{"abstract":"The two-sided distance is treated as one step.","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. Central first derivative samples. Exact operational definition: str(Fraction(right-left,2*h))","contract_signature":"left, right, h","evaluation_group":"model-66427327cee7907e","failed_approach":"Endpoint values are added rather than differenced.","family":"xn-central-first-derivative-samples","id":"FA-6386","implementations":{"attempt":{"sha256":"9bc9455026e88f28d455c447f50560ade3a9f3fb6f548d61a1c932078e35f045","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(left, right, h):\n    return str(Fraction(right+left,2*h))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 9, 1)', solve(*(1, 9, 1)), '4')\ncheck('fixture 2: (3, 3, 2)', solve(*(3, 3, 2)), '0')\ncheck('fixture 3: (9, 1, 2)', solve(*(9, 1, 2)), '-2')\ncheck('fixture 4: (-2, 2, 2)', solve(*(-2, 2, 2)), '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":"49f742bfd6e11359f7683b896b64c7206aee2df7c6713d5f169ae8142e4d4768","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(left, right, h):\n    return str(Fraction(right-left,h))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 9, 1)', solve(*(1, 9, 1)), '4')\ncheck('fixture 2: (3, 3, 2)', solve(*(3, 3, 2)), '0')\ncheck('fixture 3: (9, 1, 2)', solve(*(9, 1, 2)), '-2')\ncheck('fixture 4: (-2, 2, 2)', solve(*(-2, 2, 2)), '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-central-first-derivative-samples","generated_at":"2026-09-29T14:38:01.398417+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 two-sided distance is treated as one step.","sha256":"7f231bc1677081d58a8950e362c9197764c8e18e3b0ea5197931ad0409c2f590","title":"Central first derivative samples · 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":48.657,"exit_code":1,"observations":[{"actual":"5","check":"fixture 1: (1, 9, 1)","expected":"4","passed":false},{"actual":"3/2","check":"fixture 2: (3, 3, 2)","expected":"0","passed":false},{"actual":"5/2","check":"fixture 3: (9, 1, 2)","expected":"-2","passed":false},{"actual":"0","check":"fixture 4: (-2, 2, 2)","expected":"1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 9, 1)\", \"actual\": \"5\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"fixture 2: (3, 3, 2)\", \"actual\": \"3/2\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"fixture 3: (9, 1, 2)\", \"actual\": \"5/2\", \"expected\": \"-2\", \"passed\": false}, {\"check\": \"fixture 4: (-2, 2, 2)\", \"actual\": \"0\", \"expected\": \"1\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":84.523,"exit_code":1,"observations":[{"actual":"8","check":"fixture 1: (1, 9, 1)","expected":"4","passed":false},{"actual":"0","check":"fixture 2: (3, 3, 2)","expected":"0","passed":true},{"actual":"-4","check":"fixture 3: (9, 1, 2)","expected":"-2","passed":false},{"actual":"2","check":"fixture 4: (-2, 2, 2)","expected":"1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 9, 1)\", \"actual\": \"8\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"fixture 2: (3, 3, 2)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 3: (9, 1, 2)\", \"actual\": \"-4\", \"expected\": \"-2\", \"passed\": false}, {\"check\": \"fixture 4: (-2, 2, 2)\", \"actual\": \"2\", \"expected\": \"1\", \"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."}}