{"abstract":"The floating midpoint loses integer precision and negative floor semantics.","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 may be signed and unordered; return floor((a+b)/2) exactly. Exact operational definition: (a+b)//2","evaluation_group":"model-9cc03e271f26452b","failed_approach":"A direction-dependent correction truncates reversed odd spans.","family":"xn-midpoint-floor-no-float","id":"FA-5431","implementations":{"attempt":{"sha256":"b0e463a864a0822a4adb46b7663fca4ccf622ac2928ba58c9529702593a89d36","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):\n    return a+(b-a)//2 if a <= b else a-(a-b)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1152921504606846976, 1152921504606846978)', solve(*(1152921504606846976, 1152921504606846978)), 1152921504606846977)\ncheck('fixture 2: (-2, -1)', solve(*(-2, -1)), -2)\ncheck('fixture 3: (0, 3)', solve(*(0, 3)), 1)\ncheck('fixture 4: (3, 0)', solve(*(3, 0)), 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":"fc391f84255103992bd5b6dffe3ad3ea4b01d37cead60b27a3e59fdef1911a77","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):\n    return int((a+b)/2)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1152921504606846976, 1152921504606846978)', solve(*(1152921504606846976, 1152921504606846978)), 1152921504606846977)\ncheck('fixture 2: (-2, -1)', solve(*(-2, -1)), -2)\ncheck('fixture 3: (0, 3)', solve(*(0, 3)), 1)\ncheck('fixture 4: (3, 0)', solve(*(3, 0)), 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":"b414e44d4909d8c1dd6aa29cc927ed25f60c86448bd6825edc1de4ed0f19c9b1","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):\n    return (a+b)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1152921504606846976, 1152921504606846978)', solve(*(1152921504606846976, 1152921504606846978)), 1152921504606846977)\ncheck('fixture 2: (-2, -1)', solve(*(-2, -1)), -2)\ncheck('fixture 3: (0, 3)', solve(*(0, 3)), 1)\ncheck('fixture 4: (3, 0)', solve(*(3, 0)), 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-midpoint-floor-no-float","generated_at":"2026-09-29T14:37:49.458651+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 (a+b)//2","root_cause":"The floating midpoint loses integer precision and negative floor semantics.","sha256":"5e135840885a14c1dfd06b97d8b813eb170aecfba3d3ae2c381fa9fc618b48e8","title":"Midpoint floor no float · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.596,"exit_code":1,"observations":[{"actual":1152921504606846977,"check":"fixture 1: (1152921504606846976, 1152921504606846978)","expected":1152921504606846977,"passed":true},{"actual":-2,"check":"fixture 2: (-2, -1)","expected":-2,"passed":true},{"actual":1,"check":"fixture 3: (0, 3)","expected":1,"passed":true},{"actual":2,"check":"fixture 4: (3, 0)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1152921504606846976, 1152921504606846978)\", \"actual\": 1152921504606846977, \"expected\": 1152921504606846977, \"passed\": true}, {\"check\": \"fixture 2: (-2, -1)\", \"actual\": -2, \"expected\": -2, \"passed\": true}, {\"check\": \"fixture 3: (0, 3)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (3, 0)\", \"actual\": 2, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":135.035,"exit_code":1,"observations":[{"actual":1152921504606846976,"check":"fixture 1: (1152921504606846976, 1152921504606846978)","expected":1152921504606846977,"passed":false},{"actual":-1,"check":"fixture 2: (-2, -1)","expected":-2,"passed":false},{"actual":1,"check":"fixture 3: (0, 3)","expected":1,"passed":true},{"actual":1,"check":"fixture 4: (3, 0)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1152921504606846976, 1152921504606846978)\", \"actual\": 1152921504606846976, \"expected\": 1152921504606846977, \"passed\": false}, {\"check\": \"fixture 2: (-2, -1)\", \"actual\": -1, \"expected\": -2, \"passed\": false}, {\"check\": \"fixture 3: (0, 3)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (3, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.12,"exit_code":0,"observations":[{"actual":1152921504606846977,"check":"fixture 1: (1152921504606846976, 1152921504606846978)","expected":1152921504606846977,"passed":true},{"actual":-2,"check":"fixture 2: (-2, -1)","expected":-2,"passed":true},{"actual":1,"check":"fixture 3: (0, 3)","expected":1,"passed":true},{"actual":1,"check":"fixture 4: (3, 0)","expected":1,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1152921504606846976, 1152921504606846978)\", \"actual\": 1152921504606846977, \"expected\": 1152921504606846977, \"passed\": true}, {\"check\": \"fixture 2: (-2, -1)\", \"actual\": -2, \"expected\": -2, \"passed\": true}, {\"check\": \"fixture 3: (0, 3)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (3, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}