{"abstract":"Power coefficients are not multiplied by their degree.","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 derivative. Exact operational definition: [i*c for i,c in enumerate(coeff) if i]","contract_signature":"coeff","evaluation_group":"model-ffac292e72832f59","failed_approach":"The constant is differentiated as though it had degree one.","family":"xn-formal-polynomial-derivative","id":"FA-6106","implementations":{"attempt":{"sha256":"c959b581868ce5cb1d99ca80af4ace08db726be56b51225fb4cb6a648d0e8e37","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 [(i+1)*c 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, 6])\ncheck('fixture 2: ([4],)', solve(*([4],)), [])\ncheck('fixture 3: ([],)', solve(*([],)), [])\ncheck('fixture 4: ([0, 0, 5, 2],)', solve(*([0, 0, 5, 2],)), [0, 10, 6])\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":"f2b1df27b9183c625110f7910d6b1e634ec3eebd1adb159082a141c1bb6dc08e","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 coeff[1:]\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, 6])\ncheck('fixture 2: ([4],)', solve(*([4],)), [])\ncheck('fixture 3: ([],)', solve(*([],)), [])\ncheck('fixture 4: ([0, 0, 5, 2],)', solve(*([0, 0, 5, 2],)), [0, 10, 6])\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-derivative","generated_at":"2026-09-29T14:37:57.720830+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":"Power coefficients are not multiplied by their degree.","sha256":"e9be8dbc4e8a9719315e0f1a65602757f7c7d94c09b4d74e70d398842160f3a3","title":"Formal polynomial derivative · 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":41.37,"exit_code":1,"observations":[{"actual":[1,4,9],"check":"fixture 1: ([1, 2, 3],)","expected":[2,6],"passed":false},{"actual":[4],"check":"fixture 2: ([4],)","expected":[],"passed":false},{"actual":[],"check":"fixture 3: ([],)","expected":[],"passed":true},{"actual":[0,0,15,8],"check":"fixture 4: ([0, 0, 5, 2],)","expected":[0,10,6],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": [1, 4, 9], \"expected\": [2, 6], \"passed\": false}, {\"check\": \"fixture 2: ([4],)\", \"actual\": [4], \"expected\": [], \"passed\": false}, {\"check\": \"fixture 3: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([0, 0, 5, 2],)\", \"actual\": [0, 0, 15, 8], \"expected\": [0, 10, 6], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":135.641,"exit_code":1,"observations":[{"actual":[2,3],"check":"fixture 1: ([1, 2, 3],)","expected":[2,6],"passed":false},{"actual":[],"check":"fixture 2: ([4],)","expected":[],"passed":true},{"actual":[],"check":"fixture 3: ([],)","expected":[],"passed":true},{"actual":[0,5,2],"check":"fixture 4: ([0, 0, 5, 2],)","expected":[0,10,6],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3],)\", \"actual\": [2, 3], \"expected\": [2, 6], \"passed\": false}, {\"check\": \"fixture 2: ([4],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 3: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([0, 0, 5, 2],)\", \"actual\": [0, 5, 2], \"expected\": [0, 10, 6], \"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."}}