Web Growth Rules, Crystal Skeletons, and Computer-Aided Reasoning
A proposed collaborative visit on Kashiwara crystals, combining Lean formalization of web growth rules with LLM-assisted computational exploration of crystal skeletons.
This project pursues two connected lines of research on Kashiwara crystals using computer-aided reasoning. The first project aims to formalize the roughly one hundred "growth rules" behind the recently constructed rotation-invariant web basis for sl₄ in the Lean proof assistant and to explore whether automated reasoning could extend such results to higher rank. The second project is a computational/exploratory study of recently introduced "crystal skeletons," using SageMath, custom research code, and large language models to test conjectures and probe the deep connections between crystal skeletons and web bases.