{"abstract":"The center sample is not doubled.","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. Second central difference. Exact operational definition: [a-2*b+c for a,b,c in zip(values,values[1:],values[2:])]","contract_signature":"values","evaluation_group":"model-90ee009ce3d07e5a","failed_approach":"A first difference across two steps replaces curvature.","family":"xn-second-central-difference","id":"FA-6356","implementations":{"attempt":{"sha256":"3aae46b0d1e204ee8df80d6496e3ec2aefd6a7d740a89fbb2d576a431e1b31bd","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 [c-a for a,b,c in zip(values,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, 16],)', solve(*([1, 4, 9, 16],)), [2, 2])\ncheck('fixture 2: ([3, 3, 3],)', solve(*([3, 3, 3],)), [0])\ncheck('fixture 3: ([1, 2],)', solve(*([1, 2],)), [])\ncheck('fixture 4: ([0, 1, 0],)', solve(*([0, 1, 0],)), [-2])\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":"a76e30261ccfa72c68cd2e56246884490648d940af57287bcd2f389ab9e37824","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 [a-b+c for a,b,c in zip(values,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, 16],)', solve(*([1, 4, 9, 16],)), [2, 2])\ncheck('fixture 2: ([3, 3, 3],)', solve(*([3, 3, 3],)), [0])\ncheck('fixture 3: ([1, 2],)', solve(*([1, 2],)), [])\ncheck('fixture 4: ([0, 1, 0],)', solve(*([0, 1, 0],)), [-2])\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-second-central-difference","generated_at":"2026-09-29T14:38:00.624180+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":"The center sample is not doubled.","sha256":"d7f97d72f20fbf85212202e370d2fac0e8b7ac925fd822b83e5b41b6e0027741","title":"Second central difference · 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":45.677,"exit_code":1,"observations":[{"actual":[8,12],"check":"fixture 1: ([1, 4, 9, 16],)","expected":[2,2],"passed":false},{"actual":[0],"check":"fixture 2: ([3, 3, 3],)","expected":[0],"passed":true},{"actual":[],"check":"fixture 3: ([1, 2],)","expected":[],"passed":true},{"actual":[0],"check":"fixture 4: ([0, 1, 0],)","expected":[-2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 4, 9, 16],)\", \"actual\": [8, 12], \"expected\": [2, 2], \"passed\": false}, {\"check\": \"fixture 2: ([3, 3, 3],)\", \"actual\": [0], \"expected\": [0], \"passed\": true}, {\"check\": \"fixture 3: ([1, 2],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([0, 1, 0],)\", \"actual\": [0], \"expected\": [-2], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":51.404,"exit_code":1,"observations":[{"actual":[6,11],"check":"fixture 1: ([1, 4, 9, 16],)","expected":[2,2],"passed":false},{"actual":[3],"check":"fixture 2: ([3, 3, 3],)","expected":[0],"passed":false},{"actual":[],"check":"fixture 3: ([1, 2],)","expected":[],"passed":true},{"actual":[-1],"check":"fixture 4: ([0, 1, 0],)","expected":[-2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 4, 9, 16],)\", \"actual\": [6, 11], \"expected\": [2, 2], \"passed\": false}, {\"check\": \"fixture 2: ([3, 3, 3],)\", \"actual\": [3], \"expected\": [0], \"passed\": false}, {\"check\": \"fixture 3: ([1, 2],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([0, 1, 0],)\", \"actual\": [-1], \"expected\": [-2], \"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."}}