Topological Classification of Standard Model Particles: Geometric Unification through Sphere-Torus Phase Transitions

We present a complete topological classification of Standard Model particles based on geometric phasetransitions between spherical (S2) and toroidal (T 2) manifolds. The theory demonstrates that all knownelementary particles - six quarks, six leptons, four vector bosons, and the Higgs scalar - emerge as distinct topological excitations governed by the unified dynamics S2 ⇌ T 2. Key results: (1) Quarks as triple-point singularities in intermediate ”sperturcation” phase, (2) Leptons as twisted toroidal configurations, (3) Gauge bosons as curvature defects, (4) Higgs as oscillation amplitude. Experimental verification through quantumsimulation shows 92-96% classification fidelity.