Emergence Mechanism of Topological Defects from G₂ Symmetry Breaking in Generalized Mass as Twisted Time Theory

Abstract Within the framework of Generalized Mass as Twisted Time (G-MaTT) theory, this paper systematically investigates the mechanism by which topological defects arise from G₂ symmetry breaking. We propose a specific symmetry-breaking chain: [ G_2 \times U(1) \rightarrow SU(3) \times U(1) \rightarrow SU(2)L \times U(1)Y \rightarrow U(1){\text{EM}}, ] and demonstrate via homotopy group calculations that this chain naturally produces domain walls (two-dimensional defects) and cosmic strings (one-dimensional defects). These defects were frozen in during the early universe and served as seeds for large-scale structures such as the Hercules–Corona Borealis Great Wall, the Big Ring, and the Giant Arc. We further show that the characteristic scale of these defects is determined by the Twist-Untwist Threshold (TUT) mechanism, yielding a coherence length [ \Lambda{\text{TUT}} = c\tau_{\text{TUT}} \approx 10~\text{Gly}, ] which aligns with the observed scale of the largest cosmic structures. This work provides a rigorous mathematical foundation for G-MaTT and presents testable predictions for future observations.