Non-linear Acoustic Feedback and the 12th Decimal: A High-Precision Hydrodynamic Derivation of the Electron g-factor

This paper presents a high-precision deterministic derivation of the electron g-factor within the Substratum Hydrodynamics (SH) framework. Challenging the probabilistic heuristics of QED, the study demonstrates that the fine-structure constant (α) emerges as the mechanical stability index (Mach number) of a compressible superfluid vacuum. By resolving the recursive acoustic feedback of a vortex filament, the author analytically recovers the g-factor power series, providing a mechanistic basis for its 12-decimal precision. The emergence of mathematical constants such as ζ(3) and ln(2) is explained as a result of multi-point acoustic correlations in toroidal geometry. This work concludes the "Substratum Hydrodynamics" trilogy, offering a unified mechanical foundation for quantum phenomena.