{"abstract":"The homogeneous translation column is omitted.","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. m is a 2 by 3 affine matrix and p has length two; implicit homogeneous coordinate is one. Exact operational definition: [m[i][0]*p[0]+m[i][1]*p[1]+m[i][2] for i in range(2)]","contract_signature":"m, p","evaluation_group":"model-95c9899a6722e5d6","failed_approach":"Translation is applied before scaling instead of after the linear map.","family":"xn-two-dimensional-affine-transform","id":"FA-6091","implementations":{"attempt":{"sha256":"6825188cdf5d60a9bcb042157f024a018d798841628fd9cbe52ff96898d73b2f","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, p):\n    return [m[i][0]*(p[0]+m[i][2])+m[i][1]*p[1] for i in range(2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[2, 0, 3], [0, 2, 4]], [1, 1])', solve(*([[2, 0, 3], [0, 2, 4]], [1, 1])), [5, 6])\ncheck('fixture 2: ([[1, 0, 2], [0, 1, 3]], [0, 0])', solve(*([[1, 0, 2], [0, 1, 3]], [0, 0])), [2, 3])\ncheck('fixture 3: ([[0, -1, 0], [1, 0, 0]], [2, 3])', solve(*([[0, -1, 0], [1, 0, 0]], [2, 3])), [-3, 2])\ncheck('fixture 4: ([[1, 0, 0], [0, 1, 0]], [4, 5])', solve(*([[1, 0, 0], [0, 1, 0]], [4, 5])), [4, 5])\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":"ac4c78576d6e2a926db8f0f7feae164aa77632914bea8380be1fefbaa75c9bc1","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, p):\n    return [m[i][0]*p[0]+m[i][1]*p[1] for i in range(2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[2, 0, 3], [0, 2, 4]], [1, 1])', solve(*([[2, 0, 3], [0, 2, 4]], [1, 1])), [5, 6])\ncheck('fixture 2: ([[1, 0, 2], [0, 1, 3]], [0, 0])', solve(*([[1, 0, 2], [0, 1, 3]], [0, 0])), [2, 3])\ncheck('fixture 3: ([[0, -1, 0], [1, 0, 0]], [2, 3])', solve(*([[0, -1, 0], [1, 0, 0]], [2, 3])), [-3, 2])\ncheck('fixture 4: ([[1, 0, 0], [0, 1, 0]], [4, 5])', solve(*([[1, 0, 0], [0, 1, 0]], [4, 5])), [4, 5])\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-two-dimensional-affine-transform","generated_at":"2026-09-29T14:37:57.366641+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 homogeneous translation column is omitted.","sha256":"d57a00c925ea88a7628baeafd6e6f27288dffc21c5702c25d9fdd89e6bacdc73","title":"Two dimensional affine transform · 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":43.909,"exit_code":1,"observations":[{"actual":[8,2],"check":"fixture 1: ([[2, 0, 3], [0, 2, 4]], [1, 1])","expected":[5,6],"passed":false},{"actual":[2,0],"check":"fixture 2: ([[1, 0, 2], [0, 1, 3]], [0, 0])","expected":[2,3],"passed":false},{"actual":[-3,2],"check":"fixture 3: ([[0, -1, 0], [1, 0, 0]], [2, 3])","expected":[-3,2],"passed":true},{"actual":[4,5],"check":"fixture 4: ([[1, 0, 0], [0, 1, 0]], [4, 5])","expected":[4,5],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[2, 0, 3], [0, 2, 4]], [1, 1])\", \"actual\": [8, 2], \"expected\": [5, 6], \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0, 2], [0, 1, 3]], [0, 0])\", \"actual\": [2, 0], \"expected\": [2, 3], \"passed\": false}, {\"check\": \"fixture 3: ([[0, -1, 0], [1, 0, 0]], [2, 3])\", \"actual\": [-3, 2], \"expected\": [-3, 2], \"passed\": true}, {\"check\": \"fixture 4: ([[1, 0, 0], [0, 1, 0]], [4, 5])\", \"actual\": [4, 5], \"expected\": [4, 5], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.084,"exit_code":1,"observations":[{"actual":[2,2],"check":"fixture 1: ([[2, 0, 3], [0, 2, 4]], [1, 1])","expected":[5,6],"passed":false},{"actual":[0,0],"check":"fixture 2: ([[1, 0, 2], [0, 1, 3]], [0, 0])","expected":[2,3],"passed":false},{"actual":[-3,2],"check":"fixture 3: ([[0, -1, 0], [1, 0, 0]], [2, 3])","expected":[-3,2],"passed":true},{"actual":[4,5],"check":"fixture 4: ([[1, 0, 0], [0, 1, 0]], [4, 5])","expected":[4,5],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[2, 0, 3], [0, 2, 4]], [1, 1])\", \"actual\": [2, 2], \"expected\": [5, 6], \"passed\": false}, {\"check\": \"fixture 2: ([[1, 0, 2], [0, 1, 3]], [0, 0])\", \"actual\": [0, 0], \"expected\": [2, 3], \"passed\": false}, {\"check\": \"fixture 3: ([[0, -1, 0], [1, 0, 0]], [2, 3])\", \"actual\": [-3, 2], \"expected\": [-3, 2], \"passed\": true}, {\"check\": \"fixture 4: ([[1, 0, 0], [0, 1, 0]], [4, 5])\", \"actual\": [4, 5], \"expected\": [4, 5], \"passed\": true}], \"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."}}