{"abstract":"Banker rounding violates the upward midpoint convention.","category":"Integer arithmetic","checks":5,"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. Return the nearest multiple of step; exact halfway cases choose the greater signed result. Exact operational definition: ((2*a + step) // (2*step))*step","evaluation_group":"model-e4754d1a802981b2","failed_approach":"Adding a full step rounds every nonmultiple upward and moves exact multiples.","family":"xn-nearest-multiple-ties-up","id":"FA-5346","implementations":{"attempt":{"sha256":"e3fd984e777f67c881d10dfa0bb6981de181e6a9732c777ba44ef26a764ac61d","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, step):\n    return ((a + step) // step)*step\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 10)', solve(*(5, 10)), 10)\ncheck('fixture 2: (4, 10)', solve(*(4, 10)), 0)\ncheck('fixture 3: (-5, 10)', solve(*(-5, 10)), 0)\ncheck('fixture 4: (-6, 10)', solve(*(-6, 10)), -10)\ncheck('fixture 5: (20, 10)', solve(*(20, 10)), 20)\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":"0c32ce0b86d7fd3877e5f203e13e4df0897858e56e91912cf4177d95f364e38b","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, step):\n    return round(a/step)*step\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 10)', solve(*(5, 10)), 10)\ncheck('fixture 2: (4, 10)', solve(*(4, 10)), 0)\ncheck('fixture 3: (-5, 10)', solve(*(-5, 10)), 0)\ncheck('fixture 4: (-6, 10)', solve(*(-6, 10)), -10)\ncheck('fixture 5: (20, 10)', solve(*(20, 10)), 20)\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":"51d904438827e2fafc310ac31a0de1be1e80d786155ec739b66223940748fe1f","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, step):\n    return ((2*a + step) // (2*step))*step\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 10)', solve(*(5, 10)), 10)\ncheck('fixture 2: (4, 10)', solve(*(4, 10)), 0)\ncheck('fixture 3: (-5, 10)', solve(*(-5, 10)), 0)\ncheck('fixture 4: (-6, 10)', solve(*(-6, 10)), -10)\ncheck('fixture 5: (20, 10)', solve(*(20, 10)), 20)\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-nearest-multiple-ties-up","generated_at":"2026-09-29T14:37:48.555460+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 ((2*a + step) // (2*step))*step","root_cause":"Banker rounding violates the upward midpoint convention.","sha256":"c424804d7e2c44c379121d7b6ecb907bba945dc3bb4bb30dfed0906fd8ed14a2","title":"Nearest multiple ties up · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.589,"exit_code":1,"observations":[{"actual":10,"check":"fixture 1: (5, 10)","expected":10,"passed":true},{"actual":10,"check":"fixture 2: (4, 10)","expected":0,"passed":false},{"actual":0,"check":"fixture 3: (-5, 10)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: (-6, 10)","expected":-10,"passed":false},{"actual":30,"check":"fixture 5: (20, 10)","expected":20,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 10)\", \"actual\": 10, \"expected\": 10, \"passed\": true}, {\"check\": \"fixture 2: (4, 10)\", \"actual\": 10, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (-5, 10)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (-6, 10)\", \"actual\": 0, \"expected\": -10, \"passed\": false}, {\"check\": \"fixture 5: (20, 10)\", \"actual\": 30, \"expected\": 20, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":50.301,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (5, 10)","expected":10,"passed":false},{"actual":0,"check":"fixture 2: (4, 10)","expected":0,"passed":true},{"actual":0,"check":"fixture 3: (-5, 10)","expected":0,"passed":true},{"actual":-10,"check":"fixture 4: (-6, 10)","expected":-10,"passed":true},{"actual":20,"check":"fixture 5: (20, 10)","expected":20,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 10)\", \"actual\": 0, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 2: (4, 10)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (-5, 10)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (-6, 10)\", \"actual\": -10, \"expected\": -10, \"passed\": true}, {\"check\": \"fixture 5: (20, 10)\", \"actual\": 20, \"expected\": 20, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.663,"exit_code":0,"observations":[{"actual":10,"check":"fixture 1: (5, 10)","expected":10,"passed":true},{"actual":0,"check":"fixture 2: (4, 10)","expected":0,"passed":true},{"actual":0,"check":"fixture 3: (-5, 10)","expected":0,"passed":true},{"actual":-10,"check":"fixture 4: (-6, 10)","expected":-10,"passed":true},{"actual":20,"check":"fixture 5: (20, 10)","expected":20,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 10)\", \"actual\": 10, \"expected\": 10, \"passed\": true}, {\"check\": \"fixture 2: (4, 10)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (-5, 10)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (-6, 10)\", \"actual\": -10, \"expected\": -10, \"passed\": true}, {\"check\": \"fixture 5: (20, 10)\", \"actual\": 20, \"expected\": 20, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}