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tasks/construct-ae-p32-spherical-design-l5-s0/environment/Dockerfile

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

tasks/construct-ae-p32-spherical-design-l5-s0/environment/instance.json

@@ -0,0 +1 @@
+{"t": 19, "N": 198, "family": "ae_p32_spherical_designs", "subset": "construct"}

tasks/construct-ae-p32-spherical-design-l5-s0/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"points": [[0.2527759326534977, -0.9566791840084274, -0.14446199069694396], [-0.9071773294756267, 0.015962244615743904, 0.4204455965190948], [-0.616471714044581, -0.20797033654468083, -0.7594148832492214], [-0.6669229800600651, 0.5278085911769907, 0.5259580113921283], [-0.6636953921393339, 0.3035315017983519, 0.6836498035317884], [0.31817569095244375, -0.44817056008107137, -0.8354085101096073], [0.2326406142491498, -0.24753928264553166, 0.9405331722747018], [-0.3319418441602898, -0.9192339146644295, 0.21171589979539565], [-0.989901155923375, 0.1415575057627732, -0.007561353304026967], [-0.6940970558319106, 0.6760457881341818, -0.2473688934193353], [-0.08911173314110848, 0.9893781402186134, -0.11484770208474272], [0.2735331014272552, 0.7929939249348656, 0.5443714517128755], [0.32114904661040294, -0.6978190818804829, -0.6402435621110993], [0.21606086388133405, 0.07253477182773413, -0.9736818833555189], [0.8306685695380677, -0.4996653571337416, 0.2456099722364527], [-0.7035966501809142, 0.24681134255272794, -0.6663601991727268], [0.4543377579132473, 0.7882960418129363, -0.4149295749840217], [-0.5919086482263421, -0.7718702467816513, 0.23207859506662187], [-0.2249564240346492, 0.21451439366744082, 0.9504620887731574], [-0.8011025199330664, 0.5981993327173948, 0.019806839559972398], [0.09650672442045342, -0.7614513104034255, -0.6409979360548214], [-0.4266304636681133, -0.9044257167599649, -0.0007552043131550039], [0.5235350644098383, -0.8265605597363971, 0.20666077862439322], [-0.9261324157660965, -0.33800494493485767, 0.16742582138618242], [0.9465137815640404, -0.2113845759594981, -0.24377904412759377], [0.12400589991688678, 0.888531738466774, 0.44173961393904376], [-0.12939512081224766, -0.9899593659558957, 0.056897772066969186], [0.4100400904645589, -0.5310449354787828, 0.7415243763452094], [0.6121495060822961, 0.7885835096084429, 0.058386904155225586], [-0.7078016213647221, 0.6476889699819802, 0.281985572249986], [-0.1194170666444374, 0.8959375342669865, 0.4278264822163659], [0.6086077390900811, -0.0016517171884538452, -0.7934695279278147], [-0.308138028628882, -0.5828648450548394, -0.7518773355487612], [-0.9126931985878572, 0.10092396281459982, -0.3959867156626136], [-0.9075848215163033, 0.4135334997082516, 0.07266248256332415], [-0.7874335947163372, -0.2277029010667165, -0.5727998976587794], [0.35617243852259417, -0.7157128445966555, 0.6007464674188543], [0.49712463559744313, -0.3049878550572983, -0.8123112118822796], [0.6355129615942835, -0.7707274245027393, -0.04585316526737344], [-0.823582504518911, 0.26161188229867044, 0.5032604507514024], [-0.4201349780087122, 0.05916594126653794, 0.9055307789620757], [-0.2253379394752148, -0.8181432292461877, 0.5290221824004023], [-0.9830920749470742, -0.18146865560772074, -0.024476503185355214], [-0.8033875419800142, -0.47840137728962945, 0.3545427754146127], [0.5398038974785598, 0.2398736117536441, -0.8068905766280943], [0.18478396225343577, 0.07036047252750102, 0.9802572576623075], [0.404307861510866, 0.11963473301407422, 0.9067649550887824], [0.6778781841518116, -0.4876071985105816, 0.5502003157139269], [-0.8358098645616144, 0.43872985822206406, 0.330057543173828], [-0.14984441916540825, -0.6995632380288731, 0.6986829939561573], [0.0963038700715653, 0.6802852343346977, 0.726593121736935], [-0.33744432759092335, -0.2667688050118576, 0.9027545239151422], [-0.3038737867589575, 0.9408790043663904, -0.14969108478223306], [0.07727695919431263, 0.43760558542338684, 0.8958401772548134], [0.5002309144546911, 0.4114399071385071, 0.7618964726507665], [0.21299187911141404, 0.9597274541901863, 0.18318753534619306], [-0.033254368176864536, 0.981169112540872, 0.190266443685993], [-0.5550674692406724, -0.7413685764233726, -0.3771905864185068], [0.44738173345883014, 0.6394806495135349, -0.6252312240004652], [-0.5132747276097992, 0.35942130959293683, -0.7793364974178899], [-0.908273120300105, -0.36781789712904284, -0.1993738535813558], [-0.9768756076125094, -0.025557939745362766, -0.21227538474270402], [0.41914159368881443, -0.1457417138413139, 0.896147129263157], [0.9819720031081934, 0.051074934296201316, -0.1819954290588663], [-0.6456468813502989, -0.40889643816847426, 0.6449370569720492], [-0.730168261847292, -0.6539132126792329, -0.19812071995232802], [0.9002405973380224, 0.2173386052333339, 0.37726754111599575], [-0.658609660927967, -0.5896536350330548, 0.4674846577425333], [-0.2856532096842435, -0.338834354695996, -0.8964337810875032], [0.45615708893873547, -0.885109791409485, -0.09220285983632291], [0.7541965839668618, 0.6406478050061248, -0.14407603087797236], [0.8073817596027736, -0.02094710596910639, 0.5896574539614063], [0.1221387974181635, 0.9305767959068604, -0.3451216323051431], [0.11181964695244331, -0.9155430576224537, 0.386364175609954], [-0.8860359794901508, -0.23651242737783115, 0.3987506924693364], [-0.021795294178684615, 0.2209727617537001, 0.9750364114814416], [0.14306901425289, 0.5109208299293874, -0.8476385802362776], [-0.020096912554200586, 0.08803980061814769, -0.9959142069540456], [0.4026370219134751, 0.8707978285727904, 0.28212509696508903], [0.4959527301737703, -0.5845756082399554, -0.6421076605087885], [0.1788190994230974, -0.45893101861561447, 0.8702907846426658], [-0.36556095187326415, 0.8407639172119178, -0.39935100598343864], [-0.11794637205580971, 0.643753088529289, -0.7560890253983812], [0.8624215507412237, 0.5060954097355691, 0.009823698982011181], [0.9398678224326774, -0.293004688620821, 0.1754899678097663], [-0.3526844893273538, 0.8468217430548174, 0.3981288566249682], [0.6754400632233013, 0.4675915503976405, 0.5702094904415689], [0.08877249205595145, -0.8062034468725888, 0.5849405498894165], [0.5310150431668822, -0.763080439370121, -0.3684172457705761], [-0.3919840334282161, -0.4962128757093599, 0.7746749637864867], [0.7726359079275378, 0.5087840035682575, 0.379700660381365], [-0.6194288470162496, 0.03579306714779061, -0.7842364183256688], [0.05985044578163838, 0.33165256956803507, -0.9415011934345378], [-0.12824565900342727, 0.5369778154222951, 0.8337912668594438], [-0.5807511705169693, 0.6554449759612124, -0.482824980122586], [-0.49272174249670225, -0.6488509094724098, -0.5798428940220274], [0.8340826825905289, -0.3325409293775602, 0.44013930623303293], [-0.7684859294902381, 0.032294968844228396, 0.6390511803939299], [0.7643670735167464, 0.22568566431123574, -0.603994170375709], [-0.2527759326534968, 0.9566791840084277, 0.14446199069694388], [0.9071773294756266, -0.01596224461574326, -0.4204455965190951], [0.6164717140445807, 0.20797033654468125, 0.7594148832492216], [0.6669229800600647, -0.5278085911769923, -0.5259580113921275], [0.6636953921393342, -0.3035315017983534, -0.6836498035317875], [-0.3181756909524427, 0.448170560081072, 0.8354085101096074], [-0.23264061424914967, 0.24753928264553246, -0.9405331722747016], [0.3319418441602907, 0.919233914664429, -0.21171589979539662], [0.989901155923375, -0.14155750576277343, 0.007561353304025757], [0.694097055831911, -0.676045788134181, 0.2473688934193365], [0.08911173314110969, -0.9893781402186133, 0.1148477020847424], [-0.27353310142725545, -0.7929939249348655, -0.5443714517128756], [-0.3211490466104028, 0.6978190818804832, 0.6402435621110991], [-0.21606086388133558, -0.07253477182773363, 0.9736818833555185], [-0.8306685695380671, 0.4996653571337424, -0.2456099722364526], [0.7035966501809146, -0.24681134255272658, 0.6663601991727272], [-0.45433775791324676, -0.7882960418129371, 0.414929574984021], [0.5919086482263427, 0.7718702467816507, -0.2320785950666222], [0.22495642403464883, -0.21451439366744066, -0.9504620887731575], [0.8011025199330667, -0.5981993327173944, -0.019806839559971607], [-0.09650672442045395, 0.7614513104034264, 0.6409979360548201], [0.4266304636681138, 0.9044257167599646, 0.0007552043131546822], [-0.5235350644098381, 0.8265605597363976, -0.20666077862439178], [0.9261324157660966, 0.3380049449348574, -0.16742582138618228], [-0.9465137815640406, 0.21138457595949808, 0.2437790441275926], [-0.12400589991688762, -0.8885317384667737, -0.44173961393904404], [0.1293951208122493, 0.9899593659558954, -0.05689777206696995], [-0.41004009046456014, 0.5310449354787834, -0.7415243763452083], [-0.6121495060822965, -0.7885835096084427, -0.058386904155225246], [0.7078016213647216, -0.6476889699819816, -0.28198557224998455], [0.1194170666444368, -0.8959375342669857, -0.4278264822163674], [-0.608607739090081, 0.0016517171884530132, 0.7934695279278148], [0.30813802862888084, 0.5828648450548393, 0.7518773355487617], [0.9126931985878572, -0.10092396281459975, 0.39598671566261373], [0.9075848215163032, -0.4135334997082516, -0.07266248256332514], [0.7874335947163371, 0.2277029010667176, 0.5727998976587794], [-0.35617243852259384, 0.7157128445966562, -0.6007464674188535], [-0.49712463559744247, 0.30498785505729914, 0.8123112118822797], [-0.635512961594283, 0.7707274245027396, 0.045853165267375116], [0.8235825045189108, -0.2616118822986709, -0.5032604507514022], [0.42013497800871114, -0.059165941266537896, -0.9055307789620761], [0.22533793947521502, 0.8181432292461873, -0.5290221824004026], [0.9830920749470742, 0.18146865560772032, 0.024476503185355113], [0.803387541980014, 0.4784013772896299, -0.3545427754146124], [-0.5398038974785595, -0.23987361175364486, 0.8068905766280943], [-0.18478396225343693, -0.07036047252750098, -0.9802572576623073], [-0.40430786151086634, -0.1196347330140753, -0.9067649550887821], [-0.6778781841518111, 0.4876071985105826, -0.5502003157139266], [0.8358098645616138, -0.4387298582220654, -0.3300575431738279], [0.14984441916540825, 0.6995632380288727, -0.6986829939561577], [-0.09630387007156574, -0.6802852343346971, -0.7265931217369357], [0.33744432759092347, 0.2667688050118574, -0.9027545239151422], [0.30387378675895843, -0.94087900436639, 0.1496910847822334], [-0.07727695919431204, -0.43760558542338723, -0.8958401772548132], [-0.5002309144546915, -0.41143990713850703, -0.7618964726507663], [-0.21299187911141224, -0.9597274541901867, -0.18318753534619295], [0.03325436817686638, -0.9811691125408718, -0.19026644368599416], [0.5550674692406736, 0.7413685764233714, 0.3771905864185075], [-0.4473817334588305, -0.6394806495135353, 0.6252312240004645], [0.5132747276097999, -0.3594213095929372, 0.7793364974178892], [0.9082731203001051, 0.3678178971290424, 0.1993738535813559], [0.9768756076125096, 0.02555793974536197, 0.21227538474270327], [-0.41914159368881376, 0.145741713841313, -0.8961471292631574], [-0.9819720031081937, -0.051074934296201184, 0.18199542905886554], [0.6456468813502991, 0.40889643816847365, -0.6449370569720493], [0.7301682618472926, 0.6539132126792325, 0.19812071995232772], [-0.9002405973380221, -0.2173386052333345, -0.37726754111599625], [0.6586096609279669, 0.589653635033054, -0.46748465774253417], [0.28565320968424435, 0.3388343546959951, 0.8964337810875033], [-0.4561570889387348, 0.8851097914094853, 0.0922028598363237], [-0.754196583966862, -0.6406478050061246, 0.1440760308779729], [-0.8073817596027738, 0.020947105969107437, -0.589657453961406], [-0.12213879741816341, -0.9305767959068605, 0.34512163230514276], [-0.11181964695244383, 0.9155430576224537, -0.3863641756099539], [0.8860359794901503, 0.2365124273778322, -0.39875069246933675], [0.021795294178683994, -0.22097276175369854, -0.9750364114814419], [-0.14306901425288976, -0.510920829929387, 0.8476385802362778], [0.020096912554199767, -0.08803980061814638, 0.9959142069540458], [-0.40263702191347434, -0.8707978285727911, -0.2821250969650881], [-0.49595273017377034, 0.5845756082399551, 0.6421076605087888], [-0.1788190994230981, 0.45893101861561525, -0.8702907846426652], [0.36556095187326376, -0.8407639172119177, 0.39935100598343914], [0.11794637205580955, -0.6437530885292885, 0.7560890253983816], [-0.8624215507412235, -0.5060954097355697, -0.00982369898201106], [-0.9398678224326774, 0.29300468862082085, -0.17548996780976683], [0.35268448932735325, -0.8468217430548174, -0.3981288566249687], [-0.6754400632233021, -0.46759155039763967, -0.5702094904415687], [-0.08877249205595086, 0.8062034468725892, -0.5849405498894161], [-0.5310150431668829, 0.7630804393701205, 0.3684172457705766], [0.3919840334282165, 0.4962128757093591, -0.774674963786487], [-0.7726359079275372, -0.508784003568258, -0.3797006603813651], [0.6194288470162492, -0.035793067147790125, 0.7842364183256691], [-0.059850445781638735, -0.3316525695680343, 0.941501193434538], [0.1282456590034283, -0.5369778154222943, -0.8337912668594442], [0.5807511705169689, -0.655444975961212, 0.4828249801225871], [0.492721742496701, 0.64885090947241, 0.5798428940220283], [-0.8340826825905289, 0.3325409293775607, -0.44013930623303266], [0.7684859294902381, -0.03229496884422952, -0.6390511803939298], [-0.7643670735167466, -0.2256856643112364, 0.6039941703757086]]}
+RLMATH_EOF

tasks/construct-ae-p32-spherical-design-l5-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-l5-s0/tests/instance.json

@@ -0,0 +1 @@
+{"t": 19, "N": 198, "family": "ae_p32_spherical_designs", "subset": "construct"}

tasks/construct-ae-p32-spherical-design-l5-s0/tests/run.py

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

tasks/construct-ae-p32-spherical-design-l5-s0/tests/test.sh

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

tasks/construct-ae-p38-factorial-factors-l2-s0/environment/Dockerfile

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

tasks/construct-ae-p38-factorial-factors-l2-s0/environment/instance.json

@@ -0,0 +1 @@
+{"N": 86, "t": 24, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s0/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [288, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 31, 31, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 37, 37, 38, 38, 38, 38, 41, 41, 43, 43, 46, 46, 46, 47, 53, 59, 61, 67, 71, 73, 79, 83]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l2-s0/tests/check.py

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

tasks/construct-ae-p38-factorial-factors-l2-s0/tests/instance.json

@@ -0,0 +1 @@
+{"N": 86, "t": 24, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s0/tests/run.py

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

tasks/construct-ae-p38-factorial-factors-l2-s0/tests/test.sh

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

tasks/construct-ae-p38-factorial-factors-l2-s7/environment/Dockerfile

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

tasks/construct-ae-p38-factorial-factors-l2-s7/environment/instance.json

@@ -0,0 +1 @@
+{"N": 134, "t": 39, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s7/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [585, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 47, 47, 51, 51, 51, 51, 51, 51, 51, 53, 53, 56, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 59, 59, 61, 61, 62, 62, 62, 62, 67, 67, 71, 73, 74, 74, 74, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l2-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-l2-s7/tests/instance.json

@@ -0,0 +1 @@
+{"N": 134, "t": 39, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s7/tests/run.py

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

tasks/construct-ae-p38-factorial-factors-l2-s7/tests/test.sh

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

tasks/construct-ae-p38-factorial-factors-l2-s9/environment/Dockerfile

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

tasks/construct-ae-p38-factorial-factors-l2-s9/environment/instance.json

@@ -0,0 +1 @@
+{"N": 152, "t": 44, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s9/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [704, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 47, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 53, 53, 57, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 59, 59, 61, 61, 62, 62, 62, 62, 64, 67, 67, 71, 71, 73, 73, 74, 74, 74, 74, 79, 82, 82, 82, 83, 86, 86, 86, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l2-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-l2-s9/tests/instance.json

@@ -0,0 +1 @@
+{"N": 152, "t": 44, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s9/tests/run.py

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

tasks/construct-ae-p38-factorial-factors-l2-s9/tests/test.sh

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

tasks/construct-ae-p38-factorial-factors-l6-s1/environment/Dockerfile

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

tasks/construct-ae-p38-factorial-factors-l6-s1/environment/instance.json

@@ -0,0 +1 @@
+{"N": 5728, "t": 1856, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s1/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1857, 1857, 1857, 1857, 1857, 1857, 1857, 1857, 1857, 1858, 1858, 1858, 1858, 1858, 1858, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1859, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1860, 1861, 1861, 1861, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 1862, 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3134, 3134, 3137, 3142, 3142, 3142, 3158, 3158, 3158, 3163, 3166, 3166, 3166, 3167, 3169, 3181, 3187, 3191, 3194, 3194, 3194, 3202, 3202, 3202, 3203, 3209, 3214, 3214, 3214, 3217, 3218, 3218, 3218, 3221, 3226, 3226, 3226, 3229, 3238, 3238, 3238, 3242, 3242, 3242, 3251, 3253, 3254, 3254, 3254, 3257, 3259, 3271, 3274, 3274, 3274, 3299, 3301, 3307, 3313, 3314, 3314, 3314, 3319, 3323, 3326, 3326, 3326, 3329, 3331, 3334, 3334, 3334, 3338, 3338, 3338, 3343, 3347, 3359, 3361, 3371, 3373, 3386, 3386, 3386, 3389, 3391, 3394, 3394, 3394, 3398, 3398, 3398, 3407, 3413, 3418, 3418, 3418, 3433, 3442, 3442, 3442, 3446, 3446, 3446, 3449, 3457, 3461, 3463, 3466, 3466, 3466, 3467, 3469, 3482, 3482, 3482, 3491, 3494, 3494, 3494, 3499, 3506, 3506, 3506, 3511, 3517, 3518, 3518, 3518, 3527, 3529, 3533, 3539, 3541, 3547, 3554, 3554, 3554, 3557, 3559, 3566, 3566, 3566, 3571, 3574, 3574, 3574, 3578, 3578, 3578, 3581, 3583, 3593, 3602, 3602, 3602, 3607, 3613, 3617, 3622, 3622, 3622, 3623, 3631, 3637, 3643, 3646, 3646, 3646, 3659, 3662, 3662, 3662, 3671, 3673, 3677, 3691, 3694, 3694, 3694, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 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]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l6-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-l6-s1/tests/instance.json

@@ -0,0 +1 @@
+{"N": 5728, "t": 1856, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s1/tests/run.py

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

tasks/construct-ae-p38-factorial-factors-l6-s1/tests/test.sh

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

tasks/construct-ae-p38-factorial-factors-l6-s6/environment/Dockerfile

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

tasks/construct-ae-p38-factorial-factors-l6-s6/environment/instance.json

@@ -0,0 +1 @@
+{"N": 8484, "t": 2770, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s6/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [33240, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2770, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2771, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2772, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2773, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2774, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 2775, 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4933, 4934, 4934, 4934, 4937, 4943, 4946, 4946, 4946, 4951, 4954, 4954, 4954, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5006, 5006, 5006, 5009, 5011, 5021, 5023, 5039, 5042, 5042, 5042, 5051, 5059, 5062, 5062, 5062, 5077, 5078, 5078, 5078, 5081, 5086, 5086, 5086, 5087, 5098, 5098, 5098, 5099, 5101, 5102, 5102, 5102, 5107, 5113, 5114, 5114, 5114, 5119, 5147, 5153, 5158, 5158, 5158, 5167, 5171, 5179, 5182, 5182, 5182, 5186, 5186, 5186, 5189, 5197, 5209, 5218, 5218, 5218, 5227, 5231, 5233, 5234, 5234, 5234, 5237, 5242, 5242, 5242, 5261, 5266, 5266, 5266, 5273, 5279, 5281, 5294, 5294, 5294, 5297, 5303, 5309, 5314, 5314, 5314, 5318, 5318, 5318, 5323, 5326, 5326, 5326, 5333, 5342, 5342, 5342, 5347, 5351, 5354, 5354, 5354, 5366, 5366, 5366, 5374, 5374, 5374, 5378, 5378, 5378, 5381, 5386, 5386, 5386, 5387, 5393, 5398, 5398, 5398, 5399, 5407, 5413, 5414, 5414, 5414, 5417, 5419, 5422, 5422, 5422, 5426, 5426, 5426, 5431, 5437, 5438, 5438, 5438, 5441, 5443, 5449, 5458, 5458, 5458, 5462, 5462, 5462, 5471, 5477, 5479, 5482, 5482, 5482, 5483, 5498, 5498, 5498, 5501, 5503, 5506, 5506, 5506, 5507, 5519, 5521, 5527, 5531, 5534, 5534, 5534, 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, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l6-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-l6-s6/tests/instance.json

@@ -0,0 +1 @@
+{"N": 8484, "t": 2770, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s6/tests/run.py

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

tasks/construct-ae-p38-factorial-factors-l6-s6/tests/test.sh

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

tasks/construct-ae-p52-erdos-squarefree-l2-s2/environment/Dockerfile

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

tasks/construct-ae-p52-erdos-squarefree-l2-s2/environment/instance.json

@@ -0,0 +1 @@
+{"N": 361, "t": 15, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l2-s2/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357]}
+RLMATH_EOF

tasks/construct-ae-p52-erdos-squarefree-l2-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-l2-s2/tests/instance.json

@@ -0,0 +1 @@
+{"N": 361, "t": 15, "family": "ae_p52_erdos_squarefree", "subset": "construct"}

tasks/construct-ae-p52-erdos-squarefree-l2-s2/tests/run.py

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

tasks/construct-ae-p52-erdos-squarefree-l2-s2/tests/test.sh

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

tasks/construct-ae-p52-erdos-squarefree-l2-s5/environment/Dockerfile

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