{"abstract":"Rows of the right operand are used where columns are required.","category":"Linear algebra","checks":4,"contract":"Integer matrix/vector entries, rectangular rows, compatible multiplication dimensions, and square matrices for determinant, trace, inverse, symmetry and characteristic-polynomial operations. Rational matrix outputs are reduced Fraction strings. Matrix multiply row column. Exact operational definition: [[sum(x*y for x,y in zip(row,col)) for col in zip(*b)] for row in a]","contract_signature":"a, b","evaluation_group":"model-9f32b973d3a6ff8f","failed_approach":"Multiplying row and column sums introduces cross terms.","family":"xn-matrix-multiply-row-column","id":"FA-6036","implementations":{"attempt":{"sha256":"72da711cbc2364bd311169b23336f1423235f2c6556f09258a209a13f7b9a643","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(a, b):\n    return [[sum(row)*sum(col) for col in zip(*b)] for row in a]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 2], [3, 4]], [[5, 6], [7, 8]])', solve(*([[1, 2], [3, 4]], [[5, 6], [7, 8]])), [[19, 22], [43, 50]])\ncheck('fixture 2: ([[1, 0], [0, 1]], [[2, 3], [4, 5]])', solve(*([[1, 0], [0, 1]], [[2, 3], [4, 5]])), [[2, 3], [4, 5]])\ncheck('fixture 3: ([[2]], [[3]])', solve(*([[2]], [[3]])), [[6]])\ncheck('fixture 4: ([[0, 0]], [[1], [2]])', solve(*([[0, 0]], [[1], [2]])), [[0]])\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":"f19f4af7857db8b24f1b758cdff6fe13377d83940dc8f85ad5d1d49677c564fe","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(a, b):\n    return [[sum(x*y for x,y in zip(row,col)) for col in b] for row in a]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 2], [3, 4]], [[5, 6], [7, 8]])', solve(*([[1, 2], [3, 4]], [[5, 6], [7, 8]])), [[19, 22], [43, 50]])\ncheck('fixture 2: ([[1, 0], [0, 1]], [[2, 3], [4, 5]])', solve(*([[1, 0], [0, 1]], [[2, 3], [4, 5]])), [[2, 3], [4, 5]])\ncheck('fixture 3: ([[2]], [[3]])', solve(*([[2]], [[3]])), [[6]])\ncheck('fixture 4: ([[0, 0]], [[1], [2]])', solve(*([[0, 0]], [[1], [2]])), [[0]])\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-matrix-multiply-row-column","generated_at":"2026-09-29T14:37:56.850761+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. Linear algebra results depend on the stated convention.","root_cause":"Rows of the right operand are used where columns are required.","sha256":"5794bf200354d11df7a7f34022d0e37234f21da8ff22b0983bfbe0c7839df5a6","title":"Matrix multiply row column · 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":44.819,"exit_code":1,"observations":[{"actual":[[36,42],[84,98]],"check":"fixture 1: ([[1, 2], [3, 4]], [[5, 6], [7, 8]])","expected":[[19,22],[43,50]],"passed":false},{"actual":[[6,8],[6,8]],"check":"fixture 2: ([[1, 0], [0, 1]], [[2, 3], [4, 5]])","expected":[[2,3],[4,5]],"passed":false},{"actual":[[6]],"check":"fixture 3: ([[2]], [[3]])","expected":[[6]],"passed":true},{"actual":[[0]],"check":"fixture 4: ([[0, 0]], [[1], [2]])","expected":[[0]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]], [[5, 6], [7, 8]])\", \"actual\": [[36, 42], [84, 98]], \"expected\": [[19, 22], [43, 50]], \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]], [[2, 3], [4, 5]])\", \"actual\": [[6, 8], [6, 8]], \"expected\": [[2, 3], [4, 5]], \"passed\": false}, {\"check\": \"fixture 3: ([[2]], [[3]])\", \"actual\": [[6]], \"expected\": [[6]], \"passed\": true}, {\"check\": \"fixture 4: ([[0, 0]], [[1], [2]])\", \"actual\": [[0]], \"expected\": [[0]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.932,"exit_code":1,"observations":[{"actual":[[17,23],[39,53]],"check":"fixture 1: ([[1, 2], [3, 4]], [[5, 6], [7, 8]])","expected":[[19,22],[43,50]],"passed":false},{"actual":[[2,4],[3,5]],"check":"fixture 2: ([[1, 0], [0, 1]], [[2, 3], [4, 5]])","expected":[[2,3],[4,5]],"passed":false},{"actual":[[6]],"check":"fixture 3: ([[2]], [[3]])","expected":[[6]],"passed":true},{"actual":[[0,0]],"check":"fixture 4: ([[0, 0]], [[1], [2]])","expected":[[0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]], [[5, 6], [7, 8]])\", \"actual\": [[17, 23], [39, 53]], \"expected\": [[19, 22], [43, 50]], \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]], [[2, 3], [4, 5]])\", \"actual\": [[2, 4], [3, 5]], \"expected\": [[2, 3], [4, 5]], \"passed\": false}, {\"check\": \"fixture 3: ([[2]], [[3]])\", \"actual\": [[6]], \"expected\": [[6]], \"passed\": true}, {\"check\": \"fixture 4: ([[0, 0]], [[1], [2]])\", \"actual\": [[0, 0]], \"expected\": [[0]], \"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."}}