{"abstract":"Outgoing child links are confused with leaves.","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. Every internal vertex has exactly two children; return the leaf count from the nonnegative internal-vertex count. Exact operational definition: internal+1","contract_signature":"internal","evaluation_group":"model-bdb0710f9a413772","failed_approach":"Total node count is confused with leaf count.","family":"xn-full-binary-tree-leaf-identity","id":"FA-5716","implementations":{"attempt":{"sha256":"c80b6d7ed1c188dfaf71c30133d9e443887018239794e96ed4512deb191bdd01","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(internal):\n    return 2*internal+1\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,)), 2)\ncheck('fixture 3: (3,)', solve(*(3,)), 4)\ncheck('fixture 4: (7,)', solve(*(7,)), 8)\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":"af6aa280238e6ff569c54882e7b7228a8b1942e958d7327da8fe21c178a2c39f","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(internal):\n    return 2*internal\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,)), 2)\ncheck('fixture 3: (3,)', solve(*(3,)), 4)\ncheck('fixture 4: (7,)', solve(*(7,)), 8)\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-full-binary-tree-leaf-identity","generated_at":"2026-09-29T14:37:52.777799+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":"Outgoing child links are confused with leaves.","sha256":"349f924e40c9c10908b96dc1fb74b6ef988966a5b96b94be6c0770b4a154acaa","title":"Full binary tree leaf identity · 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":43.379,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":3,"check":"fixture 2: (1,)","expected":2,"passed":false},{"actual":7,"check":"fixture 3: (3,)","expected":4,"passed":false},{"actual":15,"check":"fixture 4: (7,)","expected":8,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 3, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 3: (3,)\", \"actual\": 7, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 4: (7,)\", \"actual\": 15, \"expected\": 8, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":51.816,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":1,"passed":false},{"actual":2,"check":"fixture 2: (1,)","expected":2,"passed":true},{"actual":6,"check":"fixture 3: (3,)","expected":4,"passed":false},{"actual":14,"check":"fixture 4: (7,)","expected":8,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: (1,)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 6, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 4: (7,)\", \"actual\": 14, \"expected\": 8, \"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."}}