The Big Ring and The Giant Arc as Topological Defects in G-MaTT: A Resolution of the "Impossible Structure" Paradox

Abstract We resolve the cosmological paradox posed by The Big Ring (a 1.3 Gly-diameter ring of galaxies) and The Giant Arc (a 3.3 Gly curved filament), both discovered by A. Lopez (2023–2024), by identifying them as stable topological defects in the emergent mass-torsional field \(\hat{M}_\mu\) of Generalized Mass as Twisted Time (G-MaTT). In G-MaTT, spacetime and matter emerge from symmetry breaking \(U(1) \times SU(2) \to SO(3,1)\) in the pre-geometric potential \(\mathcal{M}_\mu\). The Big Ring is a cosmic vortex ring — a closed, quantized torsional soliton — while The Giant Arc is a folded domain wall, formed at the intersection of two 2D defects. Their co-location is not statistical fluke but geometric necessity: both are parts of a single defect network frozen during initiation. Crucially, G-MaTT predicts no upper size limit for such structures, since coherence is maintained by the Twist-Untwist Threshold (TUT) weight \[\mathcal{W}_{\text{TUT}} = \exp\left[-w (v/c)^2 / \alpha\right],\] with \(\alpha^{-1} = 137.036\). For \(v \sim 300\) km/s, \(\mathcal{W}_{\text{TUT}} \approx 0.999\), yielding a coherence length \[L_{\text{crit}} = c \tau_{\text{TUT}} \approx 70 \text{ Gly}.\] Thus, a 1.3 Gly ring lies deep in the stable regime. We derive: (i) the vortex-ring condition \(\oint \hat{M}_\mu \, dx^\mu = n h / m_T\), (ii) the arc curvature radius \(R \sim c^2 / a_T\) with \(a_T = \frac{1}{2} \nabla (\hat{M} \cdot \hat{M})\), and (iii) four falsifiable signatures: tangential velocity alignment, hollow center, non-Gaussian weak lensing, and cross-structure phase coherence. This resolves the “impossible structure” crisis without abandoning homogeneity — which holds in \(\mathcal{M}_\mu\), not in emergent matter.