{"abstract":"Maximum row sum computes the infinity norm.","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. Return the maximum absolute column sum, with zero for an empty matrix. Exact operational definition: max((sum(abs(x) for x in col) for col in zip(*m)),default=0)","evaluation_group":"model-20ac08d5b4f28ce9","failed_approach":"Signed column sums cancel magnitudes.","family":"xn-matrix-one-norm","id":"FA-6051","implementations":{"attempt":{"sha256":"0014684dac77e84c61d4f58b1b216c6b5f2b33443105bb06f729362f64d4077e","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 max((sum(x for x in col) for col in zip(*m)),default=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]],)), 6)\ncheck('fixture 2: ([[1, -5], [2, 1]],)', solve(*([[1, -5], [2, 1]],)), 6)\ncheck('fixture 3: ([],)', solve(*([],)), 0)\ncheck('fixture 4: ([[-3]],)', solve(*([[-3]],)), 3)\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":"ad6777a02e93f585eae407ffe32ef9a4a4a561631e820a896fa648701575c4e2","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 max((sum(abs(x) for x in row) for row in m),default=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]],)), 6)\ncheck('fixture 2: ([[1, -5], [2, 1]],)', solve(*([[1, -5], [2, 1]],)), 6)\ncheck('fixture 3: ([],)', solve(*([],)), 0)\ncheck('fixture 4: ([[-3]],)', solve(*([[-3]],)), 3)\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":"f0d816d6da1dd1b08088b68e05778ed3cc9dbf458254e12342cc9c8bd4642648","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 max((sum(abs(x) for x in col) for col in zip(*m)),default=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]],)), 6)\ncheck('fixture 2: ([[1, -5], [2, 1]],)', solve(*([[1, -5], [2, 1]],)), 6)\ncheck('fixture 3: ([],)', solve(*([],)), 0)\ncheck('fixture 4: ([[-3]],)', solve(*([[-3]],)), 3)\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-one-norm","generated_at":"2026-09-29T14:37:56.950802+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 max((sum(abs(x) for x in col) for col in zip(*m)),default=0)","root_cause":"Maximum row sum computes the infinity norm.","sha256":"51736018e5253a32fe24c72bcbcf52e1868eeda2ea7cd87feecfeaff89bec1b1","title":"Matrix one norm · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.492,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":6,"passed":true},{"actual":3,"check":"fixture 2: ([[1, -5], [2, 1]],)","expected":6,"passed":false},{"actual":0,"check":"fixture 3: ([],)","expected":0,"passed":true},{"actual":-3,"check":"fixture 4: ([[-3]],)","expected":3,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: ([[1, -5], [2, 1]],)\", \"actual\": 3, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 3: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([[-3]],)\", \"actual\": -3, \"expected\": 3, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.459,"exit_code":1,"observations":[{"actual":7,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":6,"passed":false},{"actual":6,"check":"fixture 2: ([[1, -5], [2, 1]],)","expected":6,"passed":true},{"actual":0,"check":"fixture 3: ([],)","expected":0,"passed":true},{"actual":3,"check":"fixture 4: ([[-3]],)","expected":3,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 7, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: ([[1, -5], [2, 1]],)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 3: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([[-3]],)\", \"actual\": 3, \"expected\": 3, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":48.922,"exit_code":0,"observations":[{"actual":6,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":6,"passed":true},{"actual":6,"check":"fixture 2: ([[1, -5], [2, 1]],)","expected":6,"passed":true},{"actual":0,"check":"fixture 3: ([],)","expected":0,"passed":true},{"actual":3,"check":"fixture 4: ([[-3]],)","expected":3,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: ([[1, -5], [2, 1]],)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 3: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([[-3]],)\", \"actual\": 3, \"expected\": 3, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}