{"abstract":"The sum of terms is used instead of the sum of their squares.","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 sum(i*i for i from 1 through n), with n nonnegative. Exact operational definition: n*(n+1)*(2*n+1)//6","contract_signature":"n","evaluation_group":"model-f94728f0267eddf9","failed_approach":"The square-sum normalization is off by a factor of two.","family":"xn-sum-first-squares","id":"FA-5451","implementations":{"attempt":{"sha256":"254dd53fe1e276bf610eb5ae7d8248a3b0fb0b33c3d5a676e1be8e261a798dcc","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(n):\n    return n*(n+1)*(2*n+1)//3\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 14)\ncheck('fixture 4: (5,)', solve(*(5,)), 55)\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":"e6c3c4c006071bc55849ae385cbbc40c6d6b1b3f19a6010fc043f694f0550e2c","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(n):\n    return n*(n+1)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 14)\ncheck('fixture 4: (5,)', solve(*(5,)), 55)\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-sum-first-squares","generated_at":"2026-09-29T14:37:49.594399+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.","root_cause":"The sum of terms is used instead of the sum of their squares.","sha256":"dd22f844fec5da894c4d6dcc80fdbad4b09867554fbeb2e93d5cdf7b86942bc1","title":"Sum first squares · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":43.386,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":2,"check":"fixture 2: (1,)","expected":1,"passed":false},{"actual":28,"check":"fixture 3: (3,)","expected":14,"passed":false},{"actual":110,"check":"fixture 4: (5,)","expected":55,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 2, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (3,)\", \"actual\": 28, \"expected\": 14, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 110, \"expected\": 55, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.447,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":6,"check":"fixture 3: (3,)","expected":14,"passed":false},{"actual":15,"check":"fixture 4: (5,)","expected":55,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 6, \"expected\": 14, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 15, \"expected\": 55, \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}