{"abstract":"The binomial stencil coefficients are replaced with unit alternation.","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. v contains exactly four equally spaced observations. Exact operational definition: v[3]-3*v[2]+3*v[1]-v[0]","contract_signature":"v","evaluation_group":"model-b27aad65c3d0a5fc","failed_approach":"A second difference is returned for a third-difference contract.","family":"xn-binomial-forward-difference-order-three","id":"FA-6441","implementations":{"attempt":{"sha256":"53a3ffbe2d8eaa2f20f42d91927580cacd77ffaef5f91d64d036a3aa0cf0248f","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(v):\n    return v[3]-2*v[2]+v[1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 8, 27],)', solve(*([0, 1, 8, 27],)), 6)\ncheck('fixture 2: ([1, 4, 9, 16],)', solve(*([1, 4, 9, 16],)), 0)\ncheck('fixture 3: ([5, 5, 5, 5],)', solve(*([5, 5, 5, 5],)), 0)\ncheck('fixture 4: ([0, 0, 0, 1],)', solve(*([0, 0, 0, 1],)), 1)\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":"0f085ae09d6626d1b6f5a91fc88ed2b16d51670a9f8518eac1ad32325422ab2c","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(v):\n    return v[3]-v[2]+v[1]-v[0]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 8, 27],)', solve(*([0, 1, 8, 27],)), 6)\ncheck('fixture 2: ([1, 4, 9, 16],)', solve(*([1, 4, 9, 16],)), 0)\ncheck('fixture 3: ([5, 5, 5, 5],)', solve(*([5, 5, 5, 5],)), 0)\ncheck('fixture 4: ([0, 0, 0, 1],)', solve(*([0, 0, 0, 1],)), 1)\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-binomial-forward-difference-order-three","generated_at":"2026-09-29T14:38:01.974989+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 binomial stencil coefficients are replaced with unit alternation.","sha256":"6f8953d7fc5f6dc7d45099d13f27fca840cf204e8a08f1467a5659b84deebafc","title":"Binomial forward difference order three · 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":49.503,"exit_code":1,"observations":[{"actual":12,"check":"fixture 1: ([0, 1, 8, 27],)","expected":6,"passed":false},{"actual":2,"check":"fixture 2: ([1, 4, 9, 16],)","expected":0,"passed":false},{"actual":0,"check":"fixture 3: ([5, 5, 5, 5],)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: ([0, 0, 0, 1],)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 8, 27],)\", \"actual\": 12, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: ([1, 4, 9, 16],)\", \"actual\": 2, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: ([5, 5, 5, 5],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([0, 0, 0, 1],)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":51.035,"exit_code":1,"observations":[{"actual":20,"check":"fixture 1: ([0, 1, 8, 27],)","expected":6,"passed":false},{"actual":10,"check":"fixture 2: ([1, 4, 9, 16],)","expected":0,"passed":false},{"actual":0,"check":"fixture 3: ([5, 5, 5, 5],)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: ([0, 0, 0, 1],)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 8, 27],)\", \"actual\": 20, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: ([1, 4, 9, 16],)\", \"actual\": 10, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: ([5, 5, 5, 5],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([0, 0, 0, 1],)\", \"actual\": 1, \"expected\": 1, \"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."}}