THEORY OF THE SUSPENDED SOLUTION OPERATOR (Ψˢ)

THE SUSPENDED SOLUTION OPERATOR (Ψˢ): A MATHEMATICAL FRAMEWORK FOR METASTABLE EQUILIBRIUM IN COMPLEX DYNAMICAL SYSTEMS AND ARTIFICIAL INTELLIGENCE ARCHITECTURES Author: Phan Thành Trung Discipline: Operatorology / Operator Intelligence Keywords: metastability, dynamical systems, fixed point generalization, operator intelligence, artificial intelligence stability, silicon cognitive architecture, attractor states. Abstract Classical dynamical systems theory defines stability through the existence of fixed points, that is, states x satisfying the condition T(x ) = x . However, in complex high-dimensional systems such as deep neural networks, biological cognitive systems, and artificial intelligence architectures, exact fixed points often do not exist, cannot be reached, or require infinite computational resources to attain. This paper introduces the Suspended Solution Operator, denoted Ψˢ,