Quantum Superposition of Topological Phases: A Unified Framework for Particle Geometry

This paper establishes a rigorous framework for quantum superpositions of topological phases within the geometric model of elementary particles. We define Hilbert spaces for spherical (S2), toroidal (T 2), and gravitonic (half-torus) configurations, with transition operators governed by Hodge theory. The model predicts measurable Berry phase accumulation during topological transitions and anomalous scattering cross-sections. Experimental verification protocols for quantum processorsand colliders are proposed, unifying particle physics with quantum gravity through topological superposition.