{"abstract":"The off-diagonal product is added instead of subtracted.","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 two determinant. Exact operational definition: m[0][0]*m[1][1]-m[0][1]*m[1][0]","evaluation_group":"model-4ee6690d680f5227","failed_approach":"Determinant sign is discarded despite representing orientation.","family":"xn-matrix-two-determinant","id":"FA-6016","implementations":{"attempt":{"sha256":"45d1ea058f8fb1c02ae459abd4b734a90a13b0b46a85d389644da4755abc8136","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 abs(m[0][0]*m[1][1]-m[0][1]*m[1][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]],)), -2)\ncheck('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), 1)\ncheck('fixture 3: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), 0)\ncheck('fixture 4: ([[0, 1], [1, 0]],)', solve(*([[0, 1], [1, 0]],)), -1)\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":"5502633a3846c798d8e4a5e571b54711a59c5c2b15e13a922041483c14d24622","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[0][0]*m[1][1]+m[0][1]*m[1][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]],)), -2)\ncheck('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), 1)\ncheck('fixture 3: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), 0)\ncheck('fixture 4: ([[0, 1], [1, 0]],)', solve(*([[0, 1], [1, 0]],)), -1)\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":"b0add1fe72d3d322479934a99805faef4dd44da740a04353736977ca9ea907fa","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[0][0]*m[1][1]-m[0][1]*m[1][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]],)), -2)\ncheck('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), 1)\ncheck('fixture 3: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), 0)\ncheck('fixture 4: ([[0, 1], [1, 0]],)', solve(*([[0, 1], [1, 0]],)), -1)\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-two-determinant","generated_at":"2026-09-29T14:37:56.489247+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[0][0]*m[1][1]-m[0][1]*m[1][0]","root_cause":"The off-diagonal product is added instead of subtracted.","sha256":"182cae5fdb9dac0a0550e4bc1465ffb14d1b78c0b23f32dcb6b4852eeb9342ba","title":"Matrix two determinant · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":48.862,"exit_code":1,"observations":[{"actual":2,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":-2,"passed":false},{"actual":1,"check":"fixture 2: ([[1, 0], [0, 1]],)","expected":1,"passed":true},{"actual":0,"check":"fixture 3: ([[1, 2], [2, 4]],)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: ([[0, 1], [1, 0]],)","expected":-1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 2, \"expected\": -2, \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]],)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: ([[1, 2], [2, 4]],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([[0, 1], [1, 0]],)\", \"actual\": 1, \"expected\": -1, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":49.49,"exit_code":1,"observations":[{"actual":10,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":-2,"passed":false},{"actual":1,"check":"fixture 2: ([[1, 0], [0, 1]],)","expected":1,"passed":true},{"actual":8,"check":"fixture 3: ([[1, 2], [2, 4]],)","expected":0,"passed":false},{"actual":1,"check":"fixture 4: ([[0, 1], [1, 0]],)","expected":-1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 10, \"expected\": -2, \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]],)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: ([[1, 2], [2, 4]],)\", \"actual\": 8, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 4: ([[0, 1], [1, 0]],)\", \"actual\": 1, \"expected\": -1, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":50.892,"exit_code":0,"observations":[{"actual":-2,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":-2,"passed":true},{"actual":1,"check":"fixture 2: ([[1, 0], [0, 1]],)","expected":1,"passed":true},{"actual":0,"check":"fixture 3: ([[1, 2], [2, 4]],)","expected":0,"passed":true},{"actual":-1,"check":"fixture 4: ([[0, 1], [1, 0]],)","expected":-1,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": -2, \"expected\": -2, \"passed\": true}, {\"check\": \"fixture 2: ([[1, 0], [0, 1]],)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: ([[1, 2], [2, 4]],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([[0, 1], [1, 0]],)\", \"actual\": -1, \"expected\": -1, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}