What question did this study set out to answer?

To derive fundamental constants related to particle physics using Platonic solid geometry.

March 6, 2026Open Access

Geometry of Sound v6.0: Derivation of Fundamental Constants from Platonic Solid Geometry

Key Points

To derive fundamental constants related to particle physics using Platonic solid geometry.
Zero-parameter framework implemented
Derived 11 Standard Model particle masses and mixing matrices
Conducted Monte Carlo trials (35 million)
Extended Koide analysis and involved algebraic identities
Evaluated significance and exactness of predictions
All 11 particle masses derived within 1σ precision
Significant correlation identified with Monte Carlo significance σ > 10.9
Predictions include δ_PMNS/δ_CKM = 3 and improved CKM matrix with η̄ = 1/(2√2)
Derived constants include α⁻¹ = 137.036004 (within 0.04 ppm)
53 algebraic identities generated, of which 45 are exact

Abstract

A zero-parameter framework deriving 11/11 Standard Model particle masses, CKM and PMNS mixing matrices, coupling constants, and cosmological parameters from five Platonic solids. All 11 masses within 1σ (χ²/ndf = 0. 105). α⁻¹ = 137. 036004 (0. 04 ppm from PDG). Monte Carlo significance σ > 10. 9 (P < 4×10⁻²⁸). 53 algebraic identities (45 exact). Key prediction: δPMNS/δCKM = 3 = Ncolors. New in v6. 0: Extended Koide analysis (Q (H, b, τ) = 1/φ), anomalous magnetic moment identity ( (a_μ−aₑ) / (aₑα) = 20/27 = FIco/3³), Cabibbo identity sinθC = (ΣF/ΣE) ×Gᵤ, improved CKM with η̄ = 1/ (2√2), 35M Monte Carlo trials. All matter is frozen sound in Platonic geometry.

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