What question did this study set out to answer?

The research aims to derive fundamental particle masses and cosmological parameters using the geometry of Platonic solids without any free parameters.

March 5, 2026Open Access

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

Key Points

The research aims to derive fundamental particle masses and cosmological parameters using the geometry of Platonic solids without any free parameters.
Developed a master formula linking masses to the properties of five Platonic solids.
Utilized Loeschian numbers on the Merkaba lattice to determine key variables.
Conducted Monte Carlo validation for statistical accuracy.
Achieved agreement with 11 measured particle masses within 1σ.
Derived the fine structure constant with high precision (0.04 ppm).
Generated 50 algebraic identities from the G-factors of Platonic solids.
Produced multiple testable predictions for particle and cosmological parameters.

Abstract

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

اسأل الذكاء الاصطناعي

Bookmark

View Full Paper