{"abstract":"Linear extrapolation omits second differences.","category":"Discrete calculus","checks":4,"contract":"Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. At least three values are provided; extrapolate using the final three equally spaced observations. Exact operational definition: 3*values[-1]-3*values[-2]+values[-3]","contract_signature":"values","evaluation_group":"model-56fa0bbff2be79b0","failed_approach":"The middle coefficient in the quadratic stencil is too small.","family":"xn-quadratic-sequence-extrapolation","id":"FA-6411","implementations":{"attempt":{"sha256":"8b476c972581be61d0cf016b7aa67dd2009ff8347d9a81b65ae4a72b157c9be1","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(values):\n    return 3*values[-1]-values[-2]+values[-3]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 4, 9],)', solve(*([1, 4, 9],)), 16)\ncheck('fixture 2: ([0, 1, 4],)', solve(*([0, 1, 4],)), 9)\ncheck('fixture 3: ([3, 3, 3],)', solve(*([3, 3, 3],)), 3)\ncheck('fixture 4: ([1, 2, 3],)', solve(*([1, 2, 3],)), 4)\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":"a83966f8638fd1bd7995a0f1dda575b7ac91306459f98f6f5c81e129a8b5771c","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(values):\n    return 2*values[-1]-values[-2]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 4, 9],)', solve(*([1, 4, 9],)), 16)\ncheck('fixture 2: ([0, 1, 4],)', solve(*([0, 1, 4],)), 9)\ncheck('fixture 3: ([3, 3, 3],)', solve(*([3, 3, 3],)), 3)\ncheck('fixture 4: ([1, 2, 3],)', solve(*([1, 2, 3],)), 4)\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-quadratic-sequence-extrapolation","generated_at":"2026-09-29T14:38:01.542877+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. Discrete calculus results depend on the stated convention.","root_cause":"Linear extrapolation omits second differences.","sha256":"312fc1fb93c444122e249313b3d93039a1346bace10cd479755da25c4320af86","title":"Quadratic sequence extrapolation · 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":47.746,"exit_code":1,"observations":[{"actual":24,"check":"fixture 1: ([1, 4, 9],)","expected":16,"passed":false},{"actual":11,"check":"fixture 2: ([0, 1, 4],)","expected":9,"passed":false},{"actual":9,"check":"fixture 3: ([3, 3, 3],)","expected":3,"passed":false},{"actual":8,"check":"fixture 4: ([1, 2, 3],)","expected":4,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 4, 9],)\", \"actual\": 24, \"expected\": 16, \"passed\": false}, {\"check\": \"fixture 2: ([0, 1, 4],)\", \"actual\": 11, \"expected\": 9, \"passed\": false}, {\"check\": \"fixture 3: ([3, 3, 3],)\", \"actual\": 9, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 4: ([1, 2, 3],)\", \"actual\": 8, \"expected\": 4, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":57.203,"exit_code":1,"observations":[{"actual":14,"check":"fixture 1: ([1, 4, 9],)","expected":16,"passed":false},{"actual":7,"check":"fixture 2: ([0, 1, 4],)","expected":9,"passed":false},{"actual":3,"check":"fixture 3: ([3, 3, 3],)","expected":3,"passed":true},{"actual":4,"check":"fixture 4: ([1, 2, 3],)","expected":4,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 4, 9],)\", \"actual\": 14, \"expected\": 16, \"passed\": false}, {\"check\": \"fixture 2: ([0, 1, 4],)\", \"actual\": 7, \"expected\": 9, \"passed\": false}, {\"check\": \"fixture 3: ([3, 3, 3],)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 4: ([1, 2, 3],)\", \"actual\": 4, \"expected\": 4, \"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."}}