{"abstract":"Squaring a total introduces cancellation and cross terms.","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 frobenius norm squared. Exact operational definition: sum(x*x for row in m for x in row)","evaluation_group":"model-fa64d7a68b1753eb","failed_approach":"Absolute values use an entrywise one-norm instead of squared two-norm.","family":"xn-matrix-frobenius-norm-squared","id":"FA-6046","implementations":{"attempt":{"sha256":"71708cc5dca93dd67395ace607df68222a06cb09783a012aae59693f8701a25c","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 sum(abs(x) for row in m for x in row)\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]],)), 30)\ncheck('fixture 2: ([[1, -1]],)', solve(*([[1, -1]],)), 2)\ncheck('fixture 3: ([[0]],)', solve(*([[0]],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 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":"a64894b27e566b47494ff9cff8e14ef529ac02b5bc6d8b2a5eef68f31ef3e3e8","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 sum(x for row in m for x in row)**2\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]],)), 30)\ncheck('fixture 2: ([[1, -1]],)', solve(*([[1, -1]],)), 2)\ncheck('fixture 3: ([[0]],)', solve(*([[0]],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 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":"210be307855e51f50659105aab7d202bb129c754e39d74836299871b1a603978","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 sum(x*x for row in m for x in row)\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]],)), 30)\ncheck('fixture 2: ([[1, -1]],)', solve(*([[1, -1]],)), 2)\ncheck('fixture 3: ([[0]],)', solve(*([[0]],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 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-matrix-frobenius-norm-squared","generated_at":"2026-09-29T14:37:56.950331+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 sum(x*x for row in m for x in row)","root_cause":"Squaring a total introduces cancellation and cross terms.","sha256":"9e4b20f2585b8d097bd3276270c64be9636434fad8172a6d095489c952d5df48","title":"Matrix frobenius norm squared · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.512,"exit_code":1,"observations":[{"actual":10,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":30,"passed":false},{"actual":2,"check":"fixture 2: ([[1, -1]],)","expected":2,"passed":true},{"actual":0,"check":"fixture 3: ([[0]],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 10, \"expected\": 30, \"passed\": false}, {\"check\": \"fixture 2: ([[1, -1]],)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: ([[0]],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.494,"exit_code":1,"observations":[{"actual":100,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":30,"passed":false},{"actual":0,"check":"fixture 2: ([[1, -1]],)","expected":2,"passed":false},{"actual":0,"check":"fixture 3: ([[0]],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 100, \"expected\": 30, \"passed\": false}, {\"check\": \"fixture 2: ([[1, -1]],)\", \"actual\": 0, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 3: ([[0]],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":47.71,"exit_code":0,"observations":[{"actual":30,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":30,"passed":true},{"actual":2,"check":"fixture 2: ([[1, -1]],)","expected":2,"passed":true},{"actual":0,"check":"fixture 3: ([[0]],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 30, \"expected\": 30, \"passed\": true}, {\"check\": \"fixture 2: ([[1, -1]],)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: ([[0]],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}