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 micropolar kinematics, the model derives over 30 Standard Model and cosmological parameters. Exact topological derivations include the 8 gluons of SU(3) via D4 hyperplane restriction, the strictly three-generation termination limit, and the proton charge radius (Rc = 4λC = 0.8413 fm). High-precision quantitative results include the W boson mass (99.997% accuracy), the muon mass (99.98%), and the Planck mass (99.9%). Finally, the model proves the visible universe is a topologically protected surface state (v=1) and makes specific falsifiable predictions, notably a geometrically locked CKM unitarity triangle angle α = 90◦, a Vub mixing angle of 0.239◦, and a 3.55 keV dark matter decay signature corresponding to sterile acoustic phonons in the hidden H4 bulk. Email: h4collaboration@protonmail.com