Non-Commutative Rough Krein-Pseudo-Riemannian Dynamics (NC-RKPRF): Superseding Hilbert, Minkowski, and Lorentzian Geometries via Indefinite Krein Inner Products, Majorant Topologies, and Complex Torsion Field Equations

Classical Hilbert spaces lack indefinite causal signatures, Minkowski spaces are restricted to flat geometries, and smooth Lorentzian manifolds suffer from unmediated curvature singularities and quantum field unitarity conflicts. While the Krein-Pseudo-Riemannian Framework (KPRF) bridges functional analysis and differential geometry via non-degenerate indefinite inner products and majorant topologies, it remains vulnerable to projection operator unboundedness and Hawking-Penrose gravitational singularities. This paper establishes Non-Commutative Rough Krein-Pseudo-Riemannian Dynamics (NC-RKPRF) 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 rough Krein decompositions (K = K_{+}⊕_R K_{−}), torsion-bounded majorant norms, and regularized pseudo-Riemannian field equations systematically supersede classical geometric and quantum-gravitational limitations.