Multiverse Mathematics: A Categorical Framework for Resonance and Coexistence

This paper develops a formal mathematical architecture for modeling universes as modules within a resonance-based multiverse. The etherial substrate is defined as a category, with universes as objects and resonance morphisms as connective mappings. Resonance operators act on physical constants, producing predictive scaling laws across universes. A multiverse algebra encodes coexistence without contradiction, separating physical and etherial domains. This framework establishes axioms for resonance mathematics and demonstrates worked examples linking classical-like and quantum-heavy universes. It provides the formal skeleton for Resonance Cosmology and extends the taxonomy introduced in The Periodic Table of Universes.