Harmonic Genesis of Lepton Masses - A Spectral Derivation of the Lepton Hierarchy from Riemann Zeta Zeros

This paper introduces a deterministic derivation of the lepton mass hierarchy within the framework of the Arithmetic Theory of Everything (AToE). While the Standard Model of particle physics relies on empirical Yukawa couplings to explain particle masses, this study postulates that mass is an emergent property of the vacuum's arithmetic substrate. We demonstrate that the mass ratio between the muon and the electron can be expressed as a function of the first two non-trivial zeros of the Riemann zeta function (𝛾1,𝛾2). By applying a 12-dimensional geometric regularization factor we derive a theoretical ratio of 206.7682, which aligns with the current CODATA experimental value to the sixth decimal place. Key Highlights: Deterministic Mass Derivation: Replaces free parameters with fundamental arithmetic constants. Spectral Resonance Model: Particles are modeled as standing waves (harmonics) on the critical line of the Riemann zeta function. High Statistical Significance: The numerical convergence exceeds a 8-sigma threshold, suggesting a non-accidental correlation between number theory and particle physics Mathematical Appendix: Includes a step-by-step verification of the Hubble constant and the Cosmic Microwave Background (CMB) temperature as products of arithmetic coherence. This work suggests that the physical vacuum acts as a computational processor, where the laws of physics are necessitated by the distribution of prime numbers.