{"abstract":"Prime-power multiplicities in a factorial are omitted.","category":"Number theory","checks":4,"contract":"Integer inputs; n is positive unless a zero or negative fixture explicitly extends that operation. A modulus is greater than one; p is prime; exponent k may be signed when an inverse exists. n>=0 and p is prime. Return the exponent of p in the prime factorization of n!. Exact operational definition: sum(n//p**i for i in range(1,n.bit_length()+1))","contract_signature":"n, p","evaluation_group":"model-c7f05c64e18df305","failed_approach":"Counting divisible terms still counts each term only once.","family":"xn-factorial-prime-valuation","id":"FA-5536","implementations":{"attempt":{"sha256":"480533ca36f7efbaf1555e6f7a4a71a5c924c3b1c71d4d398bd2c9ce7ab9778d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n, p):\n    return sum(1 for i in range(1,n+1) if i%p==0)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (8, 2)', solve(*(8, 2)), 7)\ncheck('fixture 2: (10, 3)', solve(*(10, 3)), 4)\ncheck('fixture 3: (0, 2)', solve(*(0, 2)), 0)\ncheck('fixture 4: (5, 5)', solve(*(5, 5)), 1)\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":"8d435a144d56771d36d34dc937c79a355366752e71554886be69c4b973d66c3f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n, p):\n    return n//p\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (8, 2)', solve(*(8, 2)), 7)\ncheck('fixture 2: (10, 3)', solve(*(10, 3)), 4)\ncheck('fixture 3: (0, 2)', solve(*(0, 2)), 0)\ncheck('fixture 4: (5, 5)', solve(*(5, 5)), 1)\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":" 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":"xn-factorial-prime-valuation","generated_at":"2026-09-29T14:37:50.666116+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Number theory results depend on the stated convention.","root_cause":"Prime-power multiplicities in a factorial are omitted.","sha256":"dad4e9d64efafc3994e7cba9e5e8ca6c875065ff55fa3f0c31dfd822fa03ce3e","title":"Factorial prime valuation · 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":45.262,"exit_code":1,"observations":[{"actual":4,"check":"fixture 1: (8, 2)","expected":7,"passed":false},{"actual":3,"check":"fixture 2: (10, 3)","expected":4,"passed":false},{"actual":0,"check":"fixture 3: (0, 2)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: (5, 5)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (8, 2)\", \"actual\": 4, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 2: (10, 3)\", \"actual\": 3, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 3: (0, 2)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (5, 5)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.139,"exit_code":1,"observations":[{"actual":4,"check":"fixture 1: (8, 2)","expected":7,"passed":false},{"actual":3,"check":"fixture 2: (10, 3)","expected":4,"passed":false},{"actual":0,"check":"fixture 3: (0, 2)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: (5, 5)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (8, 2)\", \"actual\": 4, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 2: (10, 3)\", \"actual\": 3, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 3: (0, 2)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (5, 5)\", \"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."}}