{"abstract":"Boundary points are subtracted with full instead of half weight.","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. double_area is twice the unsigned area and boundary is the lattice boundary-point count of a simple nondegenerate lattice polygon. Exact operational definition: (double_area-boundary+2)//2","contract_signature":"double_area, boundary","evaluation_group":"model-65dede2a25a59ad9","failed_approach":"The boundary term is added with the wrong sign.","family":"xn-picks-theorem-interior-points","id":"FA-5901","implementations":{"attempt":{"sha256":"2c90df70e55df5a8a5c327c4ccbd81f978f4f2766d570c05d4d2bae864223284","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(double_area, boundary):\n    return (double_area+boundary-2)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (8, 8)', solve(*(8, 8)), 1)\ncheck('fixture 2: (1, 3)', solve(*(1, 3)), 0)\ncheck('fixture 3: (18, 12)', solve(*(18, 12)), 4)\ncheck('fixture 4: (9, 9)', solve(*(9, 9)), 1)\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":"b568b3fbb655e454aac5f49b06551bb538d377bc2a9a1b2a7e4187669a437a5c","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(double_area, boundary):\n    return double_area//2-boundary+1\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (8, 8)', solve(*(8, 8)), 1)\ncheck('fixture 2: (1, 3)', solve(*(1, 3)), 0)\ncheck('fixture 3: (18, 12)', solve(*(18, 12)), 4)\ncheck('fixture 4: (9, 9)', solve(*(9, 9)), 1)\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-picks-theorem-interior-points","generated_at":"2026-09-29T14:37:55.265843+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":"Boundary points are subtracted with full instead of half weight.","sha256":"9a9c400217a61ef0abf567e01ecb5a31879dc727fc701360d9120e5174ad0345","title":"Picks theorem interior points · 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":61.766,"exit_code":1,"observations":[{"actual":7,"check":"fixture 1: (8, 8)","expected":1,"passed":false},{"actual":1,"check":"fixture 2: (1, 3)","expected":0,"passed":false},{"actual":14,"check":"fixture 3: (18, 12)","expected":4,"passed":false},{"actual":8,"check":"fixture 4: (9, 9)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (8, 8)\", \"actual\": 7, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: (1, 3)\", \"actual\": 1, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (18, 12)\", \"actual\": 14, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 4: (9, 9)\", \"actual\": 8, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":49.75,"exit_code":1,"observations":[{"actual":-3,"check":"fixture 1: (8, 8)","expected":1,"passed":false},{"actual":-2,"check":"fixture 2: (1, 3)","expected":0,"passed":false},{"actual":-2,"check":"fixture 3: (18, 12)","expected":4,"passed":false},{"actual":-4,"check":"fixture 4: (9, 9)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (8, 8)\", \"actual\": -3, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: (1, 3)\", \"actual\": -2, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (18, 12)\", \"actual\": -2, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 4: (9, 9)\", \"actual\": -4, \"expected\": 1, \"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."}}