The Geometric Origin of the Fine-Structure Constant: α as the G₂ Phase-Coherence Margin in G-MaTT

Abstract We provide a parameter-free, first-principles derivation of the fine-structure constant \(\alpha^{-1} = 137.035999206\). Within the framework of Generalized Mass as Twisted Time (G-MaTT), \(\alpha\) is defined not as an empirical coupling constant, but as the Universal Phase-Coherence Margin — the maximal relative phase slip (\(\Delta\phi\)) allowable between braided excitations in the G₂ primordial potential \(\mathcal{M}_\mu\) before U(1) gauge symmetry collapses. We demonstrate that \(\alpha\) emerges as the unique fixed point of a dynamical equilibrium between spacetime synchronization (geometric pull) and entropic desynchronization (dark push). This derivation resolves the "circularity" problem by deriving the Twist-Untwist Threshold (TUT) weight from pre-geometric stability conditions and accounts for the "running" of \(\alpha\) as a scale-dependent braid-density effect.