{"abstract":"Binary float conversion erases low bits before the root.","category":"Integer arithmetic","checks":4,"contract":"Integer arguments; denominators, steps, moduli, and bit widths are positive. Unsigned word inputs fit the specified width except where masking is explicitly the operation. Sequence sizes are nonnegative. n is nonnegative. Return the greatest r such that r*r<=n. Exact operational definition: math.isqrt(n)","contract_signature":"n","evaluation_group":"model-69e90853bb3ce0f4","failed_approach":"Nearest rounding does not compute the lower integer root.","family":"xn-integer-square-root-exact","id":"FA-5351","implementations":{"attempt":{"sha256":"98f7a56dc54f3608ac8becfcd52bd65c62935908a2e508e37f187610b09bd0d6","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(n):\n    return round(math.sqrt(n))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (81129638414606681695789005144063,)', solve(*(81129638414606681695789005144063,)), 9007199254740991)\ncheck('fixture 2: (15,)', solve(*(15,)), 3)\ncheck('fixture 3: (16,)', solve(*(16,)), 4)\ncheck('fixture 4: (0,)', solve(*(0,)), 0)\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":"00693e3180d02711342c38e9275ddcfe15fe9299cf316e08670fee72c96a7d7e","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(n):\n    return int(math.sqrt(n))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (81129638414606681695789005144063,)', solve(*(81129638414606681695789005144063,)), 9007199254740991)\ncheck('fixture 2: (15,)', solve(*(15,)), 3)\ncheck('fixture 3: (16,)', solve(*(16,)), 4)\ncheck('fixture 4: (0,)', solve(*(0,)), 0)\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-integer-square-root-exact","generated_at":"2026-09-29T14:37:48.599766+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. Integer mathematics results depend on the stated convention.","root_cause":"Binary float conversion erases low bits before the root.","sha256":"13f579866129359aac32cb76d881d56064bdbcef39743c940fe4f0cfd9343782","title":"Integer square root exact · 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":47.876,"exit_code":1,"observations":[{"actual":9007199254740992,"check":"fixture 1: (81129638414606681695789005144063,)","expected":9007199254740991,"passed":false},{"actual":4,"check":"fixture 2: (15,)","expected":3,"passed":false},{"actual":4,"check":"fixture 3: (16,)","expected":4,"passed":true},{"actual":0,"check":"fixture 4: (0,)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (81129638414606681695789005144063,)\", \"actual\": 9007199254740992, \"expected\": 9007199254740991, \"passed\": false}, {\"check\": \"fixture 2: (15,)\", \"actual\": 4, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 3: (16,)\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"fixture 4: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.61,"exit_code":1,"observations":[{"actual":9007199254740992,"check":"fixture 1: (81129638414606681695789005144063,)","expected":9007199254740991,"passed":false},{"actual":3,"check":"fixture 2: (15,)","expected":3,"passed":true},{"actual":4,"check":"fixture 3: (16,)","expected":4,"passed":true},{"actual":0,"check":"fixture 4: (0,)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (81129638414606681695789005144063,)\", \"actual\": 9007199254740992, \"expected\": 9007199254740991, \"passed\": false}, {\"check\": \"fixture 2: (15,)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (16,)\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"fixture 4: (0,)\", \"actual\": 0, \"expected\": 0, \"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."}}