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 = m_Planck × α^N × 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: δ_PMNS/δ_CKM = 3 (number of colors)• Cosmology: Ω_b = 11/225, Ω_DM from Platonic ratios, Ω_total = 1.000000• Gauge structure: SU(3)×SU(2)×U(1) from E_Cub = 12 generators• Hypercharge Y = n/3 from dihedral cosine quantization• Monte Carlo validation: P < 5×10⁻¹³ (σ > 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:• Geometry_of_Sound_v5.md — main paper (24 sections, 3 appendices)• MC_validation_GoS_v5.md — Monte Carlo statistical validation Author: Yuriy S. VinogradovVersion: 5.0