In this paper, I derive the fine-structure constant $\alpha$ as an emergent and parameter-free invariant of Relator theory. The construction uses the Schrödinger equation, classical electrodynamics and mechanics, and Relator geometry with luminal evolution on the $\mathbb{C}$-space and the orthogonal spatial sector $\mathbb{R}^3$, which fixes a minimal phase cavity and the Coulombic baseline. A transverse traceless inductive channel is incorporated through a UV, IR, and OUT decomposition, and a logarithmic closure uniquely determines $\alpha$ with no fitted numbers and with no use of measured constants $e$, $c$, and $\hbar$. No quantum electrodynamics is invoked at any stage. The prediction matches the most precise independent measurements at sub-ppt accuracy and remains stable under regulator choices and multipole cutoffs.Update: Complete Physical Derivation and Mathematically Rigorous Proof (Full Version) Direct published outcome: g-factor (electron, muon, tau )+ running (without QED): https://doi.org/10.5281/zenodo.17021364 Charged–Lepton Mass Hierarchy: https://doi.org/10.5281/zenodo.17108965