{"abstract":"Coordinatewise triple multiplication omits determinant permutations.","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 scalar triple product. Exact operational definition: a[0]*(b[1]*c[2]-b[2]*c[1])+a[1]*(b[2]*c[0]-b[0]*c[2])+a[2]*(b[0]*c[1]-b[1]*c[0])","contract_signature":"a, b, c","evaluation_group":"model-1c37e0b915ba6105","failed_approach":"Taking absolute volume erases orientation.","family":"xn-three-dimensional-scalar-triple-product","id":"FA-6096","implementations":{"attempt":{"sha256":"b5347880f85509f34b390820e455bf06338440bf9905d09e973168ab96b9325d","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, c):\n    return abs(a[0]*(b[1]*c[2]-b[2]*c[1])+a[1]*(b[2]*c[0]-b[0]*c[2])+a[2]*(b[0]*c[1]-b[1]*c[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], [0, 0, 1])', solve(*([1, 0, 0], [0, 1, 0], [0, 0, 1])), 1)\ncheck('fixture 2: ([0, 1, 0], [1, 0, 0], [0, 0, 1])', solve(*([0, 1, 0], [1, 0, 0], [0, 0, 1])), -1)\ncheck('fixture 3: ([1, 2, 3], [1, 2, 3], [2, 1, 0])', solve(*([1, 2, 3], [1, 2, 3], [2, 1, 0])), 0)\ncheck('fixture 4: ([2, 0, 0], [0, 3, 0], [0, 0, 4])', solve(*([2, 0, 0], [0, 3, 0], [0, 0, 4])), 24)\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":"ccc26def3beac0d0df3c4807b93d37b887fc5e5fe872d020280b4a9e7d125bf9","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, c):\n    return sum(x*y*z for x,y,z in zip(a,b,c))\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], [0, 0, 1])', solve(*([1, 0, 0], [0, 1, 0], [0, 0, 1])), 1)\ncheck('fixture 2: ([0, 1, 0], [1, 0, 0], [0, 0, 1])', solve(*([0, 1, 0], [1, 0, 0], [0, 0, 1])), -1)\ncheck('fixture 3: ([1, 2, 3], [1, 2, 3], [2, 1, 0])', solve(*([1, 2, 3], [1, 2, 3], [2, 1, 0])), 0)\ncheck('fixture 4: ([2, 0, 0], [0, 3, 0], [0, 0, 4])', solve(*([2, 0, 0], [0, 3, 0], [0, 0, 4])), 24)\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-scalar-triple-product","generated_at":"2026-09-29T14:37:57.409610+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":"Coordinatewise triple multiplication omits determinant permutations.","sha256":"103a901608c67e7c3f13b0a4a0c90803db9bc93a790a62356dba40d5a5ea065e","title":"Three dimensional scalar triple 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":44.906,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: ([1, 0, 0], [0, 1, 0], [0, 0, 1])","expected":1,"passed":true},{"actual":1,"check":"fixture 2: ([0, 1, 0], [1, 0, 0], [0, 0, 1])","expected":-1,"passed":false},{"actual":0,"check":"fixture 3: ([1, 2, 3], [1, 2, 3], [2, 1, 0])","expected":0,"passed":true},{"actual":24,"check":"fixture 4: ([2, 0, 0], [0, 3, 0], [0, 0, 4])","expected":24,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0, 0], [0, 1, 0], [0, 0, 1])\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: ([0, 1, 0], [1, 0, 0], [0, 0, 1])\", \"actual\": 1, \"expected\": -1, \"passed\": false}, {\"check\": \"fixture 3: ([1, 2, 3], [1, 2, 3], [2, 1, 0])\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([2, 0, 0], [0, 3, 0], [0, 0, 4])\", \"actual\": 24, \"expected\": 24, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.245,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: ([1, 0, 0], [0, 1, 0], [0, 0, 1])","expected":1,"passed":false},{"actual":0,"check":"fixture 2: ([0, 1, 0], [1, 0, 0], [0, 0, 1])","expected":-1,"passed":false},{"actual":6,"check":"fixture 3: ([1, 2, 3], [1, 2, 3], [2, 1, 0])","expected":0,"passed":false},{"actual":0,"check":"fixture 4: ([2, 0, 0], [0, 3, 0], [0, 0, 4])","expected":24,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0, 0], [0, 1, 0], [0, 0, 1])\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: ([0, 1, 0], [1, 0, 0], [0, 0, 1])\", \"actual\": 0, \"expected\": -1, \"passed\": false}, {\"check\": \"fixture 3: ([1, 2, 3], [1, 2, 3], [2, 1, 0])\", \"actual\": 6, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 4: ([2, 0, 0], [0, 3, 0], [0, 0, 4])\", \"actual\": 0, \"expected\": 24, \"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."}}