{"abstract":"The next term is confused with the series sum.","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 r may be signed; n>=0. Sum a*r**i for i=0..n-1, including the zeroth-power convention. Exact operational definition: sum(a*r**i for i in range(n))","evaluation_group":"model-4683e7b3378abc6a","failed_approach":"The exponent range omits the initial term and adds one extra term.","family":"xn-geometric-integer-series","id":"FA-5466","implementations":{"attempt":{"sha256":"9b637b4094aa8a1d44ad9b70609bbd23d1f5e0a22c2057c4ebab4b91aae30487","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, r, n):\n    return sum(a*r**i for i in range(1,n+1))\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)), 80)\ncheck('fixture 2: (5, 1, 3)', solve(*(5, 1, 3)), 15)\ncheck('fixture 3: (7, 0, 3)', solve(*(7, 0, 3)), 7)\ncheck('fixture 4: (3, 2, 0)', solve(*(3, 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":"b28d787be0f898600fa110269aa5418590cf5df586037f2d4217976b108b41e2","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, r, n):\n    return a*r**n\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)), 80)\ncheck('fixture 2: (5, 1, 3)', solve(*(5, 1, 3)), 15)\ncheck('fixture 3: (7, 0, 3)', solve(*(7, 0, 3)), 7)\ncheck('fixture 4: (3, 2, 0)', solve(*(3, 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":"5f50c60f9caf271f5c19294d9ecd8a64a7b244d5ea0ace278ada6b849815b16f","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, r, n):\n    return sum(a*r**i for i in range(n))\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)), 80)\ncheck('fixture 2: (5, 1, 3)', solve(*(5, 1, 3)), 15)\ncheck('fixture 3: (7, 0, 3)', solve(*(7, 0, 3)), 7)\ncheck('fixture 4: (3, 2, 0)', solve(*(3, 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-geometric-integer-series","generated_at":"2026-09-29T14:37:49.870434+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 sum(a*r**i for i in range(n))","root_cause":"The next term is confused with the series sum.","sha256":"38326dcd6917b9fd06ca801e463cbc8ff46f2fdafe11be610bf0a2cfb6397c71","title":"Geometric integer series · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":48.345,"exit_code":1,"observations":[{"actual":240,"check":"fixture 1: (2, 3, 4)","expected":80,"passed":false},{"actual":15,"check":"fixture 2: (5, 1, 3)","expected":15,"passed":true},{"actual":0,"check":"fixture 3: (7, 0, 3)","expected":7,"passed":false},{"actual":0,"check":"fixture 4: (3, 2, 0)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3, 4)\", \"actual\": 240, \"expected\": 80, \"passed\": false}, {\"check\": \"fixture 2: (5, 1, 3)\", \"actual\": 15, \"expected\": 15, \"passed\": true}, {\"check\": \"fixture 3: (7, 0, 3)\", \"actual\": 0, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 4: (3, 2, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.653,"exit_code":1,"observations":[{"actual":162,"check":"fixture 1: (2, 3, 4)","expected":80,"passed":false},{"actual":5,"check":"fixture 2: (5, 1, 3)","expected":15,"passed":false},{"actual":0,"check":"fixture 3: (7, 0, 3)","expected":7,"passed":false},{"actual":3,"check":"fixture 4: (3, 2, 0)","expected":0,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3, 4)\", \"actual\": 162, \"expected\": 80, \"passed\": false}, {\"check\": \"fixture 2: (5, 1, 3)\", \"actual\": 5, \"expected\": 15, \"passed\": false}, {\"check\": \"fixture 3: (7, 0, 3)\", \"actual\": 0, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 4: (3, 2, 0)\", \"actual\": 3, \"expected\": 0, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.729,"exit_code":0,"observations":[{"actual":80,"check":"fixture 1: (2, 3, 4)","expected":80,"passed":true},{"actual":15,"check":"fixture 2: (5, 1, 3)","expected":15,"passed":true},{"actual":7,"check":"fixture 3: (7, 0, 3)","expected":7,"passed":true},{"actual":0,"check":"fixture 4: (3, 2, 0)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3, 4)\", \"actual\": 80, \"expected\": 80, \"passed\": true}, {\"check\": \"fixture 2: (5, 1, 3)\", \"actual\": 15, \"expected\": 15, \"passed\": true}, {\"check\": \"fixture 3: (7, 0, 3)\", \"actual\": 7, \"expected\": 7, \"passed\": true}, {\"check\": \"fixture 4: (3, 2, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}