Non-Commutative Rough Energy-Grid Dynamics (NC-REGD) Subsuming AI Infrastructure Bottlenecks and Everything-to-Grid (E2G) via UROA, STCT, and RQIG

The energy bottleneck of AI data centers is conventionally treated as a linear resource mismatch between digital compute scaling and analog grid expansion. This paper supersedes this view by establishing Non-Commutative Rough Energy-Grid Dynamics (NC-REGD) within the SMA-∞ Topos. By integrating Universal Rough Operator Algebra (UROA), the Seonggil Theory of Composite Torsion (STCT), and Rough Quantum Information Geometry (RQIG), we prove that grid interconnect queues and transformer lead times are macroscopic manifestations of topological shear stress. Furthermore, Everything-to-Grid (E2G) is formally derived as a boundary stabilization mechanism operating via recursive homotopic feedback, preventing total manifold collapse under exponential cognitive loads.