{"abstract":"The last term is multiplied by the count instead of using the endpoint average.","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 d may be signed; n>=0. Sum n terms starting with a and common difference d. Exact operational definition: n*(2*a+(n-1)*d)//2","evaluation_group":"model-e43205a6a6e5af2d","failed_approach":"The final term index is n instead of n minus one.","family":"xn-arithmetic-progression-sum","id":"FA-5461","implementations":{"attempt":{"sha256":"61ed950c8bd190fedcffc357a0d644b925d70d2d30732d2f8b98dba905c15537","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, d, n):\n    return n*(2*a+n*d)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3, 4)', solve(*(2, 3, 4)), 26)\ncheck('fixture 2: (5, 0, 3)', solve(*(5, 0, 3)), 15)\ncheck('fixture 3: (4, -1, 4)', solve(*(4, -1, 4)), 10)\ncheck('fixture 4: (9, 2, 0)', solve(*(9, 2, 0)), 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":"33b65cde83f918b5f1f1e2d691fe23ce956f421559a6eb9fd3b38e808e157079","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, d, n):\n    return n*(a+(n-1)*d)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3, 4)', solve(*(2, 3, 4)), 26)\ncheck('fixture 2: (5, 0, 3)', solve(*(5, 0, 3)), 15)\ncheck('fixture 3: (4, -1, 4)', solve(*(4, -1, 4)), 10)\ncheck('fixture 4: (9, 2, 0)', solve(*(9, 2, 0)), 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"},"fixed":{"sha256":"49a787ecf2ac40aa53773f8f9ebd78938e444de09fe96f85c5920a62df4d3e1b","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, d, n):\n    return n*(2*a+(n-1)*d)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3, 4)', solve(*(2, 3, 4)), 26)\ncheck('fixture 2: (5, 0, 3)', solve(*(5, 0, 3)), 15)\ncheck('fixture 3: (4, -1, 4)', solve(*(4, -1, 4)), 10)\ncheck('fixture 4: (9, 2, 0)', solve(*(9, 2, 0)), 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-arithmetic-progression-sum","generated_at":"2026-09-29T14:37:49.775448+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 n*(2*a+(n-1)*d)//2","root_cause":"The last term is multiplied by the count instead of using the endpoint average.","sha256":"5dfdbb9d59ba6eca1d4a10b3a9069f2c8834e11d0cc674a81853928d19b5661c","title":"Arithmetic progression sum · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":45.974,"exit_code":1,"observations":[{"actual":32,"check":"fixture 1: (2, 3, 4)","expected":26,"passed":false},{"actual":15,"check":"fixture 2: (5, 0, 3)","expected":15,"passed":true},{"actual":8,"check":"fixture 3: (4, -1, 4)","expected":10,"passed":false},{"actual":0,"check":"fixture 4: (9, 2, 0)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3, 4)\", \"actual\": 32, \"expected\": 26, \"passed\": false}, {\"check\": \"fixture 2: (5, 0, 3)\", \"actual\": 15, \"expected\": 15, \"passed\": true}, {\"check\": \"fixture 3: (4, -1, 4)\", \"actual\": 8, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 4: (9, 2, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.32,"exit_code":1,"observations":[{"actual":44,"check":"fixture 1: (2, 3, 4)","expected":26,"passed":false},{"actual":15,"check":"fixture 2: (5, 0, 3)","expected":15,"passed":true},{"actual":4,"check":"fixture 3: (4, -1, 4)","expected":10,"passed":false},{"actual":0,"check":"fixture 4: (9, 2, 0)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3, 4)\", \"actual\": 44, \"expected\": 26, \"passed\": false}, {\"check\": \"fixture 2: (5, 0, 3)\", \"actual\": 15, \"expected\": 15, \"passed\": true}, {\"check\": \"fixture 3: (4, -1, 4)\", \"actual\": 4, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 4: (9, 2, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":46.011,"exit_code":0,"observations":[{"actual":26,"check":"fixture 1: (2, 3, 4)","expected":26,"passed":true},{"actual":15,"check":"fixture 2: (5, 0, 3)","expected":15,"passed":true},{"actual":10,"check":"fixture 3: (4, -1, 4)","expected":10,"passed":true},{"actual":0,"check":"fixture 4: (9, 2, 0)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3, 4)\", \"actual\": 26, \"expected\": 26, \"passed\": true}, {\"check\": \"fixture 2: (5, 0, 3)\", \"actual\": 15, \"expected\": 15, \"passed\": true}, {\"check\": \"fixture 3: (4, -1, 4)\", \"actual\": 10, \"expected\": 10, \"passed\": true}, {\"check\": \"fixture 4: (9, 2, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}