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.