Recursive Categorical Framework

This paper presents a mathematical framework using category theory to formalize recursive self-reference in computational systems. The Recursive Categorical Framework (RCF) establishes three core mathematical structures: a triaxial operator architecture (ethical resolution, Bayesian belief updating, and eigenstate stabilization), a fiber bundle topology over an ethical manifold, and fixed-point theorems for recursive identity convergence. The framework uses the Banach fixed point theorem and fiber bundle formalism to resolve paradoxes in self referential systems. Empirical validation is provided through computational experiments testing eigenrecursion convergence and contradiction resolution. The work includes formal proofs, implementation specifications, and connections to quantum computing extensions.