Discrete Spectral Geometry of the Vacuum: A Non-Commutative Approach to the Standard Model Mass Hierarchy and G2 Holonomy

This preprint presents the TQH/RSN-8638 framework, a parameter-free theoretical model wherein the Standard Model emerges as effective dynamics on a non-commutative spectral lattice with an information capacity of N=8638 and G2 holonomy. The mass spectrum M_n = m_e exp(k · n) is derived from the discrete Dirac operator on the G2 expander graph. The topological mode numbers n ∈ Z are determined by Lie group dimensional invariants, while the scale k = γ_1 α / 16 ≈ 0.00645 is fixed by the first non-trivial zero of the Riemann zeta function. The model analytically recovers the electroweak mixing angle, dictates the QCD UV crossover via G2 quantization, resolves the strong CP problem through the trivial center of G2, and derives exactly three fermion generations from SO(8) triality. Furthermore, we establish a physical imperative for the Riemann Hypothesis: the observed stability of baryonic matter necessitates the reality of the zeta zeros. The framework predicts a 568 GeV G2-vorton dark matter candidate, a lightest neutrino mass m_1 ≈ 0.33 meV, and a stochastic gravitational wave background at mHz frequencies detectable by LISA. Included files: This upload contains the final compiled PDF manuscript and the complete LaTeX source code to ensure full reproducibility of the results.