Elementary Particle Interpolation and Three Generations Profile: A Purely Geometric Formulation of Matter, Rest Masses, and Fractional Charges Without the Higgs Field

The Standard Model of particle physics relies on the Higgs mechanism and arbitrary Yukawa coupling constants to generate the masses of elementary fermions, introducing over twenty free parameters without a definitive geometric foundation. This paper presents an alternative, strictly non-perturbative framework within Space Field Theory that explains the origin of rest masses, fractional electric charges, and the three-generation particle spectrum through pure continuum geometry. Synthesizing the concepts of directional vector energy and localized field motion, we resolve the internal topology of a fermion into a dual core-shell architecture. The invariant central core comprises a stable, spin-1/2 pendulum vortex composed of pure polar energy, while the outer shell consists of nested, multi-layered spin-1 bosonic rings whose energy density increments define the particle generations. Under this framework, particle decay is modeled as the mechanical stripping of these discrete bosonic layers ($W^\pm, Z^0, \gamma$). Furthermore, we demonstrate that the fractional quantum electric charges ($\frac{2}{3}e$ and $-\frac{1}{3}e$) of quarks are mathematical consequences of non-orthogonal spatial projections under a fixed $60^\circ$ angular inclination separating the internal color-charge planes and the electromagnetic electric plane. Finally, we establish that the near-degeneracy of the three neutrino masses is governed by the structural configuration of low-energy photon shells, rendering flavor oscillations highly sensitive to localized gravitational torsion. This geometric interpolation eliminates the need for fundamental scalar fields, preserving strict physical continuity across subatomic boundaries.