{"abstract":"Maximum column sum computes the one-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 row sum, with zero for an empty matrix. Exact operational definition: max((sum(abs(x) for x in row) for row in m),default=0)","evaluation_group":"model-ad8f91272e05fcbe","failed_approach":"An absolute value applied after summation permits cancellation.","family":"xn-matrix-infinity-norm","id":"FA-6056","implementations":{"attempt":{"sha256":"21497a416461ad5e01b0cf38be7d25e7fbd8aeb1d5ea90fc58445f61f5f17bcb","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((abs(sum(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]],)), 7)\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":"91ff71f2d6525a644281f887ebb55f74c9e5076e0ae00250201095b830b42054","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]],)), 7)\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":"0806338dcaa4b7b4085abf20ce5a0fc22aa73ae3875f1406b0d24e899bd52ce0","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]],)), 7)\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-infinity-norm","generated_at":"2026-09-29T14:37:57.000929+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 row) for row in m),default=0)","root_cause":"Maximum column sum computes the one-norm.","sha256":"bbcbdc601d57085ae3954552134bf513c82a7ad8c870ff5eea92dd5bca961e55","title":"Matrix infinity norm · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":49.457,"exit_code":1,"observations":[{"actual":7,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":7,"passed":true},{"actual":4,"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":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 2], [3, 4]],)\", \"actual\": 7, \"expected\": 7, \"passed\": true}, {\"check\": \"fixture 2: ([[1, -5], [2, 1]],)\", \"actual\": 4, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 3: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([[-3]],)\", \"actual\": 3, \"expected\": 3, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.348,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":7,"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\": 6, \"expected\": 7, \"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":48.353,"exit_code":0,"observations":[{"actual":7,"check":"fixture 1: ([[1, 2], [3, 4]],)","expected":7,"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\": 7, \"expected\": 7, \"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"}