Topological Origin of the Proton-to-Electron Mass Ratio and the $g-2$ Muon Tension

This work supersedes and extends the geometric foundations laid in Geometric Theory of Physics: The Model [6]π4 (Zenodo DOI: 10.5281/zenodo.18919147). While previous deposits established the static lattice framework, this version provides the topological resolution for dynamical anomalies, specifically the g−2 muon tension and the mp/me = 6π⁵ ratio.

Abstract

We present a model where mass hierarchy and fundamental constants emerge from a permanent geometric lattice. Through the metric confinement limit defined by π, we derive the exact relationship for the proton-to-electron mass ratio, yielding:

mp/me = 6π⁵ ≈ 1836.12

This result is in strict agreement with experimental values. This framework reinterprets the fine-structure constant as a measure of vacuum membrane reactivity and provides a geometric solution to the current muon g−2 tension by accounting for the non-linear elastic response of the lattice at higher mass scales.

The complete mathematical development of this theory, including the derivations for the electroweak and fine-structure constants, is permanently recorded and available at Zenodo (DOI: 10.5281/zenodo.18919147).

Version 2 Notes (March 17, 2026):

• Refinement of Lattice Boundary Conditions: Updated the effective lattice field definition to πeff=π (previously πeff≥π). This correction ensures the model accounts for multi-directional metric distortions (both tension and compression) in experimental environments, providing a more robust topological foundation for the g−2 anomaly resolution.

• Full mathematical consistency with the manuscript currently under review at Physical Review Letters.

Note on Author Identity: This version updates the author's name to the full academic signature (Alvaro Guillermo Perea Covarrubias) to ensure consistency with institutional records at UNED and international researcher databases. This record supersedes previous versions authored under the shortened name.