SHUM V3.2: A Discrete FCC Lattice Framework for Cosmological Bounce and Quantum Geometric Mass

This preprint proposes the SHUM V3. 2 model, a theoretical framework that unifies macroscopic cosmological bounce and microscopic particle mass generation through a discrete Face-Centered Cubic (FCC) lattice spacetime. By introducing a "core-shell dual field" and a geometric repulsion reversal (G = -1. 71), the model resolves the singularity problem in general relativity, reinterpreting the Big Bang as a bounce from a previous collapsing phase. Microscopically, particles are modeled as topological standing waves on the FCC lattice with a spatial leakage rate of 12/19. Using the double group representations of Oₕ, we derive the geometric origin of spin-1/2 and spin-1 states, yielding a fundamental dimensionless mass baseline of 12/19 0. 7947. The paper also explicitly outlines four theoretical limitations (spin-orbit coupling, discrete gauge symmetry, fermion doubling, and generation structure) to guide future research in discrete quantum gravity.