{"abstract":"The reciprocal correction is returned without averaging the current iterate.","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. x>0 and target>=0; return one exact Newton step for x*x-target=0. Exact operational definition: str((Fraction(x)+Fraction(target,x))/2)","contract_signature":"x, target","evaluation_group":"model-7d2cc406f9e5e897","failed_approach":"The Newton average lacks its factor of one half.","family":"xn-newton-step-quadratic-root","id":"FA-6446","implementations":{"attempt":{"sha256":"08681781785dfb2ec359fb5794763e3fa16b4fff552e56c3d51ae9fee425e4b5","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(x, target):\n    return str(Fraction(x)+Fraction(target,x))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 9)', solve(*(3, 9)), '3')\ncheck('fixture 2: (2, 9)', solve(*(2, 9)), '13/4')\ncheck('fixture 3: (1, 2)', solve(*(1, 2)), '3/2')\ncheck('fixture 4: (4, 0)', solve(*(4, 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":"f5eef8baed049e05cea348010ba0c8977b201dcad0fdc33772d7d0b63ed8523b","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(x, target):\n    return str(Fraction(target,x))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 9)', solve(*(3, 9)), '3')\ncheck('fixture 2: (2, 9)', solve(*(2, 9)), '13/4')\ncheck('fixture 3: (1, 2)', solve(*(1, 2)), '3/2')\ncheck('fixture 4: (4, 0)', solve(*(4, 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-newton-step-quadratic-root","generated_at":"2026-09-29T14:38:02.020419+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 reciprocal correction is returned without averaging the current iterate.","sha256":"896f6911f2c27d0b3ce5ef5370964f17be8aef3e4016690cfd34f536fd4b4ee1","title":"Newton step quadratic root · 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":139.153,"exit_code":1,"observations":[{"actual":"6","check":"fixture 1: (3, 9)","expected":"3","passed":false},{"actual":"13/2","check":"fixture 2: (2, 9)","expected":"13/4","passed":false},{"actual":"3","check":"fixture 3: (1, 2)","expected":"3/2","passed":false},{"actual":"4","check":"fixture 4: (4, 0)","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 9)\", \"actual\": \"6\", \"expected\": \"3\", \"passed\": false}, {\"check\": \"fixture 2: (2, 9)\", \"actual\": \"13/2\", \"expected\": \"13/4\", \"passed\": false}, {\"check\": \"fixture 3: (1, 2)\", \"actual\": \"3\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"fixture 4: (4, 0)\", \"actual\": \"4\", \"expected\": \"2\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.99,"exit_code":1,"observations":[{"actual":"3","check":"fixture 1: (3, 9)","expected":"3","passed":true},{"actual":"9/2","check":"fixture 2: (2, 9)","expected":"13/4","passed":false},{"actual":"2","check":"fixture 3: (1, 2)","expected":"3/2","passed":false},{"actual":"0","check":"fixture 4: (4, 0)","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 9)\", \"actual\": \"3\", \"expected\": \"3\", \"passed\": true}, {\"check\": \"fixture 2: (2, 9)\", \"actual\": \"9/2\", \"expected\": \"13/4\", \"passed\": false}, {\"check\": \"fixture 3: (1, 2)\", \"actual\": \"2\", \"expected\": \"3/2\", \"passed\": false}, {\"check\": \"fixture 4: (4, 0)\", \"actual\": \"0\", \"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."}}