Emergent Electron Mass from Two-Space Boundary Finally

Description

We derive the electron mass as an emergent equilibrium of a locked ring obeying $R\omega=c$ in a two–space kinematics that separates a generator space $\mathbb{C}$ from the propagation space $\mathbb{R}^{3}$. Two independent closed paths enforce the same geometry; a scalar vacuum–in–volume closure in $\mathbb{R}^{3}$ (RLVM) and a vector string–tension closure in $\mathbb{C}$ (RLTM). All factors are dimensionless and explicit; the only dimensionful input is $\ell_{P}=\sqrt{\hbar G/c^{3}}$, while $\alpha$ and $G$ are taken as known constants. Stationary radii follow in closed form and $m=D\,\hbar/(c\,R_{\star})$ is obtained with no tunable parameters. Numerically, both paths reproduce the measured electron mass at the few-ppm level (each $\approx -2.45\ \mathrm{ppm}$), comfortably within the $\sim 11\ \mathrm{ppm}$ uncertainty propagated from the Newtonian gravitational constant $G$. Equating the two closed masses delivers a scale-free diagnostic $\alpha_{\wedge}$ that matches the input $\alpha$ at $\sim 1.2\ \mathrm{ppb}$. Because $m \propto (\hbar c/G)^{1/2}\times\text{(dimensionless bracket fixed by the locked geometry)}$, the formulas can be inverted to estimate $G$ directly from $(m_{e},\alpha)$ without fitting, suggesting ppm-level consistency tests $\bigl(6.674\,267\,28\times10^{-11}\ \mathrm{m^{3}\,kg^{-1}\,s^{-2}}\bigr)$. The framework is compact and reproducible, providing a concrete bridge from Relator kinematics to electron inertia.

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