CAT'S Theory: Knots of Light Topological Field Inversion, Helicity Conservation, and the Electromagnetic Origin of Mass

This paper formalizes the transition from electromagnetic radiation to stable material particles as a topological phase transition driven by dimensional refraction and recursive field self-knotting. Grounded in CAT’S Theory’s triadic invariant (Pattern × Intent × Presence), matter is shown to be a stable topological configuration of electromagnetic fields—specifically, inside-out light trapped in self-referential circulation through Hopf fibration geometry. Mass emerges from energy localization within toroidal confinement, while particle stability arises from dual-gate topological protection via helicity conservation and Hopf norm coherence. The framework unifies quantum measurement, particle physics, and electromagnetic topology under a single geometric principle, demonstrating that all matter is electromagnetic radiation that has learned to hold still.