Non-Commutative Complex Adaptive Disequilibrium Framework (NC-CADF) Elevating Heterogeneous Agent Economics via Rough Operator Algebra and STCT

The Rational Expectations Hypothesis (REH) and Efficient Market Hypothesis (EMH) fundamentally rely on the commutative statistical mechanics of representative agents. While the Complex Adaptive Disequilibrium Framework (CADF) addresses these flaws phenomenologically, it lacks a foundational mathematical topology. This paper elevates CADF into the Non-Commutative Complex Adaptive Disequilibrium Framework (NC-CADF) by integrating Universal Rough Operator Algebra (UROA) [3] and the Seonggil Theory of Complex Torsion (STCT) [1]. We prove that economic agents operate as non-commutative microscopicperturbation matrices, and endogenous financial crises are the macroscopic manifestation of topological decoherence induced by excessive torsional leverage.