Case 01 — Derivation of the Muon-to-Electron Mass Ratio from Phase Resonance by Torsion in the Vibrational Field Sh

Case 01 Abstract The muon-to-electron mass ratio ($m_\mu/m_e \approx 206.768$) is derived from the master equation of the Unified Vibrational Force Theory (UVFT). Unlike the Standard Model, where lepton masses are treated as free parameters adjusted via Yukawa couplings, UVFT derives this hierarchy as a pure geometric resonance of the non-linear scalar field $S_h(x,t)$. By analyzing the phase torsion and topological stability nodes of the field, the mass ratio emerges with Class-A precision, aligning with experimental values from CODATA 2022. This document provides: The mathematical derivation of the ratio through the anchoring of the $S_h$ field's second-generation harmonics. The Python numerical validation that demonstrates the stability of the result without manual adjustments. A fundamental resolution to the lepton mass hierarchy problem, showing that particles are emergent nodes of a single vibrational vacuum.Files included: This record contains the theoretical derivation (PDF) and the source code (Python) for independent numerical validation of the $206.768$ ratio.