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.

Submission Status

• Journal: Submitted to Physical Review Letters (PRL).

• Internal Tracking ID: es2026mar12_699.

• Version Date: Matches the manuscript files processed on March 13, 2026.