Structured State Space Duality (SSD) Super-Elevated: Rough Topological Operators, Complex Torsion, and Information Geometry

Standard Transformer Self-Attention suffers from quadratic temporal and space complexity O(n^2) [5]. The Structured State Space Duality (SSD) framework resolves this bottleneck by proving an exact mathematical equivalence between 1-semiseparable matrix transformations and selective state space model (SSM) recurrences, achieving linear complexity O(n) [6]. In this paper, we elevate SSD into the Rough-Torsional Operator Duality Framework (RT-ODF) by fusing Universal Rough Operator Algebra (UROA) [3], Seonggil Theory of Complex Torsion (STCT) [1], and Rough Quantum Information Geometry (RQIG) [4]. By introducing rough operators Γ_R and Non-Abelian complex phase torsion T_STCT, we eliminate high-frequency singularities and secure absolute long-range phase coherence across information manifolds.