The Math Behind GPT Systems and Their Ontological Models

This article unpacks the operational theory behind GPT (Generalized Probability Theory) systems, defining how states, effects, and measurements are constructed. It explores how GPT systems can be simulated using ontological models, distinguishes classical from quantum behavior, and introduces univalent simulations as a tool to understand embeddability and contextuality. Together, these concepts provide a rigorous framework for analyzing how generalized probabilistic systems behave and interact.