{"abstract":"Diagonal positivity is unrelated to transpose symmetry.","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 symmetry predicate. Exact operational definition: all(m[i][j]==m[j][i] for i in range(len(m)) for j in range(len(m)))","evaluation_group":"model-6344e9aafeebd515","failed_approach":"The comparison range omits the immediately adjacent diagonal.","family":"xn-matrix-symmetry-predicate","id":"FA-6071","implementations":{"attempt":{"sha256":"06ae189b5e2b9c9bf6180cecd1a3b007cd93f06a61d77c6e2fee338755dedc86","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 all(m[i][j]==m[j][i] for i in range(len(m)) for j in range(i-1))\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]],)), False)\ncheck('fixture 2: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), True)\ncheck('fixture 3: ([[-1, 0], [0, -2]],)', solve(*([[-1, 0], [0, -2]],)), True)\ncheck('fixture 4: ([],)', solve(*([],)), True)\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":"0982467a6f86986afe730ae6e1add0aab53a30e2d6ed11c1dde96be6bd4985d7","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 all(m[i][i]>=0 for i in range(len(m)))\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]],)), False)\ncheck('fixture 2: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), True)\ncheck('fixture 3: ([[-1, 0], [0, -2]],)', solve(*([[-1, 0], [0, -2]],)), True)\ncheck('fixture 4: ([],)', solve(*([],)), True)\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":"a6818da3f13def06b0f4a2f99cd19217bf937cf208c7fba54e53e92b3d068811","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 all(m[i][j]==m[j][i] for i in range(len(m)) for j in range(len(m)))\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]],)), False)\ncheck('fixture 2: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), True)\ncheck('fixture 3: ([[-1, 0], [0, -2]],)', solve(*([[-1, 0], [0, -2]],)), True)\ncheck('fixture 4: ([],)', solve(*([],)), True)\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-symmetry-predicate","generated_at":"2026-09-29T14:37:57.049626+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 all(m[i][j]==m[j][i] for i in range(len(m)) for j in range(len(m)))","root_cause":"Diagonal positivity is unrelated to transpose symmetry.","sha256":"d5dcc1e01e8905be600df8411d04a95bfa7fcbed0e4954b179143abcca36dd5b","title":"Matrix symmetry predicate · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.212,"exit_code":1,"observations":[{"actual":true,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":false,"passed":false},{"actual":true,"check":"fixture 2: ([[1, 2], [2, 4]],)","expected":true,"passed":true},{"actual":true,"check":"fixture 3: ([[-1, 0], [0, -2]],)","expected":true,"passed":true},{"actual":true,"check":"fixture 4: ([],)","expected":true,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 2: ([[1, 2], [2, 4]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 3: ([[-1, 0], [0, -2]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.876,"exit_code":1,"observations":[{"actual":true,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":false,"passed":false},{"actual":true,"check":"fixture 2: ([[1, 2], [2, 4]],)","expected":true,"passed":true},{"actual":false,"check":"fixture 3: ([[-1, 0], [0, -2]],)","expected":true,"passed":false},{"actual":true,"check":"fixture 4: ([],)","expected":true,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 2: ([[1, 2], [2, 4]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 3: ([[-1, 0], [0, -2]],)\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 4: ([],)\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":48.648,"exit_code":0,"observations":[{"actual":false,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":false,"passed":true},{"actual":true,"check":"fixture 2: ([[1, 2], [2, 4]],)","expected":true,"passed":true},{"actual":true,"check":"fixture 3: ([[-1, 0], [0, -2]],)","expected":true,"passed":true},{"actual":true,"check":"fixture 4: ([],)","expected":true,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"fixture 2: ([[1, 2], [2, 4]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 3: ([[-1, 0], [0, -2]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}