{"abstract":"Only unit rectangles are counted.","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. Rectangular grid cell rectangle count. Exact operational definition: rows*(rows+1)*cols*(cols+1)//4","contract_signature":"rows, cols","evaluation_group":"model-402bd1b9a09102db","failed_approach":"Cell counts are used where grid-line counts are required.","family":"xn-rectangular-grid-cell-rectangle-count","id":"FA-5641","implementations":{"attempt":{"sha256":"6ce306557731ac00fd35cccc5d4e7dd1156657073c0f7dbfbf24546841d09215","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(rows, cols):\n    return math.comb(rows,2)*math.comb(cols,2)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 1)', solve(*(1, 1)), 1)\ncheck('fixture 2: (2, 3)', solve(*(2, 3)), 18)\ncheck('fixture 3: (0, 4)', solve(*(0, 4)), 0)\ncheck('fixture 4: (3, 3)', solve(*(3, 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":"3636bb9f40d3b435fa4076ce9a1fffdde751280155ffb60687ab93d5f23dd9b7","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(rows, cols):\n    return rows*cols\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 1)', solve(*(1, 1)), 1)\ncheck('fixture 2: (2, 3)', solve(*(2, 3)), 18)\ncheck('fixture 3: (0, 4)', solve(*(0, 4)), 0)\ncheck('fixture 4: (3, 3)', solve(*(3, 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-rectangular-grid-cell-rectangle-count","generated_at":"2026-09-29T14:37:51.863984+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":"Only unit rectangles are counted.","sha256":"fdc8ff6e3a33f5b88a11113e15d2d85feb916da5689e51016a93aa534a20ca10","title":"Rectangular grid cell rectangle 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":42.388,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (1, 1)","expected":1,"passed":false},{"actual":3,"check":"fixture 2: (2, 3)","expected":18,"passed":false},{"actual":0,"check":"fixture 3: (0, 4)","expected":0,"passed":true},{"actual":9,"check":"fixture 4: (3, 3)","expected":36,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 1)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: (2, 3)\", \"actual\": 3, \"expected\": 18, \"passed\": false}, {\"check\": \"fixture 3: (0, 4)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (3, 3)\", \"actual\": 9, \"expected\": 36, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":138.199,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (1, 1)","expected":1,"passed":true},{"actual":6,"check":"fixture 2: (2, 3)","expected":18,"passed":false},{"actual":0,"check":"fixture 3: (0, 4)","expected":0,"passed":true},{"actual":9,"check":"fixture 4: (3, 3)","expected":36,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 1)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (2, 3)\", \"actual\": 6, \"expected\": 18, \"passed\": false}, {\"check\": \"fixture 3: (0, 4)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (3, 3)\", \"actual\": 9, \"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."}}