{"abstract":"Exact powers of two consume an extra address bit.","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 minimum nonnegative k with 2**k>=n. Exact operational definition: 0 if n <= 1 else (n-1).bit_length()","contract_signature":"n","evaluation_group":"model-871c51fd8d83a42a","failed_approach":"Flooring the logarithm underallocates nonpowers.","family":"xn-ceil-log-two-capacity","id":"FA-5441","implementations":{"attempt":{"sha256":"1fe2a16426ab0893f39f4d21137f3abfd788a10382f2cddb9d8568159c8ab90a","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.log2(n)) if n else 0\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,)), 0)\ncheck('fixture 3: (8,)', solve(*(8,)), 3)\ncheck('fixture 4: (9,)', solve(*(9,)), 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":"74732c8d90f1a36c35802a7436815e8c6c856fee77562288873a9dacf870eba0","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.bit_length()\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,)), 0)\ncheck('fixture 3: (8,)', solve(*(8,)), 3)\ncheck('fixture 4: (9,)', solve(*(9,)), 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-ceil-log-two-capacity","generated_at":"2026-09-29T14:37:49.501170+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":"Exact powers of two consume an extra address bit.","sha256":"d3b17da31c33be3360148bc73daca54bb4d3259d2da86e4da4404d08a5de26fe","title":"Ceil log two capacity · 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":42.915,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":0,"check":"fixture 2: (1,)","expected":0,"passed":true},{"actual":3,"check":"fixture 3: (8,)","expected":3,"passed":true},{"actual":3,"check":"fixture 4: (9,)","expected":4,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (8,)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 4: (9,)\", \"actual\": 3, \"expected\": 4, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.332,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":0,"passed":false},{"actual":4,"check":"fixture 3: (8,)","expected":3,"passed":false},{"actual":4,"check":"fixture 4: (9,)","expected":4,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (8,)\", \"actual\": 4, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 4: (9,)\", \"actual\": 4, \"expected\": 4, \"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."}}