{"abstract":"The exact prime power unit factorial result violates the stated contract at unit factor multiplication.","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 v%mod still violates the unit factor multiplication invariant.","family":"s3-numerics-prime-power-unit-factorial-unit-factor-multiplication","id":"FA-15586","implementations":{"attempt":{"sha256":"0e8dc8f6fc8d4118b6eda581c9aad6e0bb6bc461cfe9065bb99ca14b6ffed6cc","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=v%mod\n    return r\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([1, 2, 1], 1), ([4, 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, 2], 1)], [([1, 2, 2], 1), ([5, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([4, 2, 2], 3), ([4, 2, 3], 3), ([4, 2, 4], 3), ([5, 2, 1], 1)], [([1, 2, 3], 1), ([6, 2, 2], 1), ([0, 2, 1], 1), ([64, 7, 4], 282), ([8, 2, 3], 3), ([8, 2, 4], 11), ([9, 2, 1], 1), ([9, 2, 2], 3)], [([1, 2, 4], 1), ([7, 2, 3], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([12, 2, 4], 15), ([13, 2, 1], 1), ([13, 2, 2], 3), ([13, 2, 3], 3)], [([2, 2, 2], 1), ([8, 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":"2aac928416505ff9274d884eb220f3497f7dd2614ee9d6eee43b3f22cf5b22f7","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 = [[([1, 2, 1], 1), ([4, 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, 2], 1)], [([1, 2, 2], 1), ([5, 2, 2], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([4, 2, 2], 3), ([4, 2, 3], 3), ([4, 2, 4], 3), ([5, 2, 1], 1)], [([1, 2, 3], 1), ([6, 2, 2], 1), ([0, 2, 1], 1), ([64, 7, 4], 282), ([8, 2, 3], 3), ([8, 2, 4], 11), ([9, 2, 1], 1), ([9, 2, 2], 3)], [([1, 2, 4], 1), ([7, 2, 3], 3), ([0, 2, 1], 1), ([64, 7, 4], 282), ([12, 2, 4], 15), ([13, 2, 1], 1), ([13, 2, 2], 3), ([13, 2, 3], 3)], [([2, 2, 2], 1), ([8, 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-unit-factor-multiplication","generated_at":"2026-09-29T14:39:28.093987+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 unit factor multiplication step uses (r+v)%mod instead of r*v%mod.","sha256":"62d4a7ab1b6d83b6e7aa30dbe2991b500fbdb2d1ebcdbb2edebff3e5bcc87b69","title":"Prime power unit factorial: unit factor multiplication · 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":43.907,"exit_code":1,"observations":[{"actual":1,"check":"explicit oracle 0","expected":1,"passed":true},{"actual":1,"check":"explicit oracle 1","expected":3,"passed":false},{"actual":1,"check":"explicit oracle 2","expected":1,"passed":true},{"actual":64,"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\": 1, \"passed\": true}, {\"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\": 64, \"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":44.29,"exit_code":1,"observations":[{"actual":0,"check":"explicit oracle 0","expected":1,"passed":false},{"actual":3,"check":"explicit oracle 1","expected":3,"passed":true},{"actual":1,"check":"explicit oracle 2","expected":1,"passed":true},{"actual":1805,"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":2,"check":"explicit oracle 7","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": 0, \"expected\": 1, \"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\": 1805, \"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\": 2, \"expected\": 1, \"passed\": false}], \"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."}}