <= 80 or PAT.fullmatch(s) is None:
+        raise Invalid("values must be nonnegative decimal or fraction strings such as '0.25' or '3/7'")
+    r = Fraction(s)
+    if r.numerator.bit_length() > 64 or r.denominator.bit_length() > 64:
+        raise Invalid("reduced numerator and denominator must fit in 64 bits")
+    return r
+
+
+def check(inst, ans):
+    k = inst["pairs"]
+    p = ans.get("pairs")
+    if not isinstance(p, list) or len(p) != k:
+        raise Invalid(f"pairs must be a list of exactly {k} pairs")
+    uv = []
+    for q in p:
+        if not isinstance(q, list) or len(q) != 2:
+            raise Invalid("each entry must be a pair [u, v]")
+        u, v = _rat(q[0]), _rat(q[1])
+        if u + v > 1:
+            raise Invalid("every pair must satisfy u + v <= 1")
+        uv.append((u, v))
+    den = 1
+    for u, v in uv:
+        for r in (u, v):
+            den = den * r.denominator // math.gcd(den, r.denominator)
+    U = [int(u * den) for u, _ in uv]
+    V = [int(v * den) for _, v in uv]
+    best = None
+    for mask in range(1 << k):
+        z = [-U[i] if mask >> i & 1 else V[i] for i in range(k)]
+        tot = sum(z)
+        pre, worst = 0, 0
+        for x in z:
+            pre += x
+            worst = max(worst, abs(2 * pre - tot))
+        if best is None or worst < best:
+            best = worst
+    return float(Fraction(best, den)), {"exact": str(Fraction(best, den))}
diff --git a/tasks/optimize-ea-ring-loading-m15/tests/instance.json b/tasks/optimize-ea-ring-loading-m15/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3ba98de863a2fed03f11490738cf7070b958889d
--- /dev/null
+++ b/tasks/optimize-ea-ring-loading-m15/tests/instance.json
@@ -0,0 +1 @@
+{"pairs": 15, "direction": "maximize", "best_known": 1.1190475684692773, "baseline": 0.5, "family": "ea_ring_loading_15", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-ring-loading-m15/tests/run.py b/tasks/optimize-ea-ring-loading-m15/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ea-ring-loading-m15/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-ring-loading-m15/tests/test.sh b/tasks/optimize-ea-ring-loading-m15/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ea-ring-loading-m15/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