{"abstract":"OR retains overlaps that Gray coding must cancel.","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 binary-reflected Gray code word. Exact operational definition: n ^ (n>>1)","evaluation_group":"model-656f10a8f312b7dd","failed_approach":"The adjacent-bit comparison uses the wrong direction.","family":"xn-binary-gray-encode","id":"FA-5421","implementations":{"attempt":{"sha256":"3b07391119dcd75daa88fc90492994934ba99646d520dda3ea9804388347af03","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: (2,)', solve(*(2,)), 3)\ncheck('fixture 4: (7,)', solve(*(7,)), 4)\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":"2a0e7699593b681a5c7b239e58dc64c966958cb7d2574a9ef88e6a8761f93159","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: (2,)', solve(*(2,)), 3)\ncheck('fixture 4: (7,)', solve(*(7,)), 4)\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":"9d5a86604af2a34b14687e40618dfe4a2455acf26a64ce78a21165f4a4323fe2","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: (2,)', solve(*(2,)), 3)\ncheck('fixture 4: (7,)', solve(*(7,)), 4)\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-encode","generated_at":"2026-09-29T14:37:49.459861+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: return n ^ (n>>1)","root_cause":"OR retains overlaps that Gray coding must cancel.","sha256":"523013402ed3956d161c3648d5f75e7e5e23f5d8a8d5180681d254f80402797c","title":"Binary gray encode · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.306,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":3,"check":"fixture 2: (1,)","expected":1,"passed":false},{"actual":6,"check":"fixture 3: (2,)","expected":3,"passed":false},{"actual":9,"check":"fixture 4: (7,)","expected":4,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 3, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (2,)\", \"actual\": 6, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 4: (7,)\", \"actual\": 9, \"expected\": 4, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":140.395,"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: (2,)","expected":3,"passed":true},{"actual":7,"check":"fixture 4: (7,)","expected":4,"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: (2,)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 4: (7,)\", \"actual\": 7, \"expected\": 4, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":47.68,"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":3,"check":"fixture 3: (2,)","expected":3,"passed":true},{"actual":4,"check":"fixture 4: (7,)","expected":4,"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: (2,)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 4: (7,)\", \"actual\": 4, \"expected\": 4, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}