{"abstract":"Only vertices are counted, excluding lattice points along edges.","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. Input is the ordered integer vertices of a simple nondegenerate lattice polygon, without a repeated closing vertex. Exact operational definition: sum(math.gcd(abs(a[0]-b[0]),abs(a[1]-b[1])) for a,b in zip(points,points[1:]+points[:1]))","contract_signature":"points","evaluation_group":"model-0349578f51ea2db7","failed_approach":"Counting both endpoints per edge duplicates every vertex.","family":"xn-polygon-boundary-lattice-points","id":"FA-5896","implementations":{"attempt":{"sha256":"dbf32b004af4ca7e53aae2acc7745b28b04fb9126a4ccef35c043db086aa84ab","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(math.gcd(abs(a[0]-b[0]),abs(a[1]-b[1]))+1 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: ([(0, 0), (2, 0), (2, 2), (0, 2)],)', solve(*([(0, 0), (2, 0), (2, 2), (0, 2)],)), 8)\ncheck('fixture 2: ([(0, 0), (1, 0), (0, 1)],)', solve(*([(0, 0), (1, 0), (0, 1)],)), 3)\ncheck('fixture 3: ([(0, 0), (3, 0), (0, 3)],)', solve(*([(0, 0), (3, 0), (0, 3)],)), 9)\ncheck('fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)', solve(*([(1, 1), (4, 1), (4, 3), (1, 3)],)), 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":"88bc9e4b0490664ebe3e8af8457b0e7b8029c52eebcfb8ff63f93028aad1d40b","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 len(points)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)', solve(*([(0, 0), (2, 0), (2, 2), (0, 2)],)), 8)\ncheck('fixture 2: ([(0, 0), (1, 0), (0, 1)],)', solve(*([(0, 0), (1, 0), (0, 1)],)), 3)\ncheck('fixture 3: ([(0, 0), (3, 0), (0, 3)],)', solve(*([(0, 0), (3, 0), (0, 3)],)), 9)\ncheck('fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)', solve(*([(1, 1), (4, 1), (4, 3), (1, 3)],)), 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-polygon-boundary-lattice-points","generated_at":"2026-09-29T14:37:55.194071+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":"Only vertices are counted, excluding lattice points along edges.","sha256":"9d6c44c749d775d2d6889f846837dc47d3763aa81459fc79ed2de70210e2590a","title":"Polygon boundary lattice 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":56.535,"exit_code":1,"observations":[{"actual":12,"check":"fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)","expected":8,"passed":false},{"actual":6,"check":"fixture 2: ([(0, 0), (1, 0), (0, 1)],)","expected":3,"passed":false},{"actual":12,"check":"fixture 3: ([(0, 0), (3, 0), (0, 3)],)","expected":9,"passed":false},{"actual":14,"check":"fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)","expected":10,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)\", \"actual\": 12, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: ([(0, 0), (1, 0), (0, 1)],)\", \"actual\": 6, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 3: ([(0, 0), (3, 0), (0, 3)],)\", \"actual\": 12, \"expected\": 9, \"passed\": false}, {\"check\": \"fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)\", \"actual\": 14, \"expected\": 10, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":56.634,"exit_code":1,"observations":[{"actual":4,"check":"fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)","expected":8,"passed":false},{"actual":3,"check":"fixture 2: ([(0, 0), (1, 0), (0, 1)],)","expected":3,"passed":true},{"actual":3,"check":"fixture 3: ([(0, 0), (3, 0), (0, 3)],)","expected":9,"passed":false},{"actual":4,"check":"fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)","expected":10,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([(0, 0), (2, 0), (2, 2), (0, 2)],)\", \"actual\": 4, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: ([(0, 0), (1, 0), (0, 1)],)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: ([(0, 0), (3, 0), (0, 3)],)\", \"actual\": 3, \"expected\": 9, \"passed\": false}, {\"check\": \"fixture 4: ([(1, 1), (4, 1), (4, 3), (1, 3)],)\", \"actual\": 4, \"expected\": 10, \"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."}}