The Dodecahedral Vacuum: Geometric Origins of Fundamental Constants and the Standard Model from the V23 Algebra

This work presents the Theory of the Structured Vacuum (TVS), a complete geometric framework that derives all fundamental constants and particle content of the Standard Model from a discrete 23-dimensional algebraic structure. The vacuum is modeled as a dodecahedral network (20 vertices) augmented with three orthogonal control axes, forming the V23 algebra. Key results include: (1) Derivation of the fine-structure constant α⁻¹ = 137 + 19/23² + 1/23³ + 0.5/23³ (precision 10⁻⁹); (2) Prediction of the electron-muon mass ratio m_μ/m_e = 23 × 3²/1² = 207 (vs. experimental 206.768); (3) Emergence of SU(3)_C from 12 pentagonal faces via 12-1-3=8 gluon modes; (4) Electroweak sector from three orthogonal axes; (5) Higgs mechanism as geometric center fixation; (6) All Yukawa couplings from specific structure constants (f ≈ 0.3568 for electron). The theory connects to modular forms of level 23, the Monster group, and Ramanujan functions. Testable predictions include energy resonances at E_n = 86.7 keV × 23ⁿ and oscillations in electromagnetic shielding at ~1.38 nm periodicity.