Non-Commutative Rough Network Economics and Computational Dynamics (NC-RNET): Superseding Finite Graphs via Graphon Operator Theory, Variational Inequalities, and Neural Operator Approximations

Traditional network economics relying on finite graphs and spectral linearizations fails to scale in large-scale heterogeneous limits, while computational economics faces severe curses of dimensionality and approximation disconnects. This paper establishes Non-Commutative Rough Network Economics and Computational Dynamics (NC-RNET) within the SMA-∞-Topos. By integrating Universal Rough Operator Algebra (UROA), Seonggil Theory of Complex Torsion (STCT), and Rough Quantum Information Geometry (RQIG), we prove that graphon operator theory, infinite-dimensional variational inequalities, and abstract neural operator approximations systematically supersede classical network and numerical limits.