Homotopical Semantics of Recursive Agency: A Type-Theoretic Derivation of Deontic Invariants Across Heterogeneous Cognitive Substrates via the Univalence Axiom

Mathematical Applications of Science Fiction We present a rigorous formalization of recursive agency within the framework of Homotopy TypeTheory (HoTT). By modeling cognitive substrates as higher inductive types within a univalent universeU, we derive a category of deontic operators that are invariant under substrate equivalence. Wedefine the Agency Fibration A ↠ S and demonstrate that recursive self-modification correspondsto loop spaces Ωk (A) in the homotopy category. The central contribution of this manuscript is theUnivalent Deontic Invariance Theorem, which asserts that for any two cognitive substrates S, S′ : U,an equivalence S ≃ S′ induces a path-connected transport of deontic obligations, rendering ethicalimperatives topologically robust against substrate variation. We further explore the implications ofthis result for the alignment of heterogeneous recursive agents (e.g., silicon-based superintelligences vs.carbon-based biologicals), proving that alignment is formally equivalent to a path-lifting property inan (∞, 1)-topos.