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tasks/construct-ae-p38-factorial-factors-l2-s3/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p38-factorial-factors-l2-s3/environment/instance.json

@@ -0,0 +1 @@
+{"N": 106, "t": 30, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s3/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [360, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 36, 36, 36, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 41, 41, 42, 43, 43, 46, 46, 46, 46, 47, 47, 49, 49, 49, 49, 49, 49, 49, 49, 53, 53, 58, 58, 58, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l2-s3/tests/check.py

@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}

tasks/construct-ae-p38-factorial-factors-l2-s3/tests/instance.json

@@ -0,0 +1 @@
+{"N": 106, "t": 30, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s3/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p38-factorial-factors-l2-s3/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p38-factorial-factors-l2-s4/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p38-factorial-factors-l2-s4/environment/instance.json

@@ -0,0 +1 @@
+{"N": 110, "t": 31, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s4/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [186, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 43, 43, 46, 46, 46, 46, 47, 47, 53, 53, 58, 58, 58, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l2-s4/tests/check.py

@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}

tasks/construct-ae-p38-factorial-factors-l2-s4/tests/instance.json

@@ -0,0 +1 @@
+{"N": 110, "t": 31, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s4/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p38-factorial-factors-l2-s4/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p38-factorial-factors-l5-s7/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p38-factorial-factors-l5-s7/environment/instance.json

@@ -0,0 +1 @@
+{"N": 3059, "t": 980, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l5-s7/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [9800, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 980, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 981, 982, 982, 982, 982, 982, 982, 983, 983, 983, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 984, 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+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l5-s7/tests/check.py

@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}

tasks/construct-ae-p38-factorial-factors-l5-s7/tests/instance.json

@@ -0,0 +1 @@
+{"N": 3059, "t": 980, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l5-s7/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p38-factorial-factors-l5-s7/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p38-factorial-factors-l6-s2/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p38-factorial-factors-l6-s2/environment/instance.json

@@ -0,0 +1 @@
+{"N": 6230, "t": 2021, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s2/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [94987, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2021, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2022, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 2023, 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4034, 4034, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l6-s2/tests/check.py

@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}

tasks/construct-ae-p38-factorial-factors-l6-s2/tests/instance.json

@@ -0,0 +1 @@
+{"N": 6230, "t": 2021, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s2/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p38-factorial-factors-l6-s2/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p52-erdos-squarefree-l1-s4/environment/instance.json

@@ -0,0 +1 @@
+{"N": 54, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l1-s4/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32]}
+RLMATH_EOF

tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/check.py

@@ -0,0 +1,38 @@
+"""Erdos squarefree problem (AlphaEvolve problem 52): A in [1, N], |A| >= t, ab+1 NOT squarefree for all a, b in A
+(a = b included). The repo's problem page says "square-free"; the notebook and the Erdos problem ask for
+"never squarefree", which is what we check. Exact: for every pair we find a prime p with p^2 | ab+1."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _primes(n):
+    s = np.ones(n + 1, dtype=bool)
+    s[:2] = False
+    for i in range(2, int(n ** .5) + 1):
+        if s[i]:
+            s[i * i::i] = False
+    return np.nonzero(s)[0]
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    a = ans.get("A")
+    if not isinstance(a, list) or not (t <= len(a) <= 2 * t + 20):
+        raise Invalid(f"A must be a list of {t}..{2 * t + 20} integers")
+    int_list(a, None, 1, n, "A")
+    if len(set(a)) != len(a):
+        raise Invalid("A must consist of distinct integers")
+    x = np.array(sorted(a), dtype=np.int64)
+    iu, ju = np.triu_indices(len(x))
+    va, vb = x[iu], x[ju]
+    left = np.ones(len(iu), dtype=bool)  # pairs without a square divisor found yet
+    for p in _primes(int((n * n + 1) ** .5) + 1):
+        q = int(p) * int(p)
+        idx = np.nonzero(left)[0]
+        hit = ((va[idx] % q) * (vb[idx] % q) + 1) % q == 0
+        left[idx[hit]] = False
+        if not left.any():
+            return None, {"size": len(a)}
+    k = int(np.nonzero(left)[0][0])
+    raise Invalid(f"{int(va[k])}*{int(vb[k])}+1 = {int(va[k]) * int(vb[k]) + 1} is squarefree")

tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/instance.json

@@ -0,0 +1 @@
+{"N": 54, "t": 2, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p52-erdos-squarefree-l1-s4/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p52-erdos-squarefree-l2-s1/environment/instance.json

@@ -0,0 +1 @@
+{"N": 124, "t": 5, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l2-s1/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32, 57, 82, 107]}
+RLMATH_EOF

tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/check.py

@@ -0,0 +1,38 @@
+"""Erdos squarefree problem (AlphaEvolve problem 52): A in [1, N], |A| >= t, ab+1 NOT squarefree for all a, b in A
+(a = b included). The repo's problem page says "square-free"; the notebook and the Erdos problem ask for
+"never squarefree", which is what we check. Exact: for every pair we find a prime p with p^2 | ab+1."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _primes(n):
+    s = np.ones(n + 1, dtype=bool)
+    s[:2] = False
+    for i in range(2, int(n ** .5) + 1):
+        if s[i]:
+            s[i * i::i] = False
+    return np.nonzero(s)[0]
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    a = ans.get("A")
+    if not isinstance(a, list) or not (t <= len(a) <= 2 * t + 20):
+        raise Invalid(f"A must be a list of {t}..{2 * t + 20} integers")
+    int_list(a, None, 1, n, "A")
+    if len(set(a)) != len(a):
+        raise Invalid("A must consist of distinct integers")
+    x = np.array(sorted(a), dtype=np.int64)
+    iu, ju = np.triu_indices(len(x))
+    va, vb = x[iu], x[ju]
+    left = np.ones(len(iu), dtype=bool)  # pairs without a square divisor found yet
+    for p in _primes(int((n * n + 1) ** .5) + 1):
+        q = int(p) * int(p)
+        idx = np.nonzero(left)[0]
+        hit = ((va[idx] % q) * (vb[idx] % q) + 1) % q == 0
+        left[idx[hit]] = False
+        if not left.any():
+            return None, {"size": len(a)}
+    k = int(np.nonzero(left)[0][0])
+    raise Invalid(f"{int(va[k])}*{int(vb[k])}+1 = {int(va[k]) * int(vb[k]) + 1} is squarefree")

tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/instance.json

@@ -0,0 +1 @@
+{"N": 124, "t": 5, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p52-erdos-squarefree-l2-s1/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p52-erdos-squarefree-l2-s8/environment/instance.json

@@ -0,0 +1 @@
+{"N": 207, "t": 9, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l2-s8/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32, 57, 82, 107, 132, 157, 182, 207]}
+RLMATH_EOF

tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/check.py

@@ -0,0 +1,38 @@
+"""Erdos squarefree problem (AlphaEvolve problem 52): A in [1, N], |A| >= t, ab+1 NOT squarefree for all a, b in A
+(a = b included). The repo's problem page says "square-free"; the notebook and the Erdos problem ask for
+"never squarefree", which is what we check. Exact: for every pair we find a prime p with p^2 | ab+1."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _primes(n):
+    s = np.ones(n + 1, dtype=bool)
+    s[:2] = False
+    for i in range(2, int(n ** .5) + 1):
+        if s[i]:
+            s[i * i::i] = False
+    return np.nonzero(s)[0]
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    a = ans.get("A")
+    if not isinstance(a, list) or not (t <= len(a) <= 2 * t + 20):
+        raise Invalid(f"A must be a list of {t}..{2 * t + 20} integers")
+    int_list(a, None, 1, n, "A")
+    if len(set(a)) != len(a):
+        raise Invalid("A must consist of distinct integers")
+    x = np.array(sorted(a), dtype=np.int64)
+    iu, ju = np.triu_indices(len(x))
+    va, vb = x[iu], x[ju]
+    left = np.ones(len(iu), dtype=bool)  # pairs without a square divisor found yet
+    for p in _primes(int((n * n + 1) ** .5) + 1):
+        q = int(p) * int(p)
+        idx = np.nonzero(left)[0]
+        hit = ((va[idx] % q) * (vb[idx] % q) + 1) % q == 0
+        left[idx[hit]] = False
+        if not left.any():
+            return None, {"size": len(a)}
+    k = int(np.nonzero(left)[0][0])
+    raise Invalid(f"{int(va[k])}*{int(vb[k])}+1 = {int(va[k]) * int(vb[k]) + 1} is squarefree")

tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/instance.json

@@ -0,0 +1 @@
+{"N": 207, "t": 9, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p52-erdos-squarefree-l2-s8/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p65-imo2025-p6-tiling-l1-s0/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json