Derivation of the Electron Mass from a 6-Dimensional Geometric Equilibrium: A parameter-free prediction from the Hubble constant, the fine-structure constant, and Newton's constant

A newer version is available. Please see https://doi.org/10.5281/zenodo.18917994. Some confusing language was removed and the work was simplified. In this work, we derive a parameter-free prediction for the electron mass using our geometric model, the Hubble constant H0, the fine structure constant α, and Newton's gravitational constant, G. Our hypothesis is that stable baryonic particles are formed by photon packets that have the exact length to form a closed loop in equilibrium with the vacuum energy density; the dark energy associated with the cosmological acceleration. We use the equilibrium condition between the particle's electromagnetic confinement radius and its gravitational (MOND) radius, and derive a cubic equation that predicts me = 9.18171764× 10-31 kg, agreeing with the CODATA value 9.1093837139 × 10-31 kg to +0.79% using the SH0ES measurement. Using the Planck measurement, we get an error of -1.87% and using DESI BAO+CMB [Plik] we get an error of -1.31%. Using this equilibrium condition we predict the current, local Hubble constant to be 71.3273 km s-1 Mpc-1. We also present a topological explanation for the proton-electron mass ratio of 6π5 agreeing with CODATA to 0.0019%.