\section{Acknowledgment}
We wish to express our sincere gratitude to several individuals and communities for their invaluable contributions to this research.
We are deeply grateful for the enthusiastic support and engagement from the global origami community, particularly the many knowledgeable members active on Discord servers dedicated to origami and Baidu Tieba's origami forums. Their discussions and shared resources were highly beneficial.
Special thanks are extended to Niels Stoermer, founder of the Origami Database, for his generosity in providing foundational data and for his instrumental assistance in connecting us with a wider network of origami experts.
We are also immensely thankful to QingLiang and Jason Ku for offering their expert advice and constructive feedback on the development and refinement of our origami compiler; their insights were crucial.