{"abstract":"The empty subset is 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. Nonempty subsets count. Exact operational definition: 2**n-1","evaluation_group":"model-4697144d18fa57e0","failed_approach":"Halving the power set removes many valid nonempty subsets.","family":"xn-nonempty-subsets-count","id":"FA-5611","implementations":{"attempt":{"sha256":"534445c7a161f567aa29a2f8c1c81f0f6fbe5cdcc3eea028555b3ad09941c6ba","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,)), 0)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 7)\ncheck('fixture 4: (5,)', solve(*(5,)), 31)\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":"fbd16344741593ac625b3e46227ec06ba6fa54e7e315ea51f372d9a6eb2374c9","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,)), 0)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (3,)', solve(*(3,)), 7)\ncheck('fixture 4: (5,)', solve(*(5,)), 31)\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"},"fixed":{"sha256":"6dc12bbfce72f3fd1916e66d8625c93d8a48782d11382fa4a4267795f13a4ffa","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\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,)), 7)\ncheck('fixture 4: (5,)', solve(*(5,)), 31)\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-nonempty-subsets-count","generated_at":"2026-09-29T14:37:51.584274+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.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return 2**n-1","root_cause":"The empty subset is included.","sha256":"6b73397c73ad25e2be64bd510956ff8ab7960b6a8b63193e373126042e256df4","title":"Nonempty subsets count · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":45.719,"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":4,"check":"fixture 3: (3,)","expected":7,"passed":false},{"actual":16,"check":"fixture 4: (5,)","expected":31,"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\": 4, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 16, \"expected\": 31, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.809,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":0,"passed":false},{"actual":2,"check":"fixture 2: (1,)","expected":1,"passed":false},{"actual":8,"check":"fixture 3: (3,)","expected":7,"passed":false},{"actual":32,"check":"fixture 4: (5,)","expected":31,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 2: (1,)\", \"actual\": 2, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (3,)\", \"actual\": 8, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 32, \"expected\": 31, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":49.691,"exit_code":0,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":7,"check":"fixture 3: (3,)","expected":7,"passed":true},{"actual":31,"check":"fixture 4: (5,)","expected":31,"passed":true}],"passed":true,"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\": 7, \"expected\": 7, \"passed\": true}, {\"check\": \"fixture 4: (5,)\", \"actual\": 31, \"expected\": 31, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}