{"abstract":"Antiderivative coefficients are shifted without degree division.","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. Formal polynomial integral zero constant. Exact operational definition: [\"0\"]+[str(Fraction(c,i+1)) for i,c in enumerate(coeff)]","evaluation_group":"model-28b44d7c78532ee6","failed_approach":"The zero integration constant is omitted from ascending order.","family":"xn-formal-polynomial-integral-zero-constant","id":"FA-6111","implementations":{"attempt":{"sha256":"e306ace5c4c5534db2d417ad121c6f06c28e943847dc853787b6900bd6375814","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):\n    return [str(Fraction(c,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: ([2, 3],)', solve(*([2, 3],)), ['0', '2', '3/2'])\ncheck('fixture 2: ([0, 0, 3],)', solve(*([0, 0, 3],)), ['0', '0', '0', '1'])\ncheck('fixture 3: ([],)', solve(*([],)), ['0'])\ncheck('fixture 4: ([5],)', solve(*([5],)), ['0', '5'])\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":"6c0cc5b779f3fbe77aa9cf3be453122aea86326c104458b8d745268a5b07ed3e","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):\n    return [\"0\"]+[str(c) for c in coeff]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([2, 3],)', solve(*([2, 3],)), ['0', '2', '3/2'])\ncheck('fixture 2: ([0, 0, 3],)', solve(*([0, 0, 3],)), ['0', '0', '0', '1'])\ncheck('fixture 3: ([],)', solve(*([],)), ['0'])\ncheck('fixture 4: ([5],)', solve(*([5],)), ['0', '5'])\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":"493834cb51b3344ca70dd5b4a0e16764650714e4b00732e4aaea358d36b49c26","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):\n    return [\"0\"]+[str(Fraction(c,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: ([2, 3],)', solve(*([2, 3],)), ['0', '2', '3/2'])\ncheck('fixture 2: ([0, 0, 3],)', solve(*([0, 0, 3],)), ['0', '0', '0', '1'])\ncheck('fixture 3: ([],)', solve(*([],)), ['0'])\ncheck('fixture 4: ([5],)', solve(*([5],)), ['0', '5'])\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-formal-polynomial-integral-zero-constant","generated_at":"2026-09-29T14:37:57.757694+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 [\"0\"]+[str(Fraction(c,i+1)) for i,c in enumerate(coeff)]","root_cause":"Antiderivative coefficients are shifted without degree division.","sha256":"97cb1f375c5e9839a0bc77453226c16cb8c9946a5c3cab0a362dbc49fe579311","title":"Formal polynomial integral zero constant · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.836,"exit_code":1,"observations":[{"actual":["2","3/2"],"check":"fixture 1: ([2, 3],)","expected":["0","2","3/2"],"passed":false},{"actual":["0","0","1"],"check":"fixture 2: ([0, 0, 3],)","expected":["0","0","0","1"],"passed":false},{"actual":[],"check":"fixture 3: ([],)","expected":["0"],"passed":false},{"actual":["5"],"check":"fixture 4: ([5],)","expected":["0","5"],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([2, 3],)\", \"actual\": [\"2\", \"3/2\"], \"expected\": [\"0\", \"2\", \"3/2\"], \"passed\": false}, {\"check\": \"fixture 2: ([0, 0, 3],)\", \"actual\": [\"0\", \"0\", \"1\"], \"expected\": [\"0\", \"0\", \"0\", \"1\"], \"passed\": false}, {\"check\": \"fixture 3: ([],)\", \"actual\": [], \"expected\": [\"0\"], \"passed\": false}, {\"check\": \"fixture 4: ([5],)\", \"actual\": [\"5\"], \"expected\": [\"0\", \"5\"], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.731,"exit_code":1,"observations":[{"actual":["0","2","3"],"check":"fixture 1: ([2, 3],)","expected":["0","2","3/2"],"passed":false},{"actual":["0","0","0","3"],"check":"fixture 2: ([0, 0, 3],)","expected":["0","0","0","1"],"passed":false},{"actual":["0"],"check":"fixture 3: ([],)","expected":["0"],"passed":true},{"actual":["0","5"],"check":"fixture 4: ([5],)","expected":["0","5"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([2, 3],)\", \"actual\": [\"0\", \"2\", \"3\"], \"expected\": [\"0\", \"2\", \"3/2\"], \"passed\": false}, {\"check\": \"fixture 2: ([0, 0, 3],)\", \"actual\": [\"0\", \"0\", \"0\", \"3\"], \"expected\": [\"0\", \"0\", \"0\", \"1\"], \"passed\": false}, {\"check\": \"fixture 3: ([],)\", \"actual\": [\"0\"], \"expected\": [\"0\"], \"passed\": true}, {\"check\": \"fixture 4: ([5],)\", \"actual\": [\"0\", \"5\"], \"expected\": [\"0\", \"5\"], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.095,"exit_code":0,"observations":[{"actual":["0","2","3/2"],"check":"fixture 1: ([2, 3],)","expected":["0","2","3/2"],"passed":true},{"actual":["0","0","0","1"],"check":"fixture 2: ([0, 0, 3],)","expected":["0","0","0","1"],"passed":true},{"actual":["0"],"check":"fixture 3: ([],)","expected":["0"],"passed":true},{"actual":["0","5"],"check":"fixture 4: ([5],)","expected":["0","5"],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([2, 3],)\", \"actual\": [\"0\", \"2\", \"3/2\"], \"expected\": [\"0\", \"2\", \"3/2\"], \"passed\": true}, {\"check\": \"fixture 2: ([0, 0, 3],)\", \"actual\": [\"0\", \"0\", \"0\", \"1\"], \"expected\": [\"0\", \"0\", \"0\", \"1\"], \"passed\": true}, {\"check\": \"fixture 3: ([],)\", \"actual\": [\"0\"], \"expected\": [\"0\"], \"passed\": true}, {\"check\": \"fixture 4: ([5],)\", \"actual\": [\"0\", \"5\"], \"expected\": [\"0\", \"5\"], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}