{"abstract":"Symmetric sums replace antisymmetric determinant 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. Three dimensional cross product. Exact operational definition: [a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]]","contract_signature":"a, b","evaluation_group":"model-082640a781d0aa8e","failed_approach":"The middle cofactor has the wrong sign.","family":"xn-three-dimensional-cross-product","id":"FA-6011","implementations":{"attempt":{"sha256":"f5b56113595a1305872a31400e38b46bef35aefc8b7d0a8b3dc62d8845cebb6c","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 [a[1]*b[2]-a[2]*b[1],a[0]*b[2]-a[2]*b[0],a[0]*b[1]-a[1]*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], [0, 1, 0])', solve(*([1, 0, 0], [0, 1, 0])), [0, 0, 1])\ncheck('fixture 2: ([1, 0, 0], [0, 0, 1])', solve(*([1, 0, 0], [0, 0, 1])), [0, -1, 0])\ncheck('fixture 3: ([1, 2, 3], [1, 2, 3])', solve(*([1, 2, 3], [1, 2, 3])), [0, 0, 0])\ncheck('fixture 4: ([0, 0, 1], [0, 1, 0])', solve(*([0, 0, 1], [0, 1, 0])), [-1, 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":"682b9508239ae0c70a28372fa5cd367c4c86a1f440f24805efff75127d1d58a3","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 [a[1]*b[2]+a[2]*b[1],a[2]*b[0]+a[0]*b[2],a[0]*b[1]+a[1]*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], [0, 1, 0])', solve(*([1, 0, 0], [0, 1, 0])), [0, 0, 1])\ncheck('fixture 2: ([1, 0, 0], [0, 0, 1])', solve(*([1, 0, 0], [0, 0, 1])), [0, -1, 0])\ncheck('fixture 3: ([1, 2, 3], [1, 2, 3])', solve(*([1, 2, 3], [1, 2, 3])), [0, 0, 0])\ncheck('fixture 4: ([0, 0, 1], [0, 1, 0])', solve(*([0, 0, 1], [0, 1, 0])), [-1, 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-three-dimensional-cross-product","generated_at":"2026-09-29T14:37:56.285410+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":"Symmetric sums replace antisymmetric determinant terms.","sha256":"d3b22f91c2e67f8b64fcf5937eccd4860b05886689e33157526899a2b8092a1b","title":"Three dimensional cross 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":44.828,"exit_code":1,"observations":[{"actual":[0,0,1],"check":"fixture 1: ([1, 0, 0], [0, 1, 0])","expected":[0,0,1],"passed":true},{"actual":[0,1,0],"check":"fixture 2: ([1, 0, 0], [0, 0, 1])","expected":[0,-1,0],"passed":false},{"actual":[0,0,0],"check":"fixture 3: ([1, 2, 3], [1, 2, 3])","expected":[0,0,0],"passed":true},{"actual":[-1,0,0],"check":"fixture 4: ([0, 0, 1], [0, 1, 0])","expected":[-1,0,0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0, 0], [0, 1, 0])\", \"actual\": [0, 0, 1], \"expected\": [0, 0, 1], \"passed\": true}, {\"check\": \"fixture 2: ([1, 0, 0], [0, 0, 1])\", \"actual\": [0, 1, 0], \"expected\": [0, -1, 0], \"passed\": false}, {\"check\": \"fixture 3: ([1, 2, 3], [1, 2, 3])\", \"actual\": [0, 0, 0], \"expected\": [0, 0, 0], \"passed\": true}, {\"check\": \"fixture 4: ([0, 0, 1], [0, 1, 0])\", \"actual\": [-1, 0, 0], \"expected\": [-1, 0, 0], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.088,"exit_code":1,"observations":[{"actual":[0,0,1],"check":"fixture 1: ([1, 0, 0], [0, 1, 0])","expected":[0,0,1],"passed":true},{"actual":[0,1,0],"check":"fixture 2: ([1, 0, 0], [0, 0, 1])","expected":[0,-1,0],"passed":false},{"actual":[12,6,4],"check":"fixture 3: ([1, 2, 3], [1, 2, 3])","expected":[0,0,0],"passed":false},{"actual":[1,0,0],"check":"fixture 4: ([0, 0, 1], [0, 1, 0])","expected":[-1,0,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0, 0], [0, 1, 0])\", \"actual\": [0, 0, 1], \"expected\": [0, 0, 1], \"passed\": true}, {\"check\": \"fixture 2: ([1, 0, 0], [0, 0, 1])\", \"actual\": [0, 1, 0], \"expected\": [0, -1, 0], \"passed\": false}, {\"check\": \"fixture 3: ([1, 2, 3], [1, 2, 3])\", \"actual\": [12, 6, 4], \"expected\": [0, 0, 0], \"passed\": false}, {\"check\": \"fixture 4: ([0, 0, 1], [0, 1, 0])\", \"actual\": [1, 0, 0], \"expected\": [-1, 0, 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."}}