{"abstract":"The exact prime power unit factorial result violates the stated contract at prime power ring modulus.","category":"Numerics","checks":8,"contract":"Input [n,p,e], n>=0 p prime e>=1; return product of positive integers<=n after removing ALL p factors from each, modulo p^e. Bounds: n<=64.","contract_signature":"x","evaluation_group":"s3-numerics-prime-power-unit-factorial","failed_approach":"The partial repair p still violates the prime power ring modulus invariant.","family":"s3-numerics-prime-power-unit-factorial-prime-power-ring-modulus","id":"FA-15566","implementations":{"attempt":{"sha256":"7738832c7c4fd0b34f9d35cc8978abe35e6029e1a14311502d965db50bb097e4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    n,p,e=x;mod=p;r=1\n    for v in range(1,n+1):\n     for _ in range(30):\n      if v%p!=0:break\n      v//=p\n     r=r*v%mod\n    return r\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([5, 2, 3], 7), ([3, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([0, 2, 2], 1), ([0, 2, 3], 1), ([0, 2, 4], 1), ([1, 2, 1], 1)], [([5, 2, 4], 15), ([4, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([4, 2, 3], 3), ([4, 2, 4], 3), ([5, 2, 1], 1), ([5, 2, 2], 3)], [([6, 2, 3], 5), ([5, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([8, 2, 3], 3), ([8, 2, 4], 11), ([9, 2, 1], 1), ([9, 2, 2], 3)], [([6, 2, 4], 13), ([6, 2, 3], 5), ([0, 2, 1], 1), ([64, 7, 4], 282), ([12, 2, 4], 15), ([13, 2, 1], 1), ([13, 2, 2], 3), ([13, 2, 3], 3)], [([7, 2, 4], 11), ([7, 2, 3], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([17, 2, 1], 1), ([17, 2, 2], 3), ([17, 2, 3], 3), ([17, 2, 4], 11)]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"96df5e4c3e0014ea7aee2649516bccded3845e10bd5b22762acf41de014083bb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    n,p,e=x;mod=p*e;r=1\n    for v in range(1,n+1):\n     for _ in range(30):\n      if v%p!=0:break\n      v//=p\n     r=r*v%mod\n    return r\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([5, 2, 3], 7), ([3, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([0, 2, 2], 1), ([0, 2, 3], 1), ([0, 2, 4], 1), ([1, 2, 1], 1)], [([5, 2, 4], 15), ([4, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([4, 2, 3], 3), ([4, 2, 4], 3), ([5, 2, 1], 1), ([5, 2, 2], 3)], [([6, 2, 3], 5), ([5, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([8, 2, 3], 3), ([8, 2, 4], 11), ([9, 2, 1], 1), ([9, 2, 2], 3)], [([6, 2, 4], 13), ([6, 2, 3], 5), ([0, 2, 1], 1), ([64, 7, 4], 282), ([12, 2, 4], 15), ([13, 2, 1], 1), ([13, 2, 2], 3), ([13, 2, 3], 3)], [([7, 2, 4], 11), ([7, 2, 3], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([17, 2, 1], 1), ([17, 2, 2], 3), ([17, 2, 3], 3), ([17, 2, 4], 11)]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model. Inputs are restricted to the explicit contract; this is not a production algebra library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-numerics-prime-power-unit-factorial-prime-power-ring-modulus","generated_at":"2026-09-29T14:39:28.094233+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.","root_cause":"The prime power ring modulus step uses p*e instead of p**e.","sha256":"296e20c73262113ee5b702bfb3f82f8ea06e93515b4d158ed4f540a6977ba6cd","title":"Prime power unit factorial: prime power ring modulus · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":46.398,"exit_code":1,"observations":[{"actual":1,"check":"explicit oracle 0","expected":7,"passed":false},{"actual":1,"check":"explicit oracle 1","expected":3,"passed":false},{"actual":1,"check":"explicit oracle 2","expected":1,"passed":true},{"actual":2,"check":"explicit oracle 3","expected":282,"passed":false},{"actual":1,"check":"explicit oracle 4","expected":1,"passed":true},{"actual":1,"check":"explicit oracle 5","expected":1,"passed":true},{"actual":1,"check":"explicit oracle 6","expected":1,"passed":true},{"actual":1,"check":"explicit oracle 7","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": 1, \"expected\": 7, \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": 1, \"expected\": 3, \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": 2, \"expected\": 282, \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.363,"exit_code":1,"observations":[{"actual":3,"check":"explicit oracle 0","expected":7,"passed":false},{"actual":3,"check":"explicit oracle 1","expected":3,"passed":true},{"actual":1,"check":"explicit oracle 2","expected":1,"passed":true},{"actual":16,"check":"explicit oracle 3","expected":282,"passed":false},{"actual":1,"check":"explicit oracle 4","expected":1,"passed":true},{"actual":1,"check":"explicit oracle 5","expected":1,"passed":true},{"actual":1,"check":"explicit oracle 6","expected":1,"passed":true},{"actual":1,"check":"explicit oracle 7","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": 3, \"expected\": 7, \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": 16, \"expected\": 282, \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}