{"abstract":"The closing polygon edge is missing from the shoelace sum.","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. Vertices are ordered around a polygon; close the last edge to the first. The empty list returns zero. Exact operational definition: sum(a[0]*b[1]-a[1]*b[0] for a,b in zip(points,points[1:]+points[:1]))","contract_signature":"points","evaluation_group":"model-520ec3f17f52b28d","failed_approach":"Taking magnitude destroys signed winding information.","family":"xn-polygon-signed-double-area","id":"FA-5891","implementations":{"attempt":{"sha256":"3b11463ced536fdec5366a738f8adcf96ca1628bb3e6a804c0f67fab4c3b917a","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(points):\n    return abs(sum(a[0]*b[1]-a[1]*b[0] for a,b in zip(points,points[1:]+points[:1])))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([(1, 1), (3, 1), (1, 4)],)', solve(*([(1, 1), (3, 1), (1, 4)],)), 6)\ncheck('fixture 2: ([(1, 4), (3, 1), (1, 1)],)', solve(*([(1, 4), (3, 1), (1, 1)],)), -6)\ncheck('fixture 3: ([(0, 0), (2, 0), (2, 2), (0, 2)],)', solve(*([(0, 0), (2, 0), (2, 2), (0, 2)],)), 8)\ncheck('fixture 4: ([],)', solve(*([],)), 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":"6a374596aadf6af0cb3171d9db1d137c82e0c4942cba08f43d3b4bb8e992b202","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(points):\n    return sum(a[0]*b[1]-a[1]*b[0] for a,b in zip(points,points[1:]))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([(1, 1), (3, 1), (1, 4)],)', solve(*([(1, 1), (3, 1), (1, 4)],)), 6)\ncheck('fixture 2: ([(1, 4), (3, 1), (1, 1)],)', solve(*([(1, 4), (3, 1), (1, 1)],)), -6)\ncheck('fixture 3: ([(0, 0), (2, 0), (2, 2), (0, 2)],)', solve(*([(0, 0), (2, 0), (2, 2), (0, 2)],)), 8)\ncheck('fixture 4: ([],)', solve(*([],)), 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-polygon-signed-double-area","generated_at":"2026-09-29T14:37:55.200742+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.","root_cause":"The closing polygon edge is missing from the shoelace sum.","sha256":"a2881e8f2d9ac9f7f4acae5837168d81394017e1bc617d7ef05b4260374dc693","title":"Polygon signed double area · 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":56.527,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: ([(1, 1), (3, 1), (1, 4)],)","expected":6,"passed":true},{"actual":6,"check":"fixture 2: ([(1, 4), (3, 1), (1, 1)],)","expected":-6,"passed":false},{"actual":8,"check":"fixture 3: ([(0, 0), (2, 0), (2, 2), (0, 2)],)","expected":8,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([(1, 1), (3, 1), (1, 4)],)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: ([(1, 4), (3, 1), (1, 1)],)\", \"actual\": 6, \"expected\": -6, \"passed\": false}, {\"check\": \"fixture 3: ([(0, 0), (2, 0), (2, 2), (0, 2)],)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":60.037,"exit_code":1,"observations":[{"actual":9,"check":"fixture 1: ([(1, 1), (3, 1), (1, 4)],)","expected":6,"passed":false},{"actual":-9,"check":"fixture 2: ([(1, 4), (3, 1), (1, 1)],)","expected":-6,"passed":false},{"actual":8,"check":"fixture 3: ([(0, 0), (2, 0), (2, 2), (0, 2)],)","expected":8,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([(1, 1), (3, 1), (1, 4)],)\", \"actual\": 9, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: ([(1, 4), (3, 1), (1, 1)],)\", \"actual\": -9, \"expected\": -6, \"passed\": false}, {\"check\": \"fixture 3: ([(0, 0), (2, 0), (2, 2), (0, 2)],)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"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."}}