{"abstract":"The product receives an unnecessary sign flip.","category":"Polynomial arithmetic","checks":4,"contract":"Integer coefficients in ascending power order and integer evaluation bounds; missing high-degree coefficients are zero. Rational outputs are reduced Fraction strings; the zero-polynomial degree is -1. a!=0; return the reduced rational product of both algebraic roots. Exact operational definition: str(Fraction(c,a))","evaluation_group":"model-3b105746f8bd7f4e","failed_approach":"The linear coefficient is used as the normalization denominator.","family":"xn-quadratic-root-product-rational","id":"FA-6141","implementations":{"attempt":{"sha256":"e84c8255a7dc7b9bbf1dd866851e22a57f36bc85d6b941fc7992567c7859c3a4","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, c):\n    return str(Fraction(c,b)) if b else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 3, 2)', solve(*(1, 3, 2)), '2')\ncheck('fixture 2: (2, -3, 1)', solve(*(2, -3, 1)), '1/2')\ncheck('fixture 3: (1, 0, -1)', solve(*(1, 0, -1)), '-1')\ncheck('fixture 4: (-2, 4, 1)', solve(*(-2, 4, 1)), '-1/2')\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":"4217251d8b4c57e8cfd62c46904de5fb8c469445d731d43302cecc72572035b3","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, c):\n    return str(Fraction(-c,a))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 3, 2)', solve(*(1, 3, 2)), '2')\ncheck('fixture 2: (2, -3, 1)', solve(*(2, -3, 1)), '1/2')\ncheck('fixture 3: (1, 0, -1)', solve(*(1, 0, -1)), '-1')\ncheck('fixture 4: (-2, 4, 1)', solve(*(-2, 4, 1)), '-1/2')\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"},"fixed":{"sha256":"7a35a528864de4855fbd90e91ba03b7ddc20c592506e91b3d182550d80a00184","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, c):\n    return str(Fraction(c,a))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 3, 2)', solve(*(1, 3, 2)), '2')\ncheck('fixture 2: (2, -3, 1)', solve(*(2, -3, 1)), '1/2')\ncheck('fixture 3: (1, 0, -1)', solve(*(1, 0, -1)), '-1')\ncheck('fixture 4: (-2, 4, 1)', solve(*(-2, 4, 1)), '-1/2')\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-quadratic-root-product-rational","generated_at":"2026-09-29T14:37:57.889317+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. Polynomial arithmetic results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return str(Fraction(c,a))","root_cause":"The product receives an unnecessary sign flip.","sha256":"eb6961ad00cbd29af2e00e897d00284c9dc58bd8407fd4a65a4f9036a092d696","title":"Quadratic root product rational · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.201,"exit_code":1,"observations":[{"actual":"2/3","check":"fixture 1: (1, 3, 2)","expected":"2","passed":false},{"actual":"-1/3","check":"fixture 2: (2, -3, 1)","expected":"1/2","passed":false},{"actual":null,"check":"fixture 3: (1, 0, -1)","expected":"-1","passed":false},{"actual":"1/4","check":"fixture 4: (-2, 4, 1)","expected":"-1/2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 3, 2)\", \"actual\": \"2/3\", \"expected\": \"2\", \"passed\": false}, {\"check\": \"fixture 2: (2, -3, 1)\", \"actual\": \"-1/3\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"fixture 3: (1, 0, -1)\", \"actual\": null, \"expected\": \"-1\", \"passed\": false}, {\"check\": \"fixture 4: (-2, 4, 1)\", \"actual\": \"1/4\", \"expected\": \"-1/2\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.42,"exit_code":1,"observations":[{"actual":"-2","check":"fixture 1: (1, 3, 2)","expected":"2","passed":false},{"actual":"-1/2","check":"fixture 2: (2, -3, 1)","expected":"1/2","passed":false},{"actual":"1","check":"fixture 3: (1, 0, -1)","expected":"-1","passed":false},{"actual":"1/2","check":"fixture 4: (-2, 4, 1)","expected":"-1/2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 3, 2)\", \"actual\": \"-2\", \"expected\": \"2\", \"passed\": false}, {\"check\": \"fixture 2: (2, -3, 1)\", \"actual\": \"-1/2\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"fixture 3: (1, 0, -1)\", \"actual\": \"1\", \"expected\": \"-1\", \"passed\": false}, {\"check\": \"fixture 4: (-2, 4, 1)\", \"actual\": \"1/2\", \"expected\": \"-1/2\", \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.638,"exit_code":0,"observations":[{"actual":"2","check":"fixture 1: (1, 3, 2)","expected":"2","passed":true},{"actual":"1/2","check":"fixture 2: (2, -3, 1)","expected":"1/2","passed":true},{"actual":"-1","check":"fixture 3: (1, 0, -1)","expected":"-1","passed":true},{"actual":"-1/2","check":"fixture 4: (-2, 4, 1)","expected":"-1/2","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 3, 2)\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}, {\"check\": \"fixture 2: (2, -3, 1)\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"fixture 3: (1, 0, -1)\", \"actual\": \"-1\", \"expected\": \"-1\", \"passed\": true}, {\"check\": \"fixture 4: (-2, 4, 1)\", \"actual\": \"-1/2\", \"expected\": \"-1/2\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}