{"abstract":"Off-diagonal cofactors lack negative signs.","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. Two by two adjugate. Exact operational definition: [[m[1][1],-m[0][1]],[-m[1][0],m[0][0]]]","evaluation_group":"model-1e86bf8200f39299","failed_approach":"The untransposed cofactor matrix is returned.","family":"xn-two-by-two-adjugate","id":"FA-6061","implementations":{"attempt":{"sha256":"fe44250288353bd65b4d9245b7a0cb03ebd82bf0fd55b5805cbdff0f3fdd6e3d","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(m):\n    return [[m[1][1],-m[1][0]],[-m[0][1],m[0][0]]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 2], [3, 4]],)', solve(*([[1, 2], [3, 4]],)), [[4, -2], [-3, 1]])\ncheck('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), [[1, 0], [0, 1]])\ncheck('fixture 3: ([[0, 1], [2, 0]],)', solve(*([[0, 1], [2, 0]],)), [[0, -1], [-2, 0]])\ncheck('fixture 4: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), [[0, 0], [0, 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":"11904c7d2105387ad3ef43c68d366b8dbf56ce161c82b03ddd47aff38f45ee1c","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(m):\n    return [[m[1][1],m[0][1]],[m[1][0],m[0][0]]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 2], [3, 4]],)', solve(*([[1, 2], [3, 4]],)), [[4, -2], [-3, 1]])\ncheck('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), [[1, 0], [0, 1]])\ncheck('fixture 3: ([[0, 1], [2, 0]],)', solve(*([[0, 1], [2, 0]],)), [[0, -1], [-2, 0]])\ncheck('fixture 4: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), [[0, 0], [0, 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"},"fixed":{"sha256":"d4a554b366a04eec0242d4fe5a64d1c11e3b32fcf818d84ab700fc993e668837","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(m):\n    return [[m[1][1],-m[0][1]],[-m[1][0],m[0][0]]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 2], [3, 4]],)', solve(*([[1, 2], [3, 4]],)), [[4, -2], [-3, 1]])\ncheck('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), [[1, 0], [0, 1]])\ncheck('fixture 3: ([[0, 1], [2, 0]],)', solve(*([[0, 1], [2, 0]],)), [[0, -1], [-2, 0]])\ncheck('fixture 4: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), [[0, 0], [0, 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-two-by-two-adjugate","generated_at":"2026-09-29T14:37:57.000754+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 [[m[1][1],-m[0][1]],[-m[1][0],m[0][0]]]","root_cause":"Off-diagonal cofactors lack negative signs.","sha256":"201f21b6f0aa004b877e54e93286f7acf549fa5008f81c192a6488782065d3a1","title":"Two by two adjugate · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":47.444,"exit_code":1,"observations":[{"actual":[[4,-3],[-2,1]],"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":[[4,-2],[-3,1]],"passed":false},{"actual":[[1,0],[0,1]],"check":"fixture 2: ([[1, 0], [0, 1]],)","expected":[[1,0],[0,1]],"passed":true},{"actual":[[0,-2],[-1,0]],"check":"fixture 3: ([[0, 1], [2, 0]],)","expected":[[0,-1],[-2,0]],"passed":false},{"actual":[[0,0],[0,0]],"check":"fixture 4: ([[0, 0], [0, 0]],)","expected":[[0,0],[0,0]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": [[4, -3], [-2, 1]], \"expected\": [[4, -2], [-3, 1]], \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]],)\", \"actual\": [[1, 0], [0, 1]], \"expected\": [[1, 0], [0, 1]], \"passed\": true}, {\"check\": \"fixture 3: ([[0, 1], [2, 0]],)\", \"actual\": [[0, -2], [-1, 0]], \"expected\": [[0, -1], [-2, 0]], \"passed\": false}, {\"check\": \"fixture 4: ([[0, 0], [0, 0]],)\", \"actual\": [[0, 0], [0, 0]], \"expected\": [[0, 0], [0, 0]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":47.568,"exit_code":1,"observations":[{"actual":[[4,2],[3,1]],"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":[[4,-2],[-3,1]],"passed":false},{"actual":[[1,0],[0,1]],"check":"fixture 2: ([[1, 0], [0, 1]],)","expected":[[1,0],[0,1]],"passed":true},{"actual":[[0,1],[2,0]],"check":"fixture 3: ([[0, 1], [2, 0]],)","expected":[[0,-1],[-2,0]],"passed":false},{"actual":[[0,0],[0,0]],"check":"fixture 4: ([[0, 0], [0, 0]],)","expected":[[0,0],[0,0]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": [[4, 2], [3, 1]], \"expected\": [[4, -2], [-3, 1]], \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]],)\", \"actual\": [[1, 0], [0, 1]], \"expected\": [[1, 0], [0, 1]], \"passed\": true}, {\"check\": \"fixture 3: ([[0, 1], [2, 0]],)\", \"actual\": [[0, 1], [2, 0]], \"expected\": [[0, -1], [-2, 0]], \"passed\": false}, {\"check\": \"fixture 4: ([[0, 0], [0, 0]],)\", \"actual\": [[0, 0], [0, 0]], \"expected\": [[0, 0], [0, 0]], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":47.612,"exit_code":0,"observations":[{"actual":[[4,-2],[-3,1]],"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":[[4,-2],[-3,1]],"passed":true},{"actual":[[1,0],[0,1]],"check":"fixture 2: ([[1, 0], [0, 1]],)","expected":[[1,0],[0,1]],"passed":true},{"actual":[[0,-1],[-2,0]],"check":"fixture 3: ([[0, 1], [2, 0]],)","expected":[[0,-1],[-2,0]],"passed":true},{"actual":[[0,0],[0,0]],"check":"fixture 4: ([[0, 0], [0, 0]],)","expected":[[0,0],[0,0]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": [[4, -2], [-3, 1]], \"expected\": [[4, -2], [-3, 1]], \"passed\": true}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]],)\", \"actual\": [[1, 0], [0, 1]], \"expected\": [[1, 0], [0, 1]], \"passed\": true}, {\"check\": \"fixture 3: ([[0, 1], [2, 0]],)\", \"actual\": [[0, -1], [-2, 0]], \"expected\": [[0, -1], [-2, 0]], \"passed\": true}, {\"check\": \"fixture 4: ([[0, 0], [0, 0]],)\", \"actual\": [[0, 0], [0, 0]], \"expected\": [[0, 0], [0, 0]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}