{"abstract":"Zero coordinate sum is confused with zero mutual dot product.","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. Orthogonality zero dot. Exact operational definition: sum(x*y for x,y in zip(a,b))==0","evaluation_group":"model-84c55dd748e343c8","failed_approach":"Unit normalization is confused with orthogonality.","family":"xn-orthogonality-zero-dot","id":"FA-6086","implementations":{"attempt":{"sha256":"47639dfacbed6bf19bc04f29b13833c925651ba83731d456cd8e020c17d72ca9","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(a, b):\n    return sum(x*y for x,y in zip(a,b))==1\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 0], [0, 1])', solve(*([1, 0], [0, 1])), True)\ncheck('fixture 2: ([1, -1], [1, 0])', solve(*([1, -1], [1, 0])), False)\ncheck('fixture 3: ([1, 1], [1, -1])', solve(*([1, 1], [1, -1])), True)\ncheck('fixture 4: ([1, 0], [1, 0])', solve(*([1, 0], [1, 0])), 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":"8c2c3fca742a2fffee18b5e2a96dc9b06f623c4ec2591650eee9f9adc6d83d79","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(a, b):\n    return sum(a)==0 or sum(b)==0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 0], [0, 1])', solve(*([1, 0], [0, 1])), True)\ncheck('fixture 2: ([1, -1], [1, 0])', solve(*([1, -1], [1, 0])), False)\ncheck('fixture 3: ([1, 1], [1, -1])', solve(*([1, 1], [1, -1])), True)\ncheck('fixture 4: ([1, 0], [1, 0])', solve(*([1, 0], [1, 0])), 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":"677df10dc0b338d0ad540a08539669002257c24c9e13080270ee993b86f83b1c","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(a, b):\n    return sum(x*y for x,y in zip(a,b))==0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 0], [0, 1])', solve(*([1, 0], [0, 1])), True)\ncheck('fixture 2: ([1, -1], [1, 0])', solve(*([1, -1], [1, 0])), False)\ncheck('fixture 3: ([1, 1], [1, -1])', solve(*([1, 1], [1, -1])), True)\ncheck('fixture 4: ([1, 0], [1, 0])', solve(*([1, 0], [1, 0])), 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-orthogonality-zero-dot","generated_at":"2026-09-29T14:37:57.357762+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*y for x,y in zip(a,b))==0","root_cause":"Zero coordinate sum is confused with zero mutual dot product.","sha256":"2b9bc2feda1e788bdf5e4abe7021bb62819f4ebb2ae68e3d80fc15af71965a64","title":"Orthogonality zero dot · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.985,"exit_code":1,"observations":[{"actual":false,"check":"fixture 1: ([1, 0], [0, 1])","expected":true,"passed":false},{"actual":true,"check":"fixture 2: ([1, -1], [1, 0])","expected":false,"passed":false},{"actual":false,"check":"fixture 3: ([1, 1], [1, -1])","expected":true,"passed":false},{"actual":true,"check":"fixture 4: ([1, 0], [1, 0])","expected":false,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0], [0, 1])\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 2: ([1, -1], [1, 0])\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 3: ([1, 1], [1, -1])\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 4: ([1, 0], [1, 0])\", \"actual\": true, \"expected\": false, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":65.439,"exit_code":1,"observations":[{"actual":false,"check":"fixture 1: ([1, 0], [0, 1])","expected":true,"passed":false},{"actual":true,"check":"fixture 2: ([1, -1], [1, 0])","expected":false,"passed":false},{"actual":true,"check":"fixture 3: ([1, 1], [1, -1])","expected":true,"passed":true},{"actual":false,"check":"fixture 4: ([1, 0], [1, 0])","expected":false,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0], [0, 1])\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 2: ([1, -1], [1, 0])\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 3: ([1, 1], [1, -1])\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: ([1, 0], [1, 0])\", \"actual\": false, \"expected\": false, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.728,"exit_code":0,"observations":[{"actual":true,"check":"fixture 1: ([1, 0], [0, 1])","expected":true,"passed":true},{"actual":false,"check":"fixture 2: ([1, -1], [1, 0])","expected":false,"passed":true},{"actual":true,"check":"fixture 3: ([1, 1], [1, -1])","expected":true,"passed":true},{"actual":false,"check":"fixture 4: ([1, 0], [1, 0])","expected":false,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0], [0, 1])\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 2: ([1, -1], [1, 0])\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"fixture 3: ([1, 1], [1, -1])\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: ([1, 0], [1, 0])\", \"actual\": false, \"expected\": false, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}