Geometry of Sound: Zero-Parameter Derivation of Fundamental Particle Masses from Platonic Solid Geometry

Geometry of Sound: Zero-Parameter Derivation of Fundamental Particle Masses, Mixing Matrices, and Cosmological Parameters from Platonic Solid Geometry A unified framework deriving all known fundamental particle masses, mixing angles, and cosmological parameters from the geometry of five Platonic solids with zero free parameters. Master formula: m = mPlanck × αN × G × (radiative) × (dual) × (environmental) where G-factors are algebraic expressions of Platonic solid properties (vertices, edges, faces, dihedral angles, inscribed sphere ratios), N is determined by Loeschian numbers on the Merkaba lattice, and α⁻¹ = 137. 036004 is derived from Platonic sums. Key results: • 11/11 measured particle masses within 1σ (χ²/ndf = 0. 105) • Fine structure constant α⁻¹ = 137. 036004 from geometry (0. 04 ppm) • 50 exact algebraic identities between G-factors• PMNS mixing angles: sin²θ₁₂ = 4/13, sin²θ₂₃ = 6/11, sin²θ₁₃ = 1/45• CKM parameters: λ = 5/ (9√6), A = 30/38, δ = φ/√2• CP violation: δPMNS/δCKM = 3 (number of colors) • Cosmology: Ωb = 11/225, ΩDM from Platonic ratios, Ωₜotal = 1. 000000• Gauge structure: SU (3) ×SU (2) ×U (1) from ECub = 12 generators• Hypercharge Y = n/3 from dihedral cosine quantization• Monte Carlo validation: P 7. 1) Testable predictions: • Dark matter mass: 123 GeV• Neutrino mass sum: Σm_ν = 60. 9 meV• PMNS CP phase: δ = 3φ/√2 = 196. 7° (DUNE/Hyper-K) Zero adjustable parameters. 80+ predictions from pure geometry. Files: • GeometryₒfSoundᵥ5. md — main paper (24 sections, 3 appendices) • MCᵥalidationGoSᵥ5. md — Monte Carlo statistical validation Author: Yuriy S. VinogradovVersion: 5. 0