{"abstract":"Interval length loses alignment to the divisor.","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. lo<=hi; count all integer multiples of positive step in the closed interval. Exact operational definition: hi//step - (lo-1)//step","evaluation_group":"model-f4a7c32e75f9d5ce","failed_approach":"Subtracting the lower quotient excludes an aligned lower endpoint.","family":"xn-inclusive-multiples-count","id":"FA-5471","implementations":{"attempt":{"sha256":"6a20e3a7fd48a333c331edf20b6a66e8551b5106d85a9894be18ef7def6e5a2b","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(lo, hi, step):\n    return hi//step - lo//step\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 9, 3)', solve(*(3, 9, 3)), 3)\ncheck('fixture 2: (-5, 5, 3)', solve(*(-5, 5, 3)), 3)\ncheck('fixture 3: (1, 2, 3)', solve(*(1, 2, 3)), 0)\ncheck('fixture 4: (0, 0, 4)', solve(*(0, 0, 4)), 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":"4f477f429eb6a6eb6d6bf844c306ec599bbb05e26f21d4d34b897883b98972fc","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(lo, hi, step):\n    return (hi-lo)//step\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 9, 3)', solve(*(3, 9, 3)), 3)\ncheck('fixture 2: (-5, 5, 3)', solve(*(-5, 5, 3)), 3)\ncheck('fixture 3: (1, 2, 3)', solve(*(1, 2, 3)), 0)\ncheck('fixture 4: (0, 0, 4)', solve(*(0, 0, 4)), 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"},"fixed":{"sha256":"945349368f8bfe214393702fd15282d9b72367fe4f7be376c1446a34060abecd","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(lo, hi, step):\n    return hi//step - (lo-1)//step\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 9, 3)', solve(*(3, 9, 3)), 3)\ncheck('fixture 2: (-5, 5, 3)', solve(*(-5, 5, 3)), 3)\ncheck('fixture 3: (1, 2, 3)', solve(*(1, 2, 3)), 0)\ncheck('fixture 4: (0, 0, 4)', solve(*(0, 0, 4)), 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-inclusive-multiples-count","generated_at":"2026-09-29T14:37:49.975089+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 hi//step - (lo-1)//step","root_cause":"Interval length loses alignment to the divisor.","sha256":"ea9a467b139d9cc64611d092c8070cc0416face254807d4629be307b36688bc7","title":"Inclusive multiples count · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.736,"exit_code":1,"observations":[{"actual":2,"check":"fixture 1: (3, 9, 3)","expected":3,"passed":false},{"actual":3,"check":"fixture 2: (-5, 5, 3)","expected":3,"passed":true},{"actual":0,"check":"fixture 3: (1, 2, 3)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: (0, 0, 4)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 9, 3)\", \"actual\": 2, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 2: (-5, 5, 3)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (1, 2, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (0, 0, 4)\", \"actual\": 0, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.722,"exit_code":1,"observations":[{"actual":2,"check":"fixture 1: (3, 9, 3)","expected":3,"passed":false},{"actual":3,"check":"fixture 2: (-5, 5, 3)","expected":3,"passed":true},{"actual":0,"check":"fixture 3: (1, 2, 3)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: (0, 0, 4)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 9, 3)\", \"actual\": 2, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 2: (-5, 5, 3)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (1, 2, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (0, 0, 4)\", \"actual\": 0, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":48.591,"exit_code":0,"observations":[{"actual":3,"check":"fixture 1: (3, 9, 3)","expected":3,"passed":true},{"actual":3,"check":"fixture 2: (-5, 5, 3)","expected":3,"passed":true},{"actual":0,"check":"fixture 3: (1, 2, 3)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: (0, 0, 4)","expected":1,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 9, 3)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 2: (-5, 5, 3)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (1, 2, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (0, 0, 4)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}