{"abstract":"Clearing the low bit is confused with extracting it.","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; retain exactly its least significant one, or return zero for zero. Exact operational definition: n & -n","contract_signature":"n","evaluation_group":"model-f968be76a53aadf2","failed_approach":"Extracting the most significant bit selects the wrong end.","family":"xn-isolate-lowest-set-bit","id":"FA-5406","implementations":{"attempt":{"sha256":"26b3c273d152eccd66e27846f676c4ccd645cdd9ce58675915e59368696fa241","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 1 << (n.bit_length()-1) if n else 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (12,)', solve(*(12,)), 4)\ncheck('fixture 2: (8,)', solve(*(8,)), 8)\ncheck('fixture 3: (0,)', solve(*(0,)), 0)\ncheck('fixture 4: (7,)', solve(*(7,)), 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":"707e5c46ae606a4ee8e37e2d865739ee1aa649f412ecfe9faec6efc13076d688","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 n & (n-1)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (12,)', solve(*(12,)), 4)\ncheck('fixture 2: (8,)', solve(*(8,)), 8)\ncheck('fixture 3: (0,)', solve(*(0,)), 0)\ncheck('fixture 4: (7,)', solve(*(7,)), 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-isolate-lowest-set-bit","generated_at":"2026-09-29T14:37:49.217938+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":"Clearing the low bit is confused with extracting it.","sha256":"eacd402a44566600af89b60c2c14b40d15443655de1aa79b336586049093c976","title":"Isolate lowest set bit · 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":49.837,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (12,)","expected":4,"passed":false},{"actual":8,"check":"fixture 2: (8,)","expected":8,"passed":true},{"actual":0,"check":"fixture 3: (0,)","expected":0,"passed":true},{"actual":4,"check":"fixture 4: (7,)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (12,)\", \"actual\": 8, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 2: (8,)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 3: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (7,)\", \"actual\": 4, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.917,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (12,)","expected":4,"passed":false},{"actual":0,"check":"fixture 2: (8,)","expected":8,"passed":false},{"actual":0,"check":"fixture 3: (0,)","expected":0,"passed":true},{"actual":6,"check":"fixture 4: (7,)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (12,)\", \"actual\": 8, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 2: (8,)\", \"actual\": 0, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 3: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (7,)\", \"actual\": 6, \"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."}}