Non-Commutative Rough Resource Dynamics (NC-RRD) Subsuming Direct Lithium Extraction (DLE) and Critical Mineral Supply Chain Limits via UROA, STCT, and RQIG

Critical mineral supply chains and Direct Lithium Extraction (DLE) are conventionally bounded by linear resource depletion and static geopolitical risk models. This paper supersedes these views by establishing Non-Commutative Rough Resource Dynamics (NC-RRD) within the SMA-∞ Topos. By integrating Universal Rough Operator Algebra (UROA), the Seonggil Theory of Composite Torsion (STCT), and Rough Quantum Information Geometry (RQIG), we prove that lead-time delays and geographic processing concentration are macroscopic topological manifestations of non-commutative temporal-spatial shear stress.Furthermore, DLE processing and closed-loop recycling are formally derived as geodesic optimization sub-loops that stabilize the global resource manifold.