{"abstract":"Underflow wraps into a large positive number.","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. a and b are unsigned words; floor a-b at zero. Exact operational definition: max(0,a-b)","contract_signature":"a, b, bits","evaluation_group":"model-3021c0488a89f258","failed_approach":"Absolute difference reverses an underflow into a positive result.","family":"xn-unsigned-saturating-subtraction","id":"FA-5376","implementations":{"attempt":{"sha256":"a813f21ba99312a7b294eee9dceff6348172b69794a2f57acdbfb570028f1fd8","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(a, b, bits):\n    return abs(a-b)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 3, 8)', solve(*(1, 3, 8)), 0)\ncheck('fixture 2: (3, 1, 8)', solve(*(3, 1, 8)), 2)\ncheck('fixture 3: (0, 0, 8)', solve(*(0, 0, 8)), 0)\ncheck('fixture 4: (255, 255, 8)', solve(*(255, 255, 8)), 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":"6bafdd7a4b26bd77e0f7c612da559d1e0e362bf904315a92d87a1d32c768a8fc","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(a, b, bits):\n    return (a-b)%(1<<bits)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 3, 8)', solve(*(1, 3, 8)), 0)\ncheck('fixture 2: (3, 1, 8)', solve(*(3, 1, 8)), 2)\ncheck('fixture 3: (0, 0, 8)', solve(*(0, 0, 8)), 0)\ncheck('fixture 4: (255, 255, 8)', solve(*(255, 255, 8)), 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-unsigned-saturating-subtraction","generated_at":"2026-09-29T14:37:48.636930+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":"Underflow wraps into a large positive number.","sha256":"6b733e6f4d8bbb05bd02e3853ef528e21db245822be470a78232da7b6ac26acf","title":"Unsigned saturating subtraction · 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":42.641,"exit_code":1,"observations":[{"actual":2,"check":"fixture 1: (1, 3, 8)","expected":0,"passed":false},{"actual":2,"check":"fixture 2: (3, 1, 8)","expected":2,"passed":true},{"actual":0,"check":"fixture 3: (0, 0, 8)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: (255, 255, 8)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 3, 8)\", \"actual\": 2, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 2: (3, 1, 8)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: (0, 0, 8)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (255, 255, 8)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.817,"exit_code":1,"observations":[{"actual":254,"check":"fixture 1: (1, 3, 8)","expected":0,"passed":false},{"actual":2,"check":"fixture 2: (3, 1, 8)","expected":2,"passed":true},{"actual":0,"check":"fixture 3: (0, 0, 8)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: (255, 255, 8)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 3, 8)\", \"actual\": 254, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 2: (3, 1, 8)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: (0, 0, 8)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (255, 255, 8)\", \"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."}}