Non-Commutative Rough General Equilibrium Dynamics (NC-RGET): Superseding Arrow-Debreu via Monotone Variational Inequalities, SMA-infty Topos, and Information Geodesic Optimization

Classical General Equilibrium Theory (GET) anchored by Arrow-Debreu relies heavily on non-constructive topological fixed-point theorems (Brouwer, Kakutani), restrictive convexity/continuity assumptions, and faces severe disconnects when extended to dynamic and stochastic regimes. This paper establishes Non-Commutative Rough General Equilibrium Dynamics (NC-RGET) 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 monotone operator theory, variational inequalities (VI), evolution VIs, and topos-theoretic fixed points systematically supersede classical GET limitations.