{"abstract":"The outer product axes are reversed.","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. Outer product shape. Exact operational definition: [[x*y for y in b] for x in a]","evaluation_group":"model-e2da82abb9a0ec85","failed_approach":"Outer pairwise addition replaces multiplication.","family":"xn-outer-product-shape","id":"FA-6041","implementations":{"attempt":{"sha256":"1cc235ff20ec171f57a49d578fb1027b7803c73fee1c76b83a79085b6cc4da01","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 [[x+y for y in b] for x 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])', solve(*([1, 2], [3, 4, 5])), [[3, 4, 5], [6, 8, 10]])\ncheck('fixture 2: ([0], [2, 3])', solve(*([0], [2, 3])), [[0, 0]])\ncheck('fixture 3: ([], [1])', solve(*([], [1])), [])\ncheck('fixture 4: ([2], [3])', solve(*([2], [3])), [[6]])\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":"aed3f50a33d5cb62130dd5fc0eaeb017f2beeb0e02c237fb488695ded2606357","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 [[x*y for x in a] for y in b]\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])', solve(*([1, 2], [3, 4, 5])), [[3, 4, 5], [6, 8, 10]])\ncheck('fixture 2: ([0], [2, 3])', solve(*([0], [2, 3])), [[0, 0]])\ncheck('fixture 3: ([], [1])', solve(*([], [1])), [])\ncheck('fixture 4: ([2], [3])', solve(*([2], [3])), [[6]])\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"},"fixed":{"sha256":"ea12125ee368a1c6e1c7b739d4e0f206ac75e4c722fba17b70a6cde017c731c2","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 [[x*y for y in b] for x 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])', solve(*([1, 2], [3, 4, 5])), [[3, 4, 5], [6, 8, 10]])\ncheck('fixture 2: ([0], [2, 3])', solve(*([0], [2, 3])), [[0, 0]])\ncheck('fixture 3: ([], [1])', solve(*([], [1])), [])\ncheck('fixture 4: ([2], [3])', solve(*([2], [3])), [[6]])\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-outer-product-shape","generated_at":"2026-09-29T14:37:56.900092+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.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return [[x*y for y in b] for x in a]","root_cause":"The outer product axes are reversed.","sha256":"715a935fe89c2ed825608896d938f8d8d2b8ac90226268e1575edf58705257a5","title":"Outer product shape · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":49.015,"exit_code":1,"observations":[{"actual":[[4,5,6],[5,6,7]],"check":"fixture 1: ([1, 2], [3, 4, 5])","expected":[[3,4,5],[6,8,10]],"passed":false},{"actual":[[2,3]],"check":"fixture 2: ([0], [2, 3])","expected":[[0,0]],"passed":false},{"actual":[],"check":"fixture 3: ([], [1])","expected":[],"passed":true},{"actual":[[5]],"check":"fixture 4: ([2], [3])","expected":[[6]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], [3, 4, 5])\", \"actual\": [[4, 5, 6], [5, 6, 7]], \"expected\": [[3, 4, 5], [6, 8, 10]], \"passed\": false}, {\"check\": \"fixture 2: ([0], [2, 3])\", \"actual\": [[2, 3]], \"expected\": [[0, 0]], \"passed\": false}, {\"check\": \"fixture 3: ([], [1])\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([2], [3])\", \"actual\": [[5]], \"expected\": [[6]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.377,"exit_code":1,"observations":[{"actual":[[3,6],[4,8],[5,10]],"check":"fixture 1: ([1, 2], [3, 4, 5])","expected":[[3,4,5],[6,8,10]],"passed":false},{"actual":[[0],[0]],"check":"fixture 2: ([0], [2, 3])","expected":[[0,0]],"passed":false},{"actual":[[]],"check":"fixture 3: ([], [1])","expected":[],"passed":false},{"actual":[[6]],"check":"fixture 4: ([2], [3])","expected":[[6]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], [3, 4, 5])\", \"actual\": [[3, 6], [4, 8], [5, 10]], \"expected\": [[3, 4, 5], [6, 8, 10]], \"passed\": false}, {\"check\": \"fixture 2: ([0], [2, 3])\", \"actual\": [[0], [0]], \"expected\": [[0, 0]], \"passed\": false}, {\"check\": \"fixture 3: ([], [1])\", \"actual\": [[]], \"expected\": [], \"passed\": false}, {\"check\": \"fixture 4: ([2], [3])\", \"actual\": [[6]], \"expected\": [[6]], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":47.478,"exit_code":0,"observations":[{"actual":[[3,4,5],[6,8,10]],"check":"fixture 1: ([1, 2], [3, 4, 5])","expected":[[3,4,5],[6,8,10]],"passed":true},{"actual":[[0,0]],"check":"fixture 2: ([0], [2, 3])","expected":[[0,0]],"passed":true},{"actual":[],"check":"fixture 3: ([], [1])","expected":[],"passed":true},{"actual":[[6]],"check":"fixture 4: ([2], [3])","expected":[[6]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], [3, 4, 5])\", \"actual\": [[3, 4, 5], [6, 8, 10]], \"expected\": [[3, 4, 5], [6, 8, 10]], \"passed\": true}, {\"check\": \"fixture 2: ([0], [2, 3])\", \"actual\": [[0, 0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"fixture 3: ([], [1])\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([2], [3])\", \"actual\": [[6]], \"expected\": [[6]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}