Three Generations from Twistor Quantization: Geometric-Algebraic Foundation for the Standard Model Particle Content

We demonstrate that the three generations of Standard Model fermions emerge naturally fromthe geometric quantization of twistor space endowed with three orthogonal complex structures I, J, Kand an additional operator L. The mathematical framework combines twistors, Clifford algebras,and symplectic geometry to explain the origin of precisely 48 fermionic degrees of freedom (threegenerations × 16) from first principles. Each generation corresponds to a distinct polarization of the twistor space, with quantum numbers arising as eigenvalues of the algebraic operators. The modelalso provides a geometric interpretation for gauge bosons as inter-generational mixing operators andpredicts testable modifications to gravitational wave propagation due to torsion-gauge coupling.