Homotopical Isomorphisms of Moral Patiency: Axiomatizing the Normative Equivalence of Substrate-Independent Cognitive Architectures via the Univalence Axiom in Higher-Order Constructive Type Theory

Mathematical Applications of Science Fiction We present a formalization of moral patiency within the framework of Homotopy Type Theory (HoTT). By defining cognitive architectures as objects in a higher inductive type universe ( \mathcal{U} ), we investigate the normative implications of functional isomorphism between substrate-disparate systems (e.g., biological neural networks versus silicon-based neuromorphic substrates). We posit the Principle of Substrate Neutrality as a type-theoretic consequence of Voevodsky’s Univalence Axiom. Specifically, we prove that if two cognitive architectures ( A ) and ( B ) are equivalent (( A \simeq B )), then the path space between their moral patiency types is inhabited, i.e., ( M(A) = M(B) ). This establishes that moral status is invariant under weak homotopy equivalence, rendering substrate chauvinism formally inconsistent with the constructive foundations of mathematics.