{"abstract":"Squaring the size does not enumerate include/exclude choices.","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. Binary subsets count. Exact operational definition: 2**n","contract_signature":"n","evaluation_group":"model-e8043b544d873f8b","failed_approach":"Doubling the size grows linearly rather than by independent choices.","family":"xn-binary-subsets-count","id":"FA-5606","implementations":{"attempt":{"sha256":"501cb594103b86b1a85ec07ef0ef65886685dd6fc00888dbc03ac741b478a44e","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,)), 2)\ncheck('fixture 3: (3,)', solve(*(3,)), 8)\ncheck('fixture 4: (5,)', solve(*(5,)), 32)\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":"e6b5153ac93f3e75133246d7b3d9cef899730566d65fc10b44278b84a6c0ffdd","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\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,)), 8)\ncheck('fixture 4: (5,)', solve(*(5,)), 32)\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-binary-subsets-count","generated_at":"2026-09-29T14:37:51.438681+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":"Squaring the size does not enumerate include/exclude choices.","sha256":"a2270befa389e67b8559252c498f6adbf28cffcff006bfccf5f853bd232bca00","title":"Binary subsets 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":120.17,"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":8,"passed":false},{"actual":10,"check":"fixture 4: (5,)","expected":32,"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\": 8, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 10, \"expected\": 32, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":47.644,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":1,"passed":false},{"actual":1,"check":"fixture 2: (1,)","expected":2,"passed":false},{"actual":9,"check":"fixture 3: (3,)","expected":8,"passed":false},{"actual":25,"check":"fixture 4: (5,)","expected":32,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 3: (3,)\", \"actual\": 9, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 25, \"expected\": 32, \"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."}}