Geometry of Sound v4.0: Zero-Parameter Derivation of All Particle Masses from Platonic Solid Geometry

Geometry of Sound v4. 0: A zero-parameter model deriving all fundamental particle masses from the geometry of five Platonic solids. MASTER FORMULA: m = mP × αN × Gₜree × (1 + cᵣad × α/π) × (1 + cdual × α/π × cos δdual) × (1 − cos²δ × αₑff/π) KEY RESULTS: • 11/11 measured masses within 1σ (χ²/ndf = 0. 075) • α⁻¹ = 137. 03600394 from Platonic sums (0. 04 ppm from PDG) • 47/47 exact algebraic identities (machine precision) • 6 sphere-ratio identities: G-factors = ratios of Platonic spheres• 5 mixing angles (all 20 PREDICTIONS: • Dark Matter mass: 123 GeV• Neutrino mass sum: 61 meV • Individual: m_ν₃=51. 35, m_ν₂=8. 56, m_ν₁=1. 03 meV• Proton decay: ~10³⁷ years Free parameters: 0. Total predictions: 60+. Updates from v2. 0: • Four-level formula (added dual + environmental corrections) • Top quark resolved: σ = 2. 5 → 0. 006• Muon resolved: σ = 27 → 0. 011 • All 11 masses now within 1σ• Environmental correction: δ = −cos²δ × αₑff/π• Dark matter invisibility explained geometrically (cos²δCub = 0) • Σcos²δ = 44/45 = 1 − αGUT