{"abstract":"A positive-composition formula excludes zero components.","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. parts>=1; count ordered vectors of parts nonnegative integers summing to n. Exact operational definition: math.comb(n+parts-1,parts-1)","contract_signature":"n, parts","evaluation_group":"model-e1040f04ee9836d2","failed_approach":"Labelled balls are counted when only component totals matter.","family":"xn-weak-composition-count","id":"FA-5676","implementations":{"attempt":{"sha256":"ad214f2d1cfaf45410258fb6df4deb5438377f4949b663b4f8ed754aea8a951a","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, parts):\n    return parts**n\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 2)', solve(*(3, 2)), 4)\ncheck('fixture 2: (0, 3)', solve(*(0, 3)), 1)\ncheck('fixture 3: (4, 3)', solve(*(4, 3)), 15)\ncheck('fixture 4: (5, 1)', solve(*(5, 1)), 1)\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":"8db369a235476290cb63cac250e1b397361f3ba5a0c701ad40a2e0651f366612","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, parts):\n    return math.comb(n-1,parts-1) if n>=parts else 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 2)', solve(*(3, 2)), 4)\ncheck('fixture 2: (0, 3)', solve(*(0, 3)), 1)\ncheck('fixture 3: (4, 3)', solve(*(4, 3)), 15)\ncheck('fixture 4: (5, 1)', solve(*(5, 1)), 1)\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-weak-composition-count","generated_at":"2026-09-29T14:37:52.300948+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":"A positive-composition formula excludes zero components.","sha256":"bb37ffc14ddd2ac98d621673389439c182edc517b493602bd493dbff2fd7f126","title":"Weak composition 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":44.599,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (3, 2)","expected":4,"passed":false},{"actual":1,"check":"fixture 2: (0, 3)","expected":1,"passed":true},{"actual":81,"check":"fixture 3: (4, 3)","expected":15,"passed":false},{"actual":1,"check":"fixture 4: (5, 1)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 2)\", \"actual\": 8, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 2: (0, 3)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (4, 3)\", \"actual\": 81, \"expected\": 15, \"passed\": false}, {\"check\": \"fixture 4: (5, 1)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.753,"exit_code":1,"observations":[{"actual":2,"check":"fixture 1: (3, 2)","expected":4,"passed":false},{"actual":0,"check":"fixture 2: (0, 3)","expected":1,"passed":false},{"actual":3,"check":"fixture 3: (4, 3)","expected":15,"passed":false},{"actual":1,"check":"fixture 4: (5, 1)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 2)\", \"actual\": 2, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 2: (0, 3)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (4, 3)\", \"actual\": 3, \"expected\": 15, \"passed\": false}, {\"check\": \"fixture 4: (5, 1)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"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."}}