{"abstract":"The whole set is retained among proper subsets.","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. Proper nonempty subsets count. Exact operational definition: max(0,2**n-2)","contract_signature":"n","evaluation_group":"model-fc817e7524992082","failed_approach":"Subtracting two distinct exclusions on an empty ground set double-counts one object.","family":"xn-proper-nonempty-subsets-count","id":"FA-5616","implementations":{"attempt":{"sha256":"a6c972410632a20827dff35238ce5d6a7d5e9303ed2b7796d7b217a2f7b8f4cf","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-2\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,)), 0)\ncheck('fixture 3: (2,)', solve(*(2,)), 2)\ncheck('fixture 4: (4,)', solve(*(4,)), 14)\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":"66ccd7d68964c67f6c0b843709c03310685428661ea3cca4b0484feb672cdbf0","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,)), 0)\ncheck('fixture 3: (2,)', solve(*(2,)), 2)\ncheck('fixture 4: (4,)', solve(*(4,)), 14)\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-proper-nonempty-subsets-count","generated_at":"2026-09-29T14:37:51.586070+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":"The whole set is retained among proper subsets.","sha256":"b23b3101b58de849113c003885e3ea400d9a2235cd71e3445bd2851718a94146","title":"Proper nonempty 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":45.356,"exit_code":1,"observations":[{"actual":-1,"check":"fixture 1: (0,)","expected":0,"passed":false},{"actual":0,"check":"fixture 2: (1,)","expected":0,"passed":true},{"actual":2,"check":"fixture 3: (2,)","expected":2,"passed":true},{"actual":14,"check":"fixture 4: (4,)","expected":14,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": -1, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 2: (1,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (2,)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 4: (4,)\", \"actual\": 14, \"expected\": 14, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.22,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":0,"passed":false},{"actual":3,"check":"fixture 3: (2,)","expected":2,"passed":false},{"actual":15,"check":"fixture 4: (4,)","expected":14,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (2,)\", \"actual\": 3, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 4: (4,)\", \"actual\": 15, \"expected\": 14, \"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."}}