{"abstract":"All functions are accepted without requiring every target.","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. n labelled source elements and k labelled target elements; every target must be used. The unique empty-to-empty function is counted. Exact operational definition: sum((-1)**i*math.comb(k,i)*(k-i)**n for i in range(k+1))","contract_signature":"n, k","evaluation_group":"model-9c1828245792b26e","failed_approach":"The first inclusion-exclusion term overcorrects overlapping missing targets.","family":"xn-onto-function-count","id":"FA-5666","implementations":{"attempt":{"sha256":"dea736e0bc5ea39aa6bc5edfd17cf45fdb299f10dc66b119d2bc2d54150f44ce","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, k):\n    return k**n-k*(k-1)**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)), 6)\ncheck('fixture 2: (2, 3)', solve(*(2, 3)), 0)\ncheck('fixture 3: (0, 0)', solve(*(0, 0)), 1)\ncheck('fixture 4: (4, 3)', solve(*(4, 3)), 36)\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":"b1b23b6a6e584ec17c1587d796b39a420321daf0435a55adec503e48b0f03439","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, k):\n    return k**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)), 6)\ncheck('fixture 2: (2, 3)', solve(*(2, 3)), 0)\ncheck('fixture 3: (0, 0)', solve(*(0, 0)), 1)\ncheck('fixture 4: (4, 3)', solve(*(4, 3)), 36)\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-onto-function-count","generated_at":"2026-09-29T14:37:52.163728+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":"All functions are accepted without requiring every target.","sha256":"6ab11485b90c9036221fce2938085a0946de1ba8f693b0ef2e09c2547ca623f2","title":"Onto function 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":64.582,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: (3, 2)","expected":6,"passed":true},{"actual":-3,"check":"fixture 2: (2, 3)","expected":0,"passed":false},{"actual":1,"check":"fixture 3: (0, 0)","expected":1,"passed":true},{"actual":33,"check":"fixture 4: (4, 3)","expected":36,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 2)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: (2, 3)\", \"actual\": -3, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (0, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (4, 3)\", \"actual\": 33, \"expected\": 36, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.48,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (3, 2)","expected":6,"passed":false},{"actual":9,"check":"fixture 2: (2, 3)","expected":0,"passed":false},{"actual":1,"check":"fixture 3: (0, 0)","expected":1,"passed":true},{"actual":81,"check":"fixture 4: (4, 3)","expected":36,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 2)\", \"actual\": 8, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: (2, 3)\", \"actual\": 9, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (0, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (4, 3)\", \"actual\": 81, \"expected\": 36, \"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."}}