{"abstract":"Nondivisibility does not imply absence of a shared factor.","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. a and b may be signed or zero; return whether gcd(a,b)=1. Exact operational definition: math.gcd(a,b)==1","contract_signature":"a, b","evaluation_group":"model-f1829591c7f646ce","failed_approach":"Unequal values may still share factors and equal units are coprime.","family":"xn-coprime-predicate","id":"FA-5491","implementations":{"attempt":{"sha256":"1b8eb4b96542bb70b092f4c7f27475a57a7b44c70c5a9caac4a39ac67b4794cd","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(a, b):\n    return a!=b\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (6, 35)', solve(*(6, 35)), True)\ncheck('fixture 2: (6, 9)', solve(*(6, 9)), False)\ncheck('fixture 3: (1, 1)', solve(*(1, 1)), True)\ncheck('fixture 4: (0, 1)', solve(*(0, 1)), True)\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":"96fa46fdbd1fde4c3f27fdf393c534e3470344097c2e7f08c697dc9b38bb5614","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(a, b):\n    return a%b != 0 if b else False\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (6, 35)', solve(*(6, 35)), True)\ncheck('fixture 2: (6, 9)', solve(*(6, 9)), False)\ncheck('fixture 3: (1, 1)', solve(*(1, 1)), True)\ncheck('fixture 4: (0, 1)', solve(*(0, 1)), True)\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-coprime-predicate","generated_at":"2026-09-29T14:37:50.172883+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":"Nondivisibility does not imply absence of a shared factor.","sha256":"6c49ea83992ab49cd08b824e84f975fbe7af5c39bdbd1c11e38b7d12367a6770","title":"Coprime predicate · 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":44.671,"exit_code":1,"observations":[{"actual":true,"check":"fixture 1: (6, 35)","expected":true,"passed":true},{"actual":true,"check":"fixture 2: (6, 9)","expected":false,"passed":false},{"actual":false,"check":"fixture 3: (1, 1)","expected":true,"passed":false},{"actual":true,"check":"fixture 4: (0, 1)","expected":true,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (6, 35)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 2: (6, 9)\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 3: (1, 1)\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 4: (0, 1)\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.943,"exit_code":1,"observations":[{"actual":true,"check":"fixture 1: (6, 35)","expected":true,"passed":true},{"actual":true,"check":"fixture 2: (6, 9)","expected":false,"passed":false},{"actual":false,"check":"fixture 3: (1, 1)","expected":true,"passed":false},{"actual":false,"check":"fixture 4: (0, 1)","expected":true,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (6, 35)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 2: (6, 9)\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 3: (1, 1)\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 4: (0, 1)\", \"actual\": false, \"expected\": true, \"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."}}