Geometric Unification of Fermion Masses: From Leptonic Triangles to Baryonic Holonomy

We present a comprehensive geometric framework unifying the mass spectra of all Standard Modelfermions. Charged leptons are shown to arise from three cycles on a torus T 2 forming a closed trianglewith Koide ratio RK = 2/3. Neutrinos correspond to tori with complex multiplication at τ = e2πi/3, yielding mass ratio m1 : m2 : m3 = 1 : √3 : 3 and Koide ratio Rν ≈ 1/3. Quarks and baryons are described by Z3-orbifold extensions where color confinement modifies the triangular closure to holonomy quantization Pβq = 2πn, leading to baryonic Koide ratio RB ≈ 1/3. All mass formulas derive from the exponential law m = m0e−κβ with geometrically determined parameters, providing a first-principles foundation for fermion mass hierarchies.我们提出了一套统一标准模型（Standard Model）所有费米子质量谱的完备几何框架。研究表明，带电轻子源自环面T²上的三条闭链，构成一个闭合三角形，其科伊德比率（Koide ratio）R_K=2/3。中微子对应于在τ=e^(2πi/3)处具备复乘法性质的环面，由此可得质量比m₁:m₂:m₃=1:√3:3，以及中微子科伊德比率R_ν≈1/3。夸克与重子可通过Z₃-轨形（Z₃-orbifold）拓展进行描述，其中色禁闭将三角形闭合条件修正为环绕量子化条件P_β q=2πn，进而得到重子科伊德比率R_B≈1/3。所有质量公式均源自形如m=m₀e^(-κβ)的指数律，其中参数均由几何方式确定，为费米子质量层级结构提供了第一性原理基础。