{"abstract":"Linear distance ignores wraparound.","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. Return the smaller nonnegative arc length on a cycle of circumference m. Exact operational definition: min((a-b)%m, (b-a)%m)","evaluation_group":"model-ddcc9d185b58bf13","failed_approach":"Reducing a forward distance still ignores the shorter reverse arc.","family":"xn-symmetric-modular-distance","id":"FA-5341","implementations":{"attempt":{"sha256":"b2572dc837149f295a7c0d738f8c5081979a9fd18ed43d2f77c2bbb89b2302e9","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, m):\n    return abs(a-b)%m\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 9, 10)', solve(*(1, 9, 10)), 2)\ncheck('fixture 2: (2, 5, 10)', solve(*(2, 5, 10)), 3)\ncheck('fixture 3: (12, 2, 10)', solve(*(12, 2, 10)), 0)\ncheck('fixture 4: (-1, 1, 10)', solve(*(-1, 1, 10)), 2)\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":"2b710dbaa35bb98e3fce9bb34a7d09a1ba99fcc1c6d95b2d32407314466ea740","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, m):\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, 9, 10)', solve(*(1, 9, 10)), 2)\ncheck('fixture 2: (2, 5, 10)', solve(*(2, 5, 10)), 3)\ncheck('fixture 3: (12, 2, 10)', solve(*(12, 2, 10)), 0)\ncheck('fixture 4: (-1, 1, 10)', solve(*(-1, 1, 10)), 2)\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":"ab00accde31fe456f5a2a85abe1221929b2d34683e3be6789ffaea05ce69a5f5","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, m):\n    return min((a-b)%m, (b-a)%m)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 9, 10)', solve(*(1, 9, 10)), 2)\ncheck('fixture 2: (2, 5, 10)', solve(*(2, 5, 10)), 3)\ncheck('fixture 3: (12, 2, 10)', solve(*(12, 2, 10)), 0)\ncheck('fixture 4: (-1, 1, 10)', solve(*(-1, 1, 10)), 2)\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-symmetric-modular-distance","generated_at":"2026-09-29T14:37:48.558880+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 min((a-b)%m, (b-a)%m)","root_cause":"Linear distance ignores wraparound.","sha256":"509181ca0b796c548f41871e962f273e0933238af336305b34c90fbdb35ad2e2","title":"Symmetric modular distance · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.657,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (1, 9, 10)","expected":2,"passed":false},{"actual":3,"check":"fixture 2: (2, 5, 10)","expected":3,"passed":true},{"actual":0,"check":"fixture 3: (12, 2, 10)","expected":0,"passed":true},{"actual":2,"check":"fixture 4: (-1, 1, 10)","expected":2,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 9, 10)\", \"actual\": 8, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 2: (2, 5, 10)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (12, 2, 10)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (-1, 1, 10)\", \"actual\": 2, \"expected\": 2, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":52.324,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (1, 9, 10)","expected":2,"passed":false},{"actual":3,"check":"fixture 2: (2, 5, 10)","expected":3,"passed":true},{"actual":10,"check":"fixture 3: (12, 2, 10)","expected":0,"passed":false},{"actual":2,"check":"fixture 4: (-1, 1, 10)","expected":2,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 9, 10)\", \"actual\": 8, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 2: (2, 5, 10)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (12, 2, 10)\", \"actual\": 10, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 4: (-1, 1, 10)\", \"actual\": 2, \"expected\": 2, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.255,"exit_code":0,"observations":[{"actual":2,"check":"fixture 1: (1, 9, 10)","expected":2,"passed":true},{"actual":3,"check":"fixture 2: (2, 5, 10)","expected":3,"passed":true},{"actual":0,"check":"fixture 3: (12, 2, 10)","expected":0,"passed":true},{"actual":2,"check":"fixture 4: (-1, 1, 10)","expected":2,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 9, 10)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 2: (2, 5, 10)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (12, 2, 10)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (-1, 1, 10)\", \"actual\": 2, \"expected\": 2, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}