Non-Commutative Rough Stochastic Social Welfare Dynamics (NC-RSSD): Superseding Arrow-Sen Impossibility and Invariant Measure Limits via Ordered Banach Lattices, Ergodic Decompositions, and Information Geodesics

Classical social choice theory anchored by Arrow’s impossibility theorem and topological social choice remains disconnected from stochastic growth and invariant measure economics. This paper establishes Non-Commutative Rough Stochastic Social Welfare Dynamics (NC-RSSD) 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 measure-valued probabilistic social welfare functionals, Markov ergodic invariant measures, and mirror-descent particle optimizationssystematically supersede classical deterministic and static welfare limits.