Vol. 7, Issue 2, Part E (2025)

The mass hierarchy of the stable leptons (electron, muon, tau) remains a foundational problem in particle physics because the Standard Model (SM) cannot predict their specific values. This work introduces a novel, deterministic theoretical framework that posits particle mass as an emergent property of a particle's structural state within a universal medium. We established an axiomatic structural model constrained by factors including the Dimensionality Factor and the Golden Ratio to define the precise relationship between lepton generations. By calibrating this model against the measured masses of the electron and muon, we derived a Law of Hyper-Acceleration governing generational growth. This structural law was then used to successfully predict the mass of the third lepton, the Tau. The calculated prediction (mτ​≈1776.91 MeV/c2) aligns precisely with current experimentally determined data (1776.86±0.12 MeV/c2), thereby achieving definitive predictive superiority over the probabilistic Standard Model. This study concludes that the fundamental structure of the universe is governed by deterministic, predictable algorithms.