Dataset of exact and Monte Carlo sampled square-lattice self-avoiding polygons

This dataset contains exact and Monte Carlo sampled square-lattice self-avoiding polygons (SAPs) for reproducible computational studies. It includes 536 exact free canonical classes at even perimeters P=4–16 and 12,152 Monte Carlo samples at P=64,128,256,512,1024, and 2048. Each polygon is represented by ordered integer coordinates and geometric descriptors. The release also provides sampling metadata, exact reference and validation data, convergence diagnostics, source code, reproducibility scripts, and checksums. The dataset is intended for benchmarking SAP enumeration and sampling methods and for studying polygon geometry and scaling behaviour.