{"abstract":"Zeroes appended at the high-degree end do not shift powers.","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. degree>=0; multiply by x**degree, representing an empty zero polynomial as []. Exact operational definition: [0]*degree+coeff if coeff else []","evaluation_group":"model-b056233b82920ee8","failed_approach":"Degree multiplication is confused with exponent shifting.","family":"xn-multiply-polynomial-by-monomial","id":"FA-6161","implementations":{"attempt":{"sha256":"f01eb82c2d7f5be5d37e3e02c3544a236ace57b1e8efc42d404eb6ef923a3213","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, degree):\n    return [c*degree for c in coeff]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2], 2)', solve(*([1, 2], 2)), [0, 0, 1, 2])\ncheck('fixture 2: ([3], 0)', solve(*([3], 0)), [3])\ncheck('fixture 3: ([], 3)', solve(*([], 3)), [])\ncheck('fixture 4: ([0, 1], 1)', solve(*([0, 1], 1)), [0, 0, 1])\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":"1f4e956bd5474acd7b4964350f710c2771f4717431160d9af2cb78a23e9efc2c","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, degree):\n    return coeff+[0]*degree\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2], 2)', solve(*([1, 2], 2)), [0, 0, 1, 2])\ncheck('fixture 2: ([3], 0)', solve(*([3], 0)), [3])\ncheck('fixture 3: ([], 3)', solve(*([], 3)), [])\ncheck('fixture 4: ([0, 1], 1)', solve(*([0, 1], 1)), [0, 0, 1])\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":"d7d1b5cf5553a5b30d3ee52fe73f171a5c5fba67394cb4c973277f36cebe9002","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, degree):\n    return [0]*degree+coeff if coeff else []\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2], 2)', solve(*([1, 2], 2)), [0, 0, 1, 2])\ncheck('fixture 2: ([3], 0)', solve(*([3], 0)), [3])\ncheck('fixture 3: ([], 3)', solve(*([], 3)), [])\ncheck('fixture 4: ([0, 1], 1)', solve(*([0, 1], 1)), [0, 0, 1])\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-multiply-polynomial-by-monomial","generated_at":"2026-09-29T14:37:58.214389+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]*degree+coeff if coeff else []","root_cause":"Zeroes appended at the high-degree end do not shift powers.","sha256":"a34530e4e2b2b0a5d27a39096f1cafee39049fae5a2838b362f6caf1969f6105","title":"Multiply polynomial by monomial · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":45.065,"exit_code":1,"observations":[{"actual":[2,4],"check":"fixture 1: ([1, 2], 2)","expected":[0,0,1,2],"passed":false},{"actual":[0],"check":"fixture 2: ([3], 0)","expected":[3],"passed":false},{"actual":[],"check":"fixture 3: ([], 3)","expected":[],"passed":true},{"actual":[0,1],"check":"fixture 4: ([0, 1], 1)","expected":[0,0,1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], 2)\", \"actual\": [2, 4], \"expected\": [0, 0, 1, 2], \"passed\": false}, {\"check\": \"fixture 2: ([3], 0)\", \"actual\": [0], \"expected\": [3], \"passed\": false}, {\"check\": \"fixture 3: ([], 3)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([0, 1], 1)\", \"actual\": [0, 1], \"expected\": [0, 0, 1], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":116.51,"exit_code":1,"observations":[{"actual":[1,2,0,0],"check":"fixture 1: ([1, 2], 2)","expected":[0,0,1,2],"passed":false},{"actual":[3],"check":"fixture 2: ([3], 0)","expected":[3],"passed":true},{"actual":[0,0,0],"check":"fixture 3: ([], 3)","expected":[],"passed":false},{"actual":[0,1,0],"check":"fixture 4: ([0, 1], 1)","expected":[0,0,1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], 2)\", \"actual\": [1, 2, 0, 0], \"expected\": [0, 0, 1, 2], \"passed\": false}, {\"check\": \"fixture 2: ([3], 0)\", \"actual\": [3], \"expected\": [3], \"passed\": true}, {\"check\": \"fixture 3: ([], 3)\", \"actual\": [0, 0, 0], \"expected\": [], \"passed\": false}, {\"check\": \"fixture 4: ([0, 1], 1)\", \"actual\": [0, 1, 0], \"expected\": [0, 0, 1], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.784,"exit_code":0,"observations":[{"actual":[0,0,1,2],"check":"fixture 1: ([1, 2], 2)","expected":[0,0,1,2],"passed":true},{"actual":[3],"check":"fixture 2: ([3], 0)","expected":[3],"passed":true},{"actual":[],"check":"fixture 3: ([], 3)","expected":[],"passed":true},{"actual":[0,0,1],"check":"fixture 4: ([0, 1], 1)","expected":[0,0,1],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], 2)\", \"actual\": [0, 0, 1, 2], \"expected\": [0, 0, 1, 2], \"passed\": true}, {\"check\": \"fixture 2: ([3], 0)\", \"actual\": [3], \"expected\": [3], \"passed\": true}, {\"check\": \"fixture 3: ([], 3)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([0, 1], 1)\", \"actual\": [0, 0, 1], \"expected\": [0, 0, 1], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}