Geometric Origin of Fermion Generations: Topological Defects, Confinement, and Neutrino Mixing

We present a complete geometric theory of fermion generations based on spacetime torsion and twistorquantization. Fermions are identified as topological defects in multi-component torsion fields, characterized by operator vectors O = (𝑜𝐼 , 𝑜𝐽 , 𝑜𝐾 , 𝑜𝐿 ) corresponding to the algebraic structure A = Cl(1, 3) ⊗ (C(1) ⊕ C(2) ⊕ C(3) ⊕ C(4) ). The three generations emerge naturally from three orthogonal complex structures in twistor space, yielding exactly 48 fermionic degrees of freedom. We prove that defects with 𝑜𝐾 = 1 (quarks) cannot be isolated, explaining color confinement geometrically. The theory predicts specific patterns for neutrino mixing angles:𝜃12 ≈ arcsin (1/√3) ≈ 35.3◦, 𝜃23 ≈ 45◦, 𝜃13 ≈ 9◦, in qualitative agreement with experiment. All Standard Model quantum numbers arise as eigenvalues of the algebraic operators, providing a unified geometric foundation for particle physics.