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.本文提出一种几何模型，其中玻色子与费米子可作为统一流形的不同拓扑相而涌现。通过受控奇异转变，球面（S²，亏格0）可与环面（T²，亏格1）相互转换。核心创新在于：转变过程中的各向异性曲率奇点可保持高斯曲率积分守恒。费米子存在于环面流形上，玻色子则位于球面流形之上，其量子数由扭操作生成。该模型预言了振荡驱动的粒子产生现象，并为自旋、电荷与禁闭效应提供了几何诠释。