Non-Commutative Rough Semiconductor Dynamics (NC-RSD) Subsuming Sub-2nm Microfabrication Limits and AI Accelerator Efficiency via UROA, STCT, and RQIG

Sub-2nm semiconductor scaling is conventionally bounded by Dennard scaling breakdown, dark silicon expansion, and severe Gate-All-Around (GAA) self-heating. This paper supersedes these views by establishing Non-Commutative Rough Semiconductor Dynamics (NC-RSD) 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 rigorously prove that dark silicon and thermal walls are macroscopic manifestations of topological buffers and geometric decoherence. Furthermore,3D packaging, chiplets, and Processing-in-Memory (PIM) are formally derived as geodesic entropy minimization sub-loops that circumvent classical power walls.