Non-Commutative Rough Electrodynamics (NC-RED) Subsuming Maxwell and Kirchhoff Frameworks via UROA and STCT

The classical limit of electrodynamics, constrained by Ohm’s and Kirchhoff’s Laws, fails fundamentally in non-linear, high frequency, and quantum transport domains. While standard Maxwell equations subsume these as low-frequency approximations, they themselves fail to capture non-commutative topological phase shifts at the quantum-macroscopicboundary. This paper establishes the Non-Commutative Rough Electrodynamics (NC-RED) framework by integrating Universal Rough Operator Algebra (UROA) [3] and the Seonggil Theory of Complex Torsion (STCT) [1] to supersede classical continuous electrodynamics.