{"abstract":"The interpolation correction omits the x span.","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. The two function observations are integers; return None for equal residuals, otherwise one exact secant step. Exact operational definition: str(Fraction(x1)-Fraction(f1*(x1-x0),f1-f0)) if f1!=f0 else None","contract_signature":"x0, f0, x1, f1","evaluation_group":"model-a19c4430f6d31efa","failed_approach":"The correction moves along rather than against the residual.","family":"xn-secant-root-step-rational","id":"FA-6451","implementations":{"attempt":{"sha256":"4132bf0deb3084582443090deb761b335c8dfa6058e4f53ad0817a6c35525570","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(x0, f0, x1, f1):\n    return str(Fraction(x1)+Fraction(f1*(x1-x0),f1-f0)) if f1!=f0 else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0, -2, 4, 2)', solve(*(0, -2, 4, 2)), '2')\ncheck('fixture 2: (1, -1, 3, 3)', solve(*(1, -1, 3, 3)), '3/2')\ncheck('fixture 3: (0, 1, 2, 1)', solve(*(0, 1, 2, 1)), None)\ncheck('fixture 4: (2, 0, 4, 2)', solve(*(2, 0, 4, 2)), '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":"47684e775c7cf98253f9da8dcba75209026e82b0cbea1fe78dde7363cf7214a7","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(x0, f0, x1, f1):\n    return str(Fraction(x1)-Fraction(f1,f1-f0)) if f1!=f0 else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0, -2, 4, 2)', solve(*(0, -2, 4, 2)), '2')\ncheck('fixture 2: (1, -1, 3, 3)', solve(*(1, -1, 3, 3)), '3/2')\ncheck('fixture 3: (0, 1, 2, 1)', solve(*(0, 1, 2, 1)), None)\ncheck('fixture 4: (2, 0, 4, 2)', solve(*(2, 0, 4, 2)), '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-secant-root-step-rational","generated_at":"2026-09-29T14:38:02.109604+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 interpolation correction omits the x span.","sha256":"6e990a7fdfe942cd51b08dc66e1bd931503042f1e7c975f199144cf76950c0f9","title":"Secant root step rational · 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":41.661,"exit_code":1,"observations":[{"actual":"6","check":"fixture 1: (0, -2, 4, 2)","expected":"2","passed":false},{"actual":"9/2","check":"fixture 2: (1, -1, 3, 3)","expected":"3/2","passed":false},{"actual":null,"check":"fixture 3: (0, 1, 2, 1)","expected":null,"passed":true},{"actual":"6","check":"fixture 4: (2, 0, 4, 2)","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0, -2, 4, 2)\", \"actual\": \"6\", \"expected\": \"2\", \"passed\": false}, {\"check\": \"fixture 2: (1, -1, 3, 3)\", \"actual\": \"9/2\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"fixture 3: (0, 1, 2, 1)\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"fixture 4: (2, 0, 4, 2)\", \"actual\": \"6\", \"expected\": \"2\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.751,"exit_code":1,"observations":[{"actual":"7/2","check":"fixture 1: (0, -2, 4, 2)","expected":"2","passed":false},{"actual":"9/4","check":"fixture 2: (1, -1, 3, 3)","expected":"3/2","passed":false},{"actual":null,"check":"fixture 3: (0, 1, 2, 1)","expected":null,"passed":true},{"actual":"3","check":"fixture 4: (2, 0, 4, 2)","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0, -2, 4, 2)\", \"actual\": \"7/2\", \"expected\": \"2\", \"passed\": false}, {\"check\": \"fixture 2: (1, -1, 3, 3)\", \"actual\": \"9/4\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"fixture 3: (0, 1, 2, 1)\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"fixture 4: (2, 0, 4, 2)\", \"actual\": \"3\", \"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."}}