{"abstract":"The product of sums introduces cross-coordinate products.","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. Vector dot product. Exact operational definition: sum(x*y for x,y in zip(a,b))","contract_signature":"a, b","evaluation_group":"model-6fac4833c5f9596b","failed_approach":"Corresponding coordinates are added rather than multiplied.","family":"xn-vector-dot-product","id":"FA-6001","implementations":{"attempt":{"sha256":"587370f6aa3a432028c0bceb2fba5b4ffd92bf57891643729ae24df49dcd07e7","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))\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])), 11)\ncheck('fixture 2: ([1, -1], [1, 1])', solve(*([1, -1], [1, 1])), 0)\ncheck('fixture 3: ([], [])', solve(*([], [])), 0)\ncheck('fixture 4: ([0, 2], [5, 0])', solve(*([0, 2], [5, 0])), 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":"e563699893836623addaaeb495d3da302303488fe9168695dc44ca125546ce2f","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)*sum(b)\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])), 11)\ncheck('fixture 2: ([1, -1], [1, 1])', solve(*([1, -1], [1, 1])), 0)\ncheck('fixture 3: ([], [])', solve(*([], [])), 0)\ncheck('fixture 4: ([0, 2], [5, 0])', solve(*([0, 2], [5, 0])), 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-vector-dot-product","generated_at":"2026-09-29T14:37:56.244780+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.","root_cause":"The product of sums introduces cross-coordinate products.","sha256":"391016b32a958a5284ec8f88aebb4d0b65b919b713aac1256ef38254c3a8ad3a","title":"Vector dot product · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":43.602,"exit_code":1,"observations":[{"actual":10,"check":"fixture 1: ([1, 2], [3, 4])","expected":11,"passed":false},{"actual":2,"check":"fixture 2: ([1, -1], [1, 1])","expected":0,"passed":false},{"actual":0,"check":"fixture 3: ([], [])","expected":0,"passed":true},{"actual":7,"check":"fixture 4: ([0, 2], [5, 0])","expected":0,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], [3, 4])\", \"actual\": 10, \"expected\": 11, \"passed\": false}, {\"check\": \"fixture 2: ([1, -1], [1, 1])\", \"actual\": 2, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: ([], [])\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([0, 2], [5, 0])\", \"actual\": 7, \"expected\": 0, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.739,"exit_code":1,"observations":[{"actual":21,"check":"fixture 1: ([1, 2], [3, 4])","expected":11,"passed":false},{"actual":0,"check":"fixture 2: ([1, -1], [1, 1])","expected":0,"passed":true},{"actual":0,"check":"fixture 3: ([], [])","expected":0,"passed":true},{"actual":10,"check":"fixture 4: ([0, 2], [5, 0])","expected":0,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2], [3, 4])\", \"actual\": 21, \"expected\": 11, \"passed\": false}, {\"check\": \"fixture 2: ([1, -1], [1, 1])\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: ([], [])\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([0, 2], [5, 0])\", \"actual\": 10, \"expected\": 0, \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}