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tasks/construct-ae-p32-spherical-design-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

tasks/construct-ae-p32-spherical-design-l6-s0/environment/instance.json

@@ -0,0 +1 @@
+{"t": 21, "N": 234, "family": "ae_p32_spherical_designs", "subset": "construct"}

tasks/construct-ae-p32-spherical-design-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'
+{"points": [[-0.9596810424419001, -0.28105208802161075, 0.0046926108213612315], [-0.7595309788778035, 0.28634046819989534, -0.5840563572087804], [-0.813730818738408, -0.3764390859035123, 0.4428721816048601], [-0.9347893044111631, 0.08032069257362744, 0.34600222933239383], [-0.2683002097771996, 0.8777526186055353, -0.3969450062220663], [0.6342524888407759, 0.7323670273520217, -0.2477141853968897], [-0.6358105294073344, 0.10945414424587627, -0.7640449993306467], [-0.6563156541418083, -0.7540754527425505, 0.02489927106418534], [-0.6786431973610589, 0.7310891291870891, -0.07037112944967187], [-0.4811873975065912, 0.6311221524080541, 0.6083942120210042], [-0.45003670932430556, 0.03878241791959169, -0.8921675203238799], [0.6228527841744597, -0.6653027350879948, 0.41161472268440236], [0.6076207751533917, 0.7684224591058331, 0.20080816204461294], [-0.47346951581333485, -0.8807991463945936, -0.004413763251659698], [-0.4682630830342496, -0.8296214355564143, 0.30406900324198416], [0.08447334066555273, -0.9784197703126144, -0.1885709621819129], [0.2965512007803297, 0.8339510970983991, -0.4653847364967197], [0.16956192196161413, 0.6582166746269409, 0.7334845355314148], [-0.9267349967770295, 0.16529078275522413, -0.33740362014187747], [0.9155363444953903, 0.35972750142374055, 0.17997034930079664], [-0.2627253443826455, 0.9008719953020612, 0.3455503458246037], [0.8529106035057721, -0.5217803533335451, 0.016993095731516174], [0.8154965487747823, -0.21995267089048656, -0.5353374650671859], [-0.006640233092314377, 0.5373492646953814, 0.8433336676759755], [-0.7483063574487001, 0.6182553747512798, -0.24041191108805907], [0.3095549491636869, -0.17792809627177064, 0.934086358965471], [0.6412214881552839, 0.5920754635639538, -0.4881410130008052], [-0.6311678912294041, 0.519087959533268, -0.5763460621437569], [-0.5221448195065524, -0.5317466636922998, -0.6667910265702275], [-0.5249865882396665, -0.6938030914144447, -0.49297703041037794], [-0.40160643749158387, 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[0.16926310288516716, -0.9584900993703757, 0.2294487555221268], [0.897204853657943, 0.12553490960663766, 0.4233963120324529], [0.053402856415211544, 0.7989620978572675, 0.599005593558366], [-0.21439356187986022, 0.9765274335157839, 0.02072612398744471], [-0.7011707501688357, -0.61941692916902, -0.35310373400247924], [-0.33731618237682154, -0.7383023287929298, -0.5840611820739874], [0.8554557563450582, 0.03283817503637466, -0.516833728772015], [-0.5634559271627959, 0.25354884099504926, 0.7862762894652117], [0.8968492815056062, -0.31262966307002854, -0.3129282026785035], [0.23461921803172875, -0.5162143097990478, 0.8236969156727934], [-0.8204680841151809, 0.48423123492129905, 0.30389510373640133], [0.10616736913570804, -0.38341718225424076, 0.91745286204961], [0.46062712280394524, -0.5594614288453051, 0.6890758763530536], [-0.1284525648298974, -0.3901420195240853, -0.9117505926459765], [-0.9981858386470472, -0.03776949080309614, -0.04688813377567692], [0.8018003081854409, -0.42333591045686064, 0.4217854581554381], [-0.804564241947829, -0.5709043128795017, -0.1635379042133632], [-0.08185104459845471, 0.1683038448200658, -0.982331014636576], [-0.7694039392163629, -0.18319863207708384, 0.6119279692279385], [0.9771855594361627, 0.10062464178253448, -0.18703760021870053], [0.5544396573972501, 0.28994491883968493, -0.7800824381719336], [-0.758345834263166, 0.6333345963987281, 0.1542688713258864], [-0.008491374376512522, -0.9134942753168819, 0.406762959872802], [-0.33408495344564276, -0.5264650528017564, -0.7818067485380684], [-0.8490007870709428, -0.37197966409990957, -0.3752716256913624], [-0.7730552646309329, -0.5612335110585454, 0.29563914472088426], [0.09753474452626759, 0.5522652919731552, -0.8279432473859555], [0.39648818965076155, -0.905216710214534, -0.15290462064907687], [-0.1569394746409091, -0.11785032825512229, 0.9805515292066987], [0.7163296125291237, -0.39081821229481717, -0.5780423956359592], [0.13548268481111322, 0.7860934232611066, 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[0.5439160463838949, 0.15421703997322497, 0.8248469185661116], [0.8832364379525733, -0.4070790706222847, 0.23276603045579253], [-0.14837564601727582, -0.987793454320691, -0.04742108465812609], [0.16844527590972794, -0.08099813714642741, -0.9823774685946864], [-0.5657172345739175, 0.8193680331828437, 0.09273638285008484], [-0.30564437074087397, 0.6990892393320208, -0.6464176313225001], [-0.33674237640441124, -0.4062997510358398, 0.8494263265532358], [0.21057631941470467, -0.37836730611748437, -0.9013854865500964], [-0.11220515108413405, 0.8641036629287703, 0.4906473925165289], [0.5858354735579581, -0.31634262021302556, 0.74613949403438], [-0.6249590778828292, -0.0718174049830824, 0.777347034028779], [0.30451610664627105, 0.9365585299609991, 0.17357436662793618], [-0.769983500323991, -0.24317770154146764, -0.5899067847565609], [0.9128149561032868, 0.22491928616326284, -0.3408521242796691], [0.7027033101604571, -0.10855427994511252, -0.703152918073398], [-0.020760184088504045, 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[0.8984870448276885, 0.4081257483950952, -0.1617232320161543], [-0.36140760751015083, 0.2170869474020804, 0.9067843175206743], [-0.8486202896097377, 0.0979673673356518, -0.5198519010256732], [-0.1278495110967629, 0.6742093541096598, 0.7273900256006773], [-0.5184273131253924, 0.8234019435730728, -0.23074306127308053], [-0.9650569845529168, -0.09810278400656879, -0.2429832511425262], [0.934683066264177, -0.35157559207303596, -0.05255633831889993], [-0.7077898258883238, -0.4704338591434147, -0.5269967234626892], [-0.3546125636716822, -0.3278751889086909, -0.8756413593385636], [-0.16926310288516747, 0.9584900993703757, -0.22944875552212646], [-0.8972048536579433, -0.12553490960663727, -0.42339631203245265], [-0.0534028564152116, -0.7989620978572671, -0.5990055935583666], [0.21439356187985967, -0.976527433515784, -0.020726123987444584], [0.7011707501688349, 0.6194169291690204, 0.35310373400247974], [0.3373161823768212, 0.7383023287929297, 0.5840611820739878], [-0.8554557563450577, -0.0328381750363741, 0.516833728772016], [0.5634559271627959, -0.25354884099504865, -0.7862762894652118], [-0.8968492815056059, 0.3126296630700283, 0.31292820267850424], [-0.23461921803172814, 0.5162143097990476, -0.8236969156727937], [0.8204680841151808, -0.48423123492129955, -0.303895103736401], [-0.1061673691357072, 0.3834171822542412, -0.9174528620496099], [-0.46062712280394497, 0.559461428845305, -0.6890758763530538], [0.12845256482989664, 0.3901420195240855, 0.9117505926459765], [0.9981858386470472, 0.03776949080309688, 0.046888133775677486], [-0.8018003081854406, 0.4233359104568611, -0.42178545815543844], [0.8045642419478288, 0.570904312879502, 0.16353790421336376], [0.08185104459845317, -0.16830384482006544, 0.9823310146365762], [0.7694039392163625, 0.18319863207708306, -0.611927969227939], [-0.9771855594361627, -0.10062464178253405, 0.18703760021870042], [-0.5544396573972512, -0.289944918839686, 0.7800824381719323], [0.758345834263166, -0.6333345963987282, -0.15426887132588604], [0.00849137437651162, 0.9134942753168819, -0.40676295987280187], [0.33408495344564276, 0.5264650528017565, 0.7818067485380683], [0.849000787070943, 0.3719796640999098, 0.37527162569136213], [0.7730552646309327, 0.5612335110585451, -0.2956391447208852], [-0.09753474452626576, -0.5522652919731545, 0.8279432473859561], [-0.39648818965076205, 0.9052167102145339, 0.15290462064907656], [0.15693947464090713, 0.11785032825512202, -0.9805515292066991], [-0.7163296125291233, 0.39081821229481706, 0.5780423956359597], [-0.13548268481111353, -0.786093423261106, 0.6030767546689295], [-0.5914606174806544, -0.32861740929478245, -0.7363320828795854], [-0.29537992934537166, 0.7383837478422289, 0.6062508872260617], [-0.0631363934443951, 0.661447958009296, -0.7473288397139288], [0.10595853244500836, -0.8106792651714273, 0.575822818602402], [0.7403016482988082, 0.04845379072284902, 0.670526434744115], [0.39589856208378216, -0.9100009927420026, 0.12313619187129096], [0.45922932850265347, 0.5350173036318514, -0.7091296839489272], [0.173117223441247, 0.9436238213650995, -0.2821427133567697], [0.11188122244125702, 0.047329593794752316, 0.9925938250947735], [0.6683760509590285, -0.565041031475324, -0.48373762232610773], [-0.9712144606432572, 0.1911485894897237, -0.1421431960155527], [-0.4427352872585862, 0.02275450780200047, 0.8963635968683389], [0.8140656997372471, 0.5794002472143348, -0.03990476211273634], [0.33591940563458067, 0.9317011148077223, -0.13817085649353636], [0.06923545147783511, 0.9458561272097492, 0.3171161283795496], [-0.5439160463838951, -0.1542170399732247, -0.8248469185661114], [-0.8832364379525734, 0.4070790706222843, -0.23276603045579286], [0.14837564601727615, 0.9877934543206909, 0.047421084658126215], [-0.1684452759097269, 0.08099813714642701, 0.9823774685946867], [0.5657172345739174, -0.8193680331828438, -0.09273638285008516], [0.3056443707408742, -0.6990892393320212, 0.6464176313224997], [0.33674237640441157, 0.4062997510358407, -0.8494263265532352], [-0.21057631941470442, 0.3783673061174838, 0.9013854865500968], [0.11220515108413351, -0.8641036629287699, -0.49064739251652956], [-0.5858354735579577, 0.316342620213026, -0.74613949403438], [0.6249590778828292, 0.07181740498308149, -0.7773470340287791], [-0.3045161066462703, -0.9365585299609994, -0.17357436662793585], [0.7699835003239904, 0.24317770154146773, 0.5899067847565614], [-0.9128149561032868, -0.22491928616326198, 0.3408521242796696], [-0.7027033101604563, 0.10855427994511174, 0.7031529180733989], [0.020760184088504535, -0.24789364919648157, -0.9685647905249618], [-0.4714908883810563, -0.7023783523013324, 0.5332550912950645], [0.4358909668539541, -0.7691980152869542, 0.46726168074616986], [-0.6175210102440782, 0.7194187886331092, 0.31796919421353204], [0.28258906393499733, 0.1383212542658797, 0.9492158087403811], [0.30845294738623813, -0.5188463293337621, -0.7972799168332437], [0.44816421533186007, -0.7947501233527184, -0.4092933880809911], [0.9823715121471721, -0.146985163876001, -0.11550573025622408], [-0.13128252284828998, -0.3485470596677601, 0.9280516399379655], [0.3735569086981984, 0.17931860402404787, -0.9101099242480067]]}
+RLMATH_EOF

tasks/construct-ae-p32-spherical-design-l6-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)}

tasks/construct-ae-p32-spherical-design-l6-s0/tests/instance.json

@@ -0,0 +1 @@
+{"t": 21, "N": 234, "family": "ae_p32_spherical_designs", "subset": "construct"}

tasks/construct-ae-p32-spherical-design-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()

tasks/construct-ae-p32-spherical-design-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

tasks/construct-ae-p38-factorial-factors-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

tasks/construct-ae-p38-factorial-factors-l1-s9/environment/instance.json

@@ -0,0 +1 @@
+{"N": 59, "t": 17, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-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'
+{"factors": [17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 26, 26, 26, 26, 29, 29, 31, 37, 41, 43, 47, 53, 59]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l1-s9/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-l1-s9/tests/instance.json

@@ -0,0 +1 @@
+{"N": 59, "t": 17, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-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()

tasks/construct-ae-p38-factorial-factors-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

tasks/construct-ae-p38-factorial-factors-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

tasks/construct-ae-p38-factorial-factors-l5-s1/environment/instance.json

@@ -0,0 +1 @@
+{"N": 1725, "t": 546, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-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'
+{"factors": [546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 546, 547, 547, 547, 548, 548, 548, 548, 548, 548, 548, 548, 548, 548, 548, 548, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 549, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 550, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 551, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 552, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 553, 554, 554, 554, 554, 554, 554, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 555, 556, 556, 556, 556, 556, 556, 556, 556, 556, 556, 556, 556, 557, 557, 557, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 558, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 559, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 560, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 561, 562, 562, 562, 562, 562, 562, 563, 563, 563, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 564, 565, 565, 565, 565, 565, 565, 565, 565, 565, 565, 565, 565, 565, 565, 565, 566, 566, 566, 566, 566, 566, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 567, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 568, 569, 569, 569, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 570, 571, 571, 571, 573, 573, 573, 573, 573, 573, 573, 573, 573, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 574, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 576, 577, 577, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 578, 579, 579, 579, 579, 579, 579, 579, 579, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 582, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 583, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 584, 586, 586, 586, 586, 586, 587, 587, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 590, 591, 591, 591, 591, 591, 591, 591, 591, 592, 593, 593, 596, 596, 596, 596, 596, 596, 596, 596, 596, 596, 596, 597, 597, 597, 597, 597, 597, 597, 597, 599, 599, 601, 601, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 603, 604, 604, 604, 604, 604, 604, 604, 604, 604, 604, 604, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 606, 607, 607, 613, 613, 614, 614, 614, 614, 614, 617, 617, 618, 618, 618, 618, 618, 618, 618, 618, 618, 618, 618, 618, 618, 618, 618, 618, 619, 619, 622, 622, 622, 622, 622, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 623, 626, 626, 626, 626, 626, 628, 628, 628, 628, 628, 628, 628, 628, 628, 628, 631, 631, 633, 633, 633, 633, 633, 633, 633, 633, 634, 634, 634, 634, 634, 635, 635, 635, 635, 635, 635, 635, 635, 635, 635, 635, 635, 635, 637, 637, 640, 641, 641, 642, 642, 642, 642, 642, 642, 642, 642, 642, 642, 642, 642, 642, 642, 642, 642, 643, 643, 647, 647, 652, 652, 652, 652, 652, 652, 652, 652, 652, 652, 653, 653, 654, 654, 654, 654, 654, 654, 654, 654, 654, 654, 654, 654, 654, 654, 654, 655, 655, 655, 655, 655, 655, 655, 655, 655, 655, 655, 655, 655, 659, 659, 661, 661, 662, 662, 662, 662, 662, 668, 668, 668, 668, 668, 668, 668, 668, 668, 668, 669, 669, 669, 669, 669, 669, 669, 673, 673, 674, 674, 674, 674, 674, 677, 677, 681, 681, 681, 681, 681, 681, 681, 683, 683, 687, 687, 687, 687, 687, 687, 687, 691, 691, 692, 692, 692, 692, 692, 692, 692, 692, 692, 694, 694, 694, 694, 698, 698, 698, 698, 699, 699, 699, 699, 699, 699, 699, 701, 701, 706, 706, 706, 706, 709, 709, 716, 716, 716, 716, 716, 716, 716, 716, 716, 717, 717, 717, 717, 717, 717, 717, 718, 718, 718, 718, 719, 719, 723, 723, 723, 723, 723, 723, 723, 724, 724, 724, 724, 724, 724, 724, 724, 724, 727, 727, 733, 733, 734, 734, 734, 734, 739, 739, 743, 743, 746, 746, 746, 746, 751, 751, 753, 753, 753, 753, 753, 753, 757, 757, 758, 758, 758, 758, 761, 761, 766, 766, 766, 766, 769, 769, 771, 771, 771, 771, 771, 771, 773, 773, 778, 778, 778, 778, 787, 787, 789, 789, 789, 789, 789, 789, 794, 794, 794, 794, 797, 797, 802, 802, 802, 802, 807, 807, 807, 807, 807, 807, 809, 809, 811, 811, 813, 813, 813, 813, 813, 813, 818, 818, 818, 818, 821, 821, 823, 823, 827, 827, 829, 829, 838, 838, 838, 838, 839, 839, 842, 842, 842, 842, 853, 853, 857, 857, 859, 859, 862, 862, 862, 862, 863, 866, 866, 866, 877, 878, 878, 878, 881, 883, 886, 886, 886, 887, 898, 898, 898, 907, 911, 914, 914, 914, 919, 922, 922, 922, 926, 926, 926, 929, 934, 934, 934, 937, 941, 947, 953, 958, 958, 958, 967, 971, 974, 974, 974, 977, 982, 982, 982, 983, 991, 997, 998, 998, 998, 1006, 1006, 1006, 1009, 1013, 1018, 1018, 1018, 1019, 1021, 1031, 1033, 1039, 1042, 1042, 1042, 1046, 1046, 1046, 1049, 1051, 1061, 1063, 1069, 1082, 1082, 1082, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l5-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)}

tasks/construct-ae-p38-factorial-factors-l5-s1/tests/instance.json

@@ -0,0 +1 @@
+{"N": 1725, "t": 546, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-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()

tasks/construct-ae-p38-factorial-factors-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

tasks/construct-ae-p38-factorial-factors-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

tasks/construct-ae-p38-factorial-factors-l5-s6/environment/instance.json

@@ -0,0 +1 @@
+{"N": 2989, "t": 956, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-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'
+{"factors": [2868, 956, 956, 956, 956, 956, 956, 956, 956, 956, 956, 956, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 957, 958, 958, 958, 958, 958, 958, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 959, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 960, 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2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l5-s6/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-s6/tests/instance.json

@@ -0,0 +1 @@
+{"N": 2989, "t": 956, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-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()

tasks/construct-ae-p38-factorial-factors-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

tasks/construct-ae-p52-erdos-squarefree-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

tasks/construct-ae-p52-erdos-squarefree-l1-s2/environment/instance.json

@@ -0,0 +1 @@
+{"N": 91, "t": 4, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l1-s2/solution/solve.sh

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

tasks/construct-ae-p52-erdos-squarefree-l1-s2/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-s2/tests/instance.json

@@ -0,0 +1 @@
+{"N": 91, "t": 4, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-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()

tasks/construct-ae-p52-erdos-squarefree-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

tasks/construct-ae-p52-erdos-squarefree-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

tasks/construct-ae-p52-erdos-squarefree-l1-s5/environment/instance.json

@@ -0,0 +1 @@
+{"N": 80, "t": 3, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l1-s5/solution/solve.sh

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

tasks/construct-ae-p52-erdos-squarefree-l1-s5/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-s5/tests/instance.json

@@ -0,0 +1 @@
+{"N": 80, "t": 3, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-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()

tasks/construct-ae-p52-erdos-squarefree-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

tasks/construct-mc-all-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

tasks/construct-mc-all-interval-l1-s0/environment/instance.json

@@ -0,0 +1 @@
+{"n": 7, "fixed": [], "family": "mc_all_interval", "subset": "construct"}

tasks/construct-mc-all-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'
+{"x": [0, 6, 1, 5, 2, 4, 3]}
+RLMATH_EOF

tasks/construct-mc-all-interval-l1-s0/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, {}

tasks/construct-mc-all-interval-l1-s0/tests/instance.json

@@ -0,0 +1 @@
+{"n": 7, "fixed": [], "family": "mc_all_interval", "subset": "construct"}

tasks/construct-mc-all-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()

tasks/construct-mc-all-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

tasks/construct-mc-all-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