{"abstract":"Coefficient sum evaluates at positive one rather than negative one.","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. Polynomial value at minus one. Exact operational definition: sum(c*(-1)**i for i,c in enumerate(coeff))","evaluation_group":"model-a5a75bc4119fd1b8","failed_approach":"Alternating signs begin with negative instead of positive.","family":"xn-polynomial-value-at-minus-one","id":"FA-6146","implementations":{"attempt":{"sha256":"3617c5ee3384e92e09e235566805d21e10b2d6d0cd115b2d69e508120f893251","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 sum(c*(-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, 3],)', solve(*([1, 2, 3],)), 2)\ncheck('fixture 2: ([5],)', solve(*([5],)), 5)\ncheck('fixture 3: ([0, 1],)', solve(*([0, 1],)), -1)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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":"aaeec7f3432cbaeac5418b644c9b2fc793046235af26f041eb3208e7b538c730","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 sum(coeff)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3],)', solve(*([1, 2, 3],)), 2)\ncheck('fixture 2: ([5],)', solve(*([5],)), 5)\ncheck('fixture 3: ([0, 1],)', solve(*([0, 1],)), -1)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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":"ec17339a726e6e92b92d2aa28b2c780b06f9c5edf3e19d81d10f0f1114a34a63","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 sum(c*(-1)**i 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, 3],)', solve(*([1, 2, 3],)), 2)\ncheck('fixture 2: ([5],)', solve(*([5],)), 5)\ncheck('fixture 3: ([0, 1],)', solve(*([0, 1],)), -1)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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-value-at-minus-one","generated_at":"2026-09-29T14:37:57.938233+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 sum(c*(-1)**i for i,c in enumerate(coeff))","root_cause":"Coefficient sum evaluates at positive one rather than negative one.","sha256":"dad3d996b699200f331cb0fd033fe8b4402689e2a0c456c95ab02b9dde370e97","title":"Polynomial value at minus one · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.481,"exit_code":1,"observations":[{"actual":-2,"check":"fixture 1: ([1, 2, 3],)","expected":2,"passed":false},{"actual":-5,"check":"fixture 2: ([5],)","expected":5,"passed":false},{"actual":1,"check":"fixture 3: ([0, 1],)","expected":-1,"passed":false},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": -2, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 2: ([5],)\", \"actual\": -5, \"expected\": 5, \"passed\": false}, {\"check\": \"fixture 3: ([0, 1],)\", \"actual\": 1, \"expected\": -1, \"passed\": false}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.278,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: ([1, 2, 3],)","expected":2,"passed":false},{"actual":5,"check":"fixture 2: ([5],)","expected":5,"passed":true},{"actual":1,"check":"fixture 3: ([0, 1],)","expected":-1,"passed":false},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": 6, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 2: ([5],)\", \"actual\": 5, \"expected\": 5, \"passed\": true}, {\"check\": \"fixture 3: ([0, 1],)\", \"actual\": 1, \"expected\": -1, \"passed\": false}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":47.695,"exit_code":0,"observations":[{"actual":2,"check":"fixture 1: ([1, 2, 3],)","expected":2,"passed":true},{"actual":5,"check":"fixture 2: ([5],)","expected":5,"passed":true},{"actual":-1,"check":"fixture 3: ([0, 1],)","expected":-1,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 2: ([5],)\", \"actual\": 5, \"expected\": 5, \"passed\": true}, {\"check\": \"fixture 3: ([0, 1],)\", \"actual\": -1, \"expected\": -1, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}