Analytic Emergence of the Electron g–Factor in the Relator Theory

We derive closed, gauge-invariant, divergence-free formulas for the lepton magnetic moment from the Relator postulate \(R\omega=c\). The mechanism is geometric; a slowdown of the gauge-invariant phase evolution in $\mathbb{R}^3$-space by the particle's own Coulomb field on logarithmic shells--- $\mathbb{C}$-space --- combined with the vector self-magnetic backreaction (S1–S4) and a scalar, mass-dependent channel \(\chi\). The final map is \(g=2/\sqrt{1-\delta_{\rm tot}}\) with \(\delta_{\rm tot}=\delta_{S4}+\Delta\delta_{\chi}\) and \(\Delta\delta_{\chi}=\delta_{S3}^{2}\,c_{\rm eff}(n)\,\ln(m_n/m_e)\); all kernels and the outer subtraction are analytic (no renormalization, no QED loops, no fit parameters). Numerically we obtain \(g_e^{\rm pred}=2.002\,319\,304\,392\,795\) (deviation \(+3.28\times10^{-11}\), \(+16.38\) ppt). The same construction yields a simple, closed-form mass dependence (running of \(\alpha\)) consistent with leptonic vacuum polarization. These results—achieved without QED and without UV divergences—show that high-precision lepton \(g\) emerges directly from Relator geometry and Coulombic self-interaction, challenging the conventional necessity of perturbative QED for explaining \(g\).