{"abstract":"The antiderivative at the lower bound is omitted.","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 and b may be in either order; return the exact signed definite integral. Exact operational definition: str(sum((Fraction(c*(b**(i+1)-a**(i+1)),i+1) for i,c in enumerate(coeff)),Fraction()))","contract_signature":"coeff, a, b","evaluation_group":"model-7ef54a43a00154cf","failed_approach":"Endpoint antiderivatives are added rather than subtracted.","family":"xn-polynomial-definite-integral-rational","id":"FA-6166","implementations":{"attempt":{"sha256":"21923c6870f0e3932d3509ccba4fc3ec6003fd17c668256221572f7cf66b576e","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(coeff, a, b):\n    return str(sum(Fraction(c*(b**(i+1)+a**(i+1)),i+1) for i,c in enumerate(coeff)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2], 1, 3)', solve(*([1, 2], 1, 3)), '10')\ncheck('fixture 2: ([0, 1], -1, 1)', solve(*([0, 1], -1, 1)), '0')\ncheck('fixture 3: ([3], 4, 4)', solve(*([3], 4, 4)), '0')\ncheck('fixture 4: ([2], 3, 1)', solve(*([2], 3, 1)), '-4')\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":"230f48837dcb972d90f0b5ddb60631ca2ef1ec1794f456fd8c980ecc8f0cbbfa","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(coeff, a, b):\n    return str(sum(Fraction(c*b**(i+1),i+1) for i,c in enumerate(coeff)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2], 1, 3)', solve(*([1, 2], 1, 3)), '10')\ncheck('fixture 2: ([0, 1], -1, 1)', solve(*([0, 1], -1, 1)), '0')\ncheck('fixture 3: ([3], 4, 4)', solve(*([3], 4, 4)), '0')\ncheck('fixture 4: ([2], 3, 1)', solve(*([2], 3, 1)), '-4')\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-polynomial-definite-integral-rational","generated_at":"2026-09-29T14:37:58.260597+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":"The antiderivative at the lower bound is omitted.","sha256":"a10f1a9d72fbc0cb3874a9945ceaf1377dd9d8dcff6d7dd4f4d2f280727f87a2","title":"Polynomial definite integral 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":44.128,"exit_code":1,"observations":[{"actual":"14","check":"fixture 1: ([1, 2], 1, 3)","expected":"10","passed":false},{"actual":"1","check":"fixture 2: ([0, 1], -1, 1)","expected":"0","passed":false},{"actual":"24","check":"fixture 3: ([3], 4, 4)","expected":"0","passed":false},{"actual":"8","check":"fixture 4: ([2], 3, 1)","expected":"-4","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], 1, 3)\", \"actual\": \"14\", \"expected\": \"10\", \"passed\": false}, {\"check\": \"fixture 2: ([0, 1], -1, 1)\", \"actual\": \"1\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"fixture 3: ([3], 4, 4)\", \"actual\": \"24\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"fixture 4: ([2], 3, 1)\", \"actual\": \"8\", \"expected\": \"-4\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.494,"exit_code":1,"observations":[{"actual":"12","check":"fixture 1: ([1, 2], 1, 3)","expected":"10","passed":false},{"actual":"1/2","check":"fixture 2: ([0, 1], -1, 1)","expected":"0","passed":false},{"actual":"12","check":"fixture 3: ([3], 4, 4)","expected":"0","passed":false},{"actual":"2","check":"fixture 4: ([2], 3, 1)","expected":"-4","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], 1, 3)\", \"actual\": \"12\", \"expected\": \"10\", \"passed\": false}, {\"check\": \"fixture 2: ([0, 1], -1, 1)\", \"actual\": \"1/2\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"fixture 3: ([3], 4, 4)\", \"actual\": \"12\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"fixture 4: ([2], 3, 1)\", \"actual\": \"2\", \"expected\": \"-4\", \"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."}}