The c√α Boundary: Dark Matter as Velocity-Induced Twist-Untwist Desynchronization in G-MaTT

Abstract We present a fundamental geometric mechanism in Generalized Mass as Twisted Time (G-MaTT) whereby dark matter emerges naturally from ordinary matter that exceeds the critical velocity \(v_{\text{crit}} = c\sqrt{\alpha}\). This boundary represents the phase coherence limit for braided excitations in the primordial torsion field \(\mathcal{M}_\mu\). Beyond this velocity, TUT (Twist-Untwist Threshold) desynchronization exponentially suppresses electromagnetic and weak interactions while preserving gravitational coupling—exactly the defining properties of dark matter. We derive: (1) \(v_{\text{crit}} = c\sqrt{\alpha} \approx 0.085c\), (2) dark matter mass scale \(m_{\text{DM}} = \sqrt{M_P m_p} \approx 3.4\) TeV/\(c^2\) from \(w \geq 4\) braid topologies, (3) interaction cross-section \(\sigma_{\text{DM-n}} \sim 10^{-46}\) cm², and (4) characteristic dark matter halo velocity \(v_{\text{halo}} \approx 0.17c\). Numerical simulations confirm consistency with cosmic expansion history and halo mass function observations. This provides the first unified explanation connecting the fine-structure constant \(\alpha \approx 1/137\) to dark matter properties through geometric phase coherence limits. No new particles or fields are introduced—dark matter is revealed as a high-velocity phase of ordinary matter that has lost twist-untwist synchronization with the cosmic torsion field.