Electric Charge as a Topological Quantum Number from Z3 Symmetry Breaking on Fermionic Tori

We derive the quantization of electric charge from topological constraints on Z3 symmetry breaking of toroidal fermion geometry. Fermions are modeled astori T2 = C/(Z + τZ), with three generations corresponding to three fundamental cycles. The modular parameter τ distinguishes neutral (τ = ω = e2πi/3) and charged (τ = iτ2) states. Electric charge q is identified with the winding number measuringdeviation from the symmetric point ω. Spontaneous symmetry breaking leads to q = ±1 for leptons. Further factorization via T2/Z3 orbifolding yields fractionalcharges q = ±1/3, ±2/3 for quarks, with confinement arising from monodromy conditions. Koide ratios R = 1/3 for neutral triplets (neutrinos) and confinedsystems (baryons), and R = 2/3 for charged lepton triplets emerge as geometric invariants of the mass triangle. The model provides a unified topological origin for charge quantization, fermion generations, and mass hierarchies.