Electron Mass from 6D Geometric Equilibrium: A Parameter-Free Prediction via $H_0$, $\alpha$, and $G$

The electron mass is a free parameter in the Standard Model with no known theoretical origin. We present a derivation of me from a 6-dimensional geometric model in which massive particles are photons confined to closed helical loops spanning two orthogonal planes. The equilibrium condition between the particle’s electromagnetic confinement radius and its gravitational (MOND) radius yields a cubic equation whose unique real solution predicts me = 8.93902826 × 10-31 kg, agreeing with the CODATA value 9.10938 × 10-31 kg to 1.87% using the Planck measurement and 0.79% using the SH0ES measurement, without any fitted parameters. The derivation links the electron mass to the Hubble constant H0, the dark-energy fraction ΩΛ, the fine-structure constant α, and Newton’s constant G through a single formula. The presented geometric framework also gives us the proton-electron mass ratio as ≈ 1836.118108712, agreeing with the CODATA value to 0.00188%.