A Discrete H4 Crystalline Model of the Vacuum: Derivation of Standard Model Parameters from 4D Geometric Constraints

We present a geometric unification framework modeling the vacuum of spacetime as a discrete, four-dimensional hyper-elastic Cosserat solid governed by the H4 (600-cell) and $D_4$ (24-cell) root system symmetries. The framework's sole structural input is the geometry of the 600-cell, characterized by a discrete grain parameter δ = 1/120 derived from the discrete Gauss-Bonnet theorem. The vacuum expectation value v = 246.22 GeV emerges internally as the absolute macroscopic Frenkel yield stress of the lattice, corresponding to the t-¯t threshold energy E24/√2. By classifying particles via formal homotopy theory within the S3 boundary and mapping physical constants to the orthogonal tensor spaces of Cosserat…