{"abstract":"Vieta root sum has the opposite sign.","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 sum of both algebraic roots, including complex roots counted algebraically. Exact operational definition: str(Fraction(-b,a))","contract_signature":"a, b, c","evaluation_group":"model-d818f64b1143fb56","failed_approach":"The single-root quadratic denominator is reused for a root sum.","family":"xn-quadratic-root-sum-rational","id":"FA-6136","implementations":{"attempt":{"sha256":"29c51ab037b3e91d6e7c08b2365601f64f6036676357c6ffaa891de91145816a","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(-b,2*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)), '-3')\ncheck('fixture 2: (2, -3, 1)', solve(*(2, -3, 1)), '3/2')\ncheck('fixture 3: (1, 0, -1)', solve(*(1, 0, -1)), '0')\ncheck('fixture 4: (-2, 4, 1)', solve(*(-2, 4, 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":"df8968773d1b92b4cb1ef78ea2ba8366c8d4a9b4f730aef272be6dfb74b03f08","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(b,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)), '-3')\ncheck('fixture 2: (2, -3, 1)', solve(*(2, -3, 1)), '3/2')\ncheck('fixture 3: (1, 0, -1)', solve(*(1, 0, -1)), '0')\ncheck('fixture 4: (-2, 4, 1)', solve(*(-2, 4, 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-sum-rational","generated_at":"2026-09-29T14:37:57.855184+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.","root_cause":"Vieta root sum has the opposite sign.","sha256":"e277fd5fad088e68da8398f2908426e958771f30b744280ef7c3b9d369d896dd","title":"Quadratic root sum rational · 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":42.334,"exit_code":1,"observations":[{"actual":"-3/2","check":"fixture 1: (1, 3, 2)","expected":"-3","passed":false},{"actual":"3/4","check":"fixture 2: (2, -3, 1)","expected":"3/2","passed":false},{"actual":"0","check":"fixture 3: (1, 0, -1)","expected":"0","passed":true},{"actual":"1","check":"fixture 4: (-2, 4, 1)","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 3, 2)\", \"actual\": \"-3/2\", \"expected\": \"-3\", \"passed\": false}, {\"check\": \"fixture 2: (2, -3, 1)\", \"actual\": \"3/4\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"fixture 3: (1, 0, -1)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: (-2, 4, 1)\", \"actual\": \"1\", \"expected\": \"2\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.653,"exit_code":1,"observations":[{"actual":"3","check":"fixture 1: (1, 3, 2)","expected":"-3","passed":false},{"actual":"-3/2","check":"fixture 2: (2, -3, 1)","expected":"3/2","passed":false},{"actual":"0","check":"fixture 3: (1, 0, -1)","expected":"0","passed":true},{"actual":"-2","check":"fixture 4: (-2, 4, 1)","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 3, 2)\", \"actual\": \"3\", \"expected\": \"-3\", \"passed\": false}, {\"check\": \"fixture 2: (2, -3, 1)\", \"actual\": \"-3/2\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"fixture 3: (1, 0, -1)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: (-2, 4, 1)\", \"actual\": \"-2\", \"expected\": \"2\", \"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."}}