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 crystalline solid governed by the H4 (600-cell) and D4 (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 t-¯t threshold energy E24/√2, where E24 = 24(mμ · α−1) is the 4D kissing shell energy. Utilizing these geometric constraints, 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 governed by 4D regular polychora, and the proton charge radius (Rc = 4λC = 0.8413 fm, 99.98% accuracy). 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 makes specific falsifiable predictions, notably a geometrically locked CKM unitarity triangle angle α = 90◦, a Vub mixing angle of 0.239◦ (above current experimental upper bounds), and a 3.55 keV dark matter decay signature corresponding to hidden H4 lattice nodes. Email: h4collaboration@protonmail.com