Quantifying Galaxy–Defect Correspondence via Mirror Symmetry in G-MaTT

Abstract We derive the quantitative relation between the topological defect network emerging from pre-geometric symmetry breaking U(1) \times SU(2) \to SO(3,1) in Generalized Mass as Twisted Time (G-MaTT) and the observed galaxy distribution using mirror symmetry as a phase–torsion duality. The duality exchanges the complex structure (phase branching) and Kähler structure (torsional volume) sectors of the compactified primordial potential \mathcal{M}_\mu, mapping defect densities to galaxy number densities. We predict the two-point correlation function \xi(r) = \xi_0 \frac{\sin(r/\lambda_\alpha)}{r/\lambda_\alpha} e^{-r/\Lambda_{\text{TUT}}}, where \lambda_\alpha = \alpha^{-1/2} c/H_0 \approx 110\ \text{Mpc} (fixing the BAO scale) and \Lambda_{\text{TUT}} = c \tau_{\text{TUT}} \approx 10\ \text{Gly} (the coherence horizon). The fine-structure constant \alpha^{-1}=137.035999206 enters as the duality-preserving fixed point. The model reproduces filamentarity, cosmic voids as torsion-minima, and predicts oscillatory features in the three-point function testable with DESI/Euclid. Mirror symmetry thus elevates G-MaTT from a qualitative geometric picture to a quantitative, falsifiable structure-formation framework.