{"abstract":"Odd-cardinality subsets are included.","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. Even subset count. Exact operational definition: 1 if n==0 else 2**(n-1)","contract_signature":"n","evaluation_group":"model-fdf51ad3c0fb2351","failed_approach":"The empty-set boundary loses its unique even subset.","family":"xn-even-subset-count","id":"FA-5736","implementations":{"attempt":{"sha256":"28d087daabf3f1860ffa95aa085a1e0aa0b3da9ec18e44b2773a73303489f774","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 2**(n-1) if n else 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 4)\ncheck('fixture 4: (5,)', solve(*(5,)), 16)\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":"96cfb8203d7f9e1e46e05f7ce8d08bc55e5bae47151f07ab1d3a566097044b67","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 2**n\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 4)\ncheck('fixture 4: (5,)', solve(*(5,)), 16)\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-even-subset-count","generated_at":"2026-09-29T14:37:53.012935+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":"Odd-cardinality subsets are included.","sha256":"da5b148c03f98e6b49a98494b7630f38c83e3adb7119fb2e6976add6ef112f33","title":"Even subset 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":49.678,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":1,"passed":false},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":4,"check":"fixture 3: (3,)","expected":4,"passed":true},{"actual":16,"check":"fixture 4: (5,)","expected":16,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"fixture 4: (5,)\", \"actual\": 16, \"expected\": 16, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":50.91,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":2,"check":"fixture 2: (1,)","expected":1,"passed":false},{"actual":8,"check":"fixture 3: (3,)","expected":4,"passed":false},{"actual":32,"check":"fixture 4: (5,)","expected":16,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 2, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (3,)\", \"actual\": 8, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 32, \"expected\": 16, \"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."}}