Clay: A Geometric and Topological Framework for Universal Knowledge Representation

We introduce a mathematical framework for the Clay architecture, a universal, first-principles model for knowledge representation. Leveraging topology, vector calculus, and geometric graph theory, we demonstrate a system that builds an internal, verifiable model of a knowledge domain’s structure, moving beyond statistical correlation. This work is not presented as a finished product, but as an invitation—a call to explore a new foundation for AI built on architectural elegance, mathematical transparency, and verifiable understanding.