{"abstract":"Nonzero diagonal entries do not constrain off-diagonal entries.","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 diagonal predicate. Exact operational definition: all(i==j or m[i][j]==0 for i in range(len(m)) for j in range(len(m)))","evaluation_group":"model-2ddefc73c0f12bcc","failed_approach":"Only one triangular half is tested.","family":"xn-matrix-diagonal-predicate","id":"FA-6076","implementations":{"attempt":{"sha256":"968f5c8ee1e45b629794902d5f053e8cef3c8dcd47b546c07240c4f2a61859ed","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]==0 for i in range(len(m)) for j in range(i))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 2], [0, 3]],)', solve(*([[1, 2], [0, 3]],)), False)\ncheck('fixture 2: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), True)\ncheck('fixture 3: ([[2, 0], [0, 3]],)', solve(*([[2, 0], [0, 3]],)), True)\ncheck('fixture 4: ([[1, 0], [2, 3]],)', solve(*([[1, 0], [2, 3]],)), False)\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":"3cdf1ae3778016699f81cf54b012961f33dbe08e5c0b4e677189d5ceadf52121","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], [0, 3]],)', solve(*([[1, 2], [0, 3]],)), False)\ncheck('fixture 2: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), True)\ncheck('fixture 3: ([[2, 0], [0, 3]],)', solve(*([[2, 0], [0, 3]],)), True)\ncheck('fixture 4: ([[1, 0], [2, 3]],)', solve(*([[1, 0], [2, 3]],)), False)\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":"7c44e0c24fe3ddf6b8ab8eaca0a1fcf2d002421cd5020a8bfc6e4531f78addaf","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(i==j or m[i][j]==0 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], [0, 3]],)', solve(*([[1, 2], [0, 3]],)), False)\ncheck('fixture 2: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), True)\ncheck('fixture 3: ([[2, 0], [0, 3]],)', solve(*([[2, 0], [0, 3]],)), True)\ncheck('fixture 4: ([[1, 0], [2, 3]],)', solve(*([[1, 0], [2, 3]],)), False)\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-diagonal-predicate","generated_at":"2026-09-29T14:37:57.045262+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(i==j or m[i][j]==0 for i in range(len(m)) for j in range(len(m)))","root_cause":"Nonzero diagonal entries do not constrain off-diagonal entries.","sha256":"bd76dc1b1f7f59003f727a13bf6e9df61b397ee6a711641e3089022d1564352e","title":"Matrix diagonal predicate · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.093,"exit_code":1,"observations":[{"actual":true,"check":"fixture 1: ([[1, 2], [0, 3]],)","expected":false,"passed":false},{"actual":true,"check":"fixture 2: ([[0, 0], [0, 0]],)","expected":true,"passed":true},{"actual":true,"check":"fixture 3: ([[2, 0], [0, 3]],)","expected":true,"passed":true},{"actual":false,"check":"fixture 4: ([[1, 0], [2, 3]],)","expected":false,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [0, 3]],)\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 2: ([[0, 0], [0, 0]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 3: ([[2, 0], [0, 3]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: ([[1, 0], [2, 3]],)\", \"actual\": false, \"expected\": false, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.375,"exit_code":1,"observations":[{"actual":true,"check":"fixture 1: ([[1, 2], [0, 3]],)","expected":false,"passed":false},{"actual":false,"check":"fixture 2: ([[0, 0], [0, 0]],)","expected":true,"passed":false},{"actual":true,"check":"fixture 3: ([[2, 0], [0, 3]],)","expected":true,"passed":true},{"actual":true,"check":"fixture 4: ([[1, 0], [2, 3]],)","expected":false,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [0, 3]],)\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 2: ([[0, 0], [0, 0]],)\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 3: ([[2, 0], [0, 3]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: ([[1, 0], [2, 3]],)\", \"actual\": true, \"expected\": false, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.212,"exit_code":0,"observations":[{"actual":false,"check":"fixture 1: ([[1, 2], [0, 3]],)","expected":false,"passed":true},{"actual":true,"check":"fixture 2: ([[0, 0], [0, 0]],)","expected":true,"passed":true},{"actual":true,"check":"fixture 3: ([[2, 0], [0, 3]],)","expected":true,"passed":true},{"actual":false,"check":"fixture 4: ([[1, 0], [2, 3]],)","expected":false,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [0, 3]],)\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"fixture 2: ([[0, 0], [0, 0]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 3: ([[2, 0], [0, 3]],)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: ([[1, 0], [2, 3]],)\", \"actual\": false, \"expected\": false, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}