Non-Commutative Rough Photonic Interconnect Dynamics (NC-RPID) Subsuming Optical Interconnects and Silicon Photonics Limits via UROA, STCT, and RQIG

Optical interconnects and silicon photonics are conventionally bounded by raw band width scaling and strict power envelops. This paper supersedes these independent subsystem views by establishing Non-Commutative Rough Photonic Interconnect Dynamics (NC-RPID) within the SMA-∞ Topos. By rigorously integrating Universal Rough Operator Algebra (UROA), the Seonggil Theory of Composite Torsion (STCT), and Rough Quantum Information Geometry (RQIG), we prove that electrical skin effects and E-O/O-E conversion losses are macroscopic topological manifestations of non-commutative boundary scattering and opto-thermal manifold torsion. Furthermore, Co-Packaged Optics (CPO) and DWDM multiplexing are formally derived as geodesic optimization sub-loops protecting the ultra-scale data manifold.