{"abstract":"Removing odd positions compresses the remaining 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. Polynomial even part. Exact operational definition: [c if i%2==0 else 0 for i,c in enumerate(coeff)]","contract_signature":"coeff","evaluation_group":"model-0c9e1858a7038a6b","failed_approach":"Parity selects the odd part instead of the even part.","family":"xn-polynomial-even-part","id":"FA-6151","implementations":{"attempt":{"sha256":"e4b5bd7c948b35fbef7820638c86ae713b4cf20bc2f76c78be75ef036d348022","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 [c if i%2 else 0 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, 4],)', solve(*([1, 2, 3, 4],)), [1, 0, 3, 0])\ncheck('fixture 2: ([0, 1],)', solve(*([0, 1],)), [0, 0])\ncheck('fixture 3: ([5],)', solve(*([5],)), [5])\ncheck('fixture 4: ([],)', solve(*([],)), [])\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":"e1d49f25c1cfcc2e13344b455f8d8450a6f5fc76e35b798e106313b046554714","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 [c for i,c in enumerate(coeff) if i%2==0]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3, 4],)', solve(*([1, 2, 3, 4],)), [1, 0, 3, 0])\ncheck('fixture 2: ([0, 1],)', solve(*([0, 1],)), [0, 0])\ncheck('fixture 3: ([5],)', solve(*([5],)), [5])\ncheck('fixture 4: ([],)', solve(*([],)), [])\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-even-part","generated_at":"2026-09-29T14:37:57.948774+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":"Removing odd positions compresses the remaining powers.","sha256":"6203d260698708e9df3fd87c9a3887295678e91f97696ad5ff6aa427afb3575b","title":"Polynomial even part · 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":48.805,"exit_code":1,"observations":[{"actual":[0,2,0,4],"check":"fixture 1: ([1, 2, 3, 4],)","expected":[1,0,3,0],"passed":false},{"actual":[0,1],"check":"fixture 2: ([0, 1],)","expected":[0,0],"passed":false},{"actual":[0],"check":"fixture 3: ([5],)","expected":[5],"passed":false},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3, 4],)\", \"actual\": [0, 2, 0, 4], \"expected\": [1, 0, 3, 0], \"passed\": false}, {\"check\": \"fixture 2: ([0, 1],)\", \"actual\": [0, 1], \"expected\": [0, 0], \"passed\": false}, {\"check\": \"fixture 3: ([5],)\", \"actual\": [0], \"expected\": [5], \"passed\": false}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.283,"exit_code":1,"observations":[{"actual":[1,3],"check":"fixture 1: ([1, 2, 3, 4],)","expected":[1,0,3,0],"passed":false},{"actual":[0],"check":"fixture 2: ([0, 1],)","expected":[0,0],"passed":false},{"actual":[5],"check":"fixture 3: ([5],)","expected":[5],"passed":true},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3, 4],)\", \"actual\": [1, 3], \"expected\": [1, 0, 3, 0], \"passed\": false}, {\"check\": \"fixture 2: ([0, 1],)\", \"actual\": [0], \"expected\": [0, 0], \"passed\": false}, {\"check\": \"fixture 3: ([5],)\", \"actual\": [5], \"expected\": [5], \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"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."}}