{"abstract":"The determinant adds its cross terms instead of subtracting.","category":"Planar geometry","checks":4,"contract":"Integer coordinates and lengths, with exact arithmetic except for indicated division results. Lengths are nonnegative. Rectangles are (xmin,ymin,xmax,ymax) with ordered bounds; coordinate vectors have matching dimensions. a,b,c are planar points; return twice signed triangle area, positive for counterclockwise order. Exact operational definition: (b[0]-a[0])*(c[1]-a[1])-(b[1]-a[1])*(c[0]-a[0])","evaluation_group":"model-3526c16299acd91d","failed_approach":"Absolute area erases orientation required by the contract.","family":"xn-oriented-triangle-double-area","id":"FA-5761","implementations":{"attempt":{"sha256":"4263967e0e2b8c970f57114a41533c2f57fdb11a5458e5155c295bee2d6f5cbd","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((b[0]-a[0])*(c[1]-a[1])-(b[1]-a[1])*(c[0]-a[0]))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ((0, 0), (2, 0), (0, 3))', solve(*((0, 0), (2, 0), (0, 3))), 6)\ncheck('fixture 2: ((0, 0), (0, 3), (2, 0))', solve(*((0, 0), (0, 3), (2, 0))), -6)\ncheck('fixture 3: ((1, 1), (2, 2), (3, 3))', solve(*((1, 1), (2, 2), (3, 3))), 0)\ncheck('fixture 4: ((2, 1), (4, 3), (1, 5))', solve(*((2, 1), (4, 3), (1, 5))), 10)\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":"fa2ff03d853e291865156053303444a1eaa40e36402379e5ec8cda62a390c5f4","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 (b[0]-a[0])*(c[1]-a[1])+(b[1]-a[1])*(c[0]-a[0])\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ((0, 0), (2, 0), (0, 3))', solve(*((0, 0), (2, 0), (0, 3))), 6)\ncheck('fixture 2: ((0, 0), (0, 3), (2, 0))', solve(*((0, 0), (0, 3), (2, 0))), -6)\ncheck('fixture 3: ((1, 1), (2, 2), (3, 3))', solve(*((1, 1), (2, 2), (3, 3))), 0)\ncheck('fixture 4: ((2, 1), (4, 3), (1, 5))', solve(*((2, 1), (4, 3), (1, 5))), 10)\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":"790785ae0e3acf9724b95ea51e9963c343ceb80550cba5e4b47ebacd0959c2dd","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 (b[0]-a[0])*(c[1]-a[1])-(b[1]-a[1])*(c[0]-a[0])\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ((0, 0), (2, 0), (0, 3))', solve(*((0, 0), (2, 0), (0, 3))), 6)\ncheck('fixture 2: ((0, 0), (0, 3), (2, 0))', solve(*((0, 0), (0, 3), (2, 0))), -6)\ncheck('fixture 3: ((1, 1), (2, 2), (3, 3))', solve(*((1, 1), (2, 2), (3, 3))), 0)\ncheck('fixture 4: ((2, 1), (4, 3), (1, 5))', solve(*((2, 1), (4, 3), (1, 5))), 10)\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-oriented-triangle-double-area","generated_at":"2026-09-29T14:37:53.416652+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. Planar geometry results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return (b[0]-a[0])*(c[1]-a[1])-(b[1]-a[1])*(c[0]-a[0])","root_cause":"The determinant adds its cross terms instead of subtracting.","sha256":"8419208baf6a0877f0e29e7707c6f409fdbd75ca9577aea695a72b936bc812b8","title":"Oriented triangle double area · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":48.313,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: ((0, 0), (2, 0), (0, 3))","expected":6,"passed":true},{"actual":6,"check":"fixture 2: ((0, 0), (0, 3), (2, 0))","expected":-6,"passed":false},{"actual":0,"check":"fixture 3: ((1, 1), (2, 2), (3, 3))","expected":0,"passed":true},{"actual":10,"check":"fixture 4: ((2, 1), (4, 3), (1, 5))","expected":10,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ((0, 0), (2, 0), (0, 3))\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: ((0, 0), (0, 3), (2, 0))\", \"actual\": 6, \"expected\": -6, \"passed\": false}, {\"check\": \"fixture 3: ((1, 1), (2, 2), (3, 3))\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ((2, 1), (4, 3), (1, 5))\", \"actual\": 10, \"expected\": 10, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":47.24,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: ((0, 0), (2, 0), (0, 3))","expected":6,"passed":true},{"actual":6,"check":"fixture 2: ((0, 0), (0, 3), (2, 0))","expected":-6,"passed":false},{"actual":4,"check":"fixture 3: ((1, 1), (2, 2), (3, 3))","expected":0,"passed":false},{"actual":6,"check":"fixture 4: ((2, 1), (4, 3), (1, 5))","expected":10,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ((0, 0), (2, 0), (0, 3))\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: ((0, 0), (0, 3), (2, 0))\", \"actual\": 6, \"expected\": -6, \"passed\": false}, {\"check\": \"fixture 3: ((1, 1), (2, 2), (3, 3))\", \"actual\": 4, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 4: ((2, 1), (4, 3), (1, 5))\", \"actual\": 6, \"expected\": 10, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":47.759,"exit_code":0,"observations":[{"actual":6,"check":"fixture 1: ((0, 0), (2, 0), (0, 3))","expected":6,"passed":true},{"actual":-6,"check":"fixture 2: ((0, 0), (0, 3), (2, 0))","expected":-6,"passed":true},{"actual":0,"check":"fixture 3: ((1, 1), (2, 2), (3, 3))","expected":0,"passed":true},{"actual":10,"check":"fixture 4: ((2, 1), (4, 3), (1, 5))","expected":10,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ((0, 0), (2, 0), (0, 3))\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: ((0, 0), (0, 3), (2, 0))\", \"actual\": -6, \"expected\": -6, \"passed\": true}, {\"check\": \"fixture 3: ((1, 1), (2, 2), (3, 3))\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ((2, 1), (4, 3), (1, 5))\", \"actual\": 10, \"expected\": 10, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}