{"abstract":"Encoding a Gray word again does not decode 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 a nonnegative Gray code word; return its decoded binary integer. Exact operational definition: result=0\nwhile n:\n    result ^= n\n    n >>= 1\nreturn result","evaluation_group":"model-e8c01050ea928faf","failed_approach":"A single OR cannot accumulate the prefix XOR.","family":"xn-binary-gray-decode","id":"FA-5426","implementations":{"attempt":{"sha256":"1707a76f6f5150286f79334a5e3f4a06110f3b9ca7e013b237f30d338334fce3","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: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 2)\ncheck('fixture 4: (4,)', solve(*(4,)), 7)\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":"9e68373068a567b06d11373ea7e453ce243dd29c8db9efbfac29deedc1943e23","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: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 2)\ncheck('fixture 4: (4,)', solve(*(4,)), 7)\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"},"fixed":{"sha256":"1a8e6ea1a5660af8895cbd5625132b15c6d43e8124d9766e63e56a9c2d476835","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    result=0\n    while n:\n        result ^= n\n        n >>= 1\n    return result\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 2)\ncheck('fixture 4: (4,)', solve(*(4,)), 7)\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-binary-gray-decode","generated_at":"2026-09-29T14:37:49.457537+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.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: result=0\nwhile n:\n    result ^= n\n    n >>= 1\nreturn result","root_cause":"Encoding a Gray word again does not decode it.","sha256":"b5288af1f4a00289c02701fd0fae99037d3a1a2e4424ecceac4b4f7fdf9faace","title":"Binary gray decode · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.684,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":3,"check":"fixture 3: (3,)","expected":2,"passed":false},{"actual":6,"check":"fixture 4: (4,)","expected":7,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 3, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 4: (4,)\", \"actual\": 6, \"expected\": 7, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":137.284,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":2,"check":"fixture 3: (3,)","expected":2,"passed":true},{"actual":6,"check":"fixture 4: (4,)","expected":7,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 4: (4,)\", \"actual\": 6, \"expected\": 7, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.548,"exit_code":0,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":2,"check":"fixture 3: (3,)","expected":2,"passed":true},{"actual":7,"check":"fixture 4: (4,)","expected":7,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 4: (4,)\", \"actual\": 7, \"expected\": 7, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}