{"abstract":"Polygon sides are included as diagonals.","category":"Combinatorics","checks":4,"contract":"Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. n>=3; count unordered vertex pairs excluding adjacent vertices. Exact operational definition: n*(n-3)//2","contract_signature":"n","evaluation_group":"model-f361c3db250ddf78","failed_approach":"Each diagonal is counted from both endpoints.","family":"xn-polygon-diagonal-count","id":"FA-5636","implementations":{"attempt":{"sha256":"3165b5f8293c7d71ce9eee2e51441112052866f25edaa4b5ad3f3bc05c94c924","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-3)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3,)', solve(*(3,)), 0)\ncheck('fixture 2: (4,)', solve(*(4,)), 2)\ncheck('fixture 3: (5,)', solve(*(5,)), 5)\ncheck('fixture 4: (8,)', solve(*(8,)), 20)\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":"050d49f215318e87737b01fd16a59990c4223c75a004f373c20eadb1d28691e8","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: (3,)', solve(*(3,)), 0)\ncheck('fixture 2: (4,)', solve(*(4,)), 2)\ncheck('fixture 3: (5,)', solve(*(5,)), 5)\ncheck('fixture 4: (8,)', solve(*(8,)), 20)\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-polygon-diagonal-count","generated_at":"2026-09-29T14:37:51.867263+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. Combinatorics results depend on the stated convention.","root_cause":"Polygon sides are included as diagonals.","sha256":"3e71be20217ff5ca8d8256ffa165ceefa812b9c07594572cf01939b234d3e4f8","title":"Polygon diagonal count · 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":45.377,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (3,)","expected":0,"passed":true},{"actual":4,"check":"fixture 2: (4,)","expected":2,"passed":false},{"actual":10,"check":"fixture 3: (5,)","expected":5,"passed":false},{"actual":40,"check":"fixture 4: (8,)","expected":20,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (4,)\", \"actual\": 4, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 3: (5,)\", \"actual\": 10, \"expected\": 5, \"passed\": false}, {\"check\": \"fixture 4: (8,)\", \"actual\": 40, \"expected\": 20, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":138.032,"exit_code":1,"observations":[{"actual":3,"check":"fixture 1: (3,)","expected":0,"passed":false},{"actual":6,"check":"fixture 2: (4,)","expected":2,"passed":false},{"actual":10,"check":"fixture 3: (5,)","expected":5,"passed":false},{"actual":28,"check":"fixture 4: (8,)","expected":20,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3,)\", \"actual\": 3, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 2: (4,)\", \"actual\": 6, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 3: (5,)\", \"actual\": 10, \"expected\": 5, \"passed\": false}, {\"check\": \"fixture 4: (8,)\", \"actual\": 28, \"expected\": 20, \"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."}}