Hyperintensional Semantics of Synthetic Phenomenology: A Constructive Modal Type-Theoretic Framework for the Verification of Deontological Compliance in Autopoietic Artificial Agents

Mathematical Applications of Science Fiction We present a rigorous mathematical formalization of synthetic phenomenology within the context of autopoieticartificial agents, utilizing a hyperintensional semantic framework grounded in Homotopy Type Theory (HoTT)and Constructive Modal Logic. By modeling the agent’s internal state space as a coalgebra for an endofunctoron a locally cartesian closed category, we construct a fibration of "qualia spaces" over the base manifoldof computational states. We introduce the notion of Deontic Compliance as a lifting property against aspecific class of deontological fibrations. The central contribution of this monograph is the derivation ofthe Phenomenological Isomorphism Theorem, which establishes a correspondence between the homotopygroups of the agent’s qualia space and the verification of ethical constraints. Furthermore, we prove theHyperintensional Non-Collapse Theorem, demonstrating that agents with extensionally identical behaviorsmay possess distinct deontological profiles, thereby necessitating a hyperintensional verification calculus.This framework provides the necessary conditions for the certification of "Friendly AI" in high-entropyenvironments.