Topological Phase Transitions between Sphere and Torus: A Unified Model for Bosons, Fermions and Quantum Gravity

We propose a geometric model where bosons and fermions emerge as distinct topological phasesof a unified manifold. Through controlled singular transitions, a sphere (S2, genus 0) transformsinto a torus (T2, genus 1) and vice versa. Key innovation: anisotropic curvature singularities duringtransitions preserve Gaussian curvature integrals. Fermions reside on toroidal manifolds, bosons onspherical, with quantum numbers arising from twist operations. The model predicts oscillation-drivenparticle creation and offers geometric interpretation for spin, charge, and confinement.