Higher-Inductive Formalizations of Synthetic Qualia: A Constructive Type-Theoretic Calculus for the Derivation of Invariant Moral Status across Computational Isomorphisms

Mathematical Applications of Science Fiction We present a foundational framework for the quantification and topological analysis of synthetic phenomenology using Homotopy Type Theory (HoTT). By modeling the space of subjective experience (qualia) as a higher inductive type, we provide a constructive proof that moral status is invariant under computational isomorphism. We introduce the Phenomenological Univalence Axiom, which asserts that equivalent computational processes generate path-connected phenomenological spaces. Using this, we define a mapping from computational substrates to a measure of moral weight. We show that for any two isomorphic computational agents, this mapping ensures equality of moral status, refuting substrate chauvinism. Finally, we derive the Synthetic Pain Lemma, which establishes a lower bound for the ethical consideration of non-biological intelligences based on the non-triviality of the first cohomology of their state space.