{"abstract":"The path count is confused with grid area.","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. Lattice monotone path count. Exact operational definition: math.comb(right+down,right)","contract_signature":"right, down","evaluation_group":"model-4adb6d55f4650e68","failed_approach":"Identical steps are treated as distinguishable permutations.","family":"xn-lattice-monotone-path-count","id":"FA-5651","implementations":{"attempt":{"sha256":"89d4a54bc73276574df0391e379b8994dfa6cf1c73b3164043c598737b8dca9f","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(right, down):\n    return math.factorial(right+down)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3)', solve(*(2, 3)), 10)\ncheck('fixture 2: (0, 4)', solve(*(0, 4)), 1)\ncheck('fixture 3: (0, 0)', solve(*(0, 0)), 1)\ncheck('fixture 4: (3, 3)', solve(*(3, 3)), 20)\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":"5138fa3757b29e81882d520b48c216adef528d2503a1b89a0fb7c5a74454a780","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(right, down):\n    return right*down\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3)', solve(*(2, 3)), 10)\ncheck('fixture 2: (0, 4)', solve(*(0, 4)), 1)\ncheck('fixture 3: (0, 0)', solve(*(0, 0)), 1)\ncheck('fixture 4: (3, 3)', solve(*(3, 3)), 20)\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-lattice-monotone-path-count","generated_at":"2026-09-29T14:37:51.864885+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 path count is confused with grid area.","sha256":"a713f5e929c7b38296d18c3113a12d37549fa1c416f33ad3585f122eec22f13a","title":"Lattice monotone path 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":43.168,"exit_code":1,"observations":[{"actual":120,"check":"fixture 1: (2, 3)","expected":10,"passed":false},{"actual":24,"check":"fixture 2: (0, 4)","expected":1,"passed":false},{"actual":1,"check":"fixture 3: (0, 0)","expected":1,"passed":true},{"actual":720,"check":"fixture 4: (3, 3)","expected":20,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3)\", \"actual\": 120, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 2: (0, 4)\", \"actual\": 24, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (0, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (3, 3)\", \"actual\": 720, \"expected\": 20, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":134.336,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: (2, 3)","expected":10,"passed":false},{"actual":0,"check":"fixture 2: (0, 4)","expected":1,"passed":false},{"actual":0,"check":"fixture 3: (0, 0)","expected":1,"passed":false},{"actual":9,"check":"fixture 4: (3, 3)","expected":20,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3)\", \"actual\": 6, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 2: (0, 4)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (0, 0)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 4: (3, 3)\", \"actual\": 9, \"expected\": 20, \"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."}}