Global Complexity Stability Theory (GCST) A Field-Theoretic Framework for the Dynamics of Accelerating Complex Systems

Abstract Complex systems exhibit critical transitions, self-organization and rate-induced instabilities under accelerating external parameters. Existing frameworks often describe these phenomena in isolation. This preprint introduces Global Complexity Stability Theory (GCST) — a unified field-theoretic approach that describes system dynamics through the interaction of stability, structural complexity and evolution rate. The central object is the scalar critical sensitivity field Ψ(x,t). Its evolution is governed by a reaction-diffusion equation with a rate-induced source term. The theory defines stability energy functional, complexity entropy, a variational principle, geometric interpretation of state space and a universal scaling law near critical points. The resulting GCST equation links stability, complexity growth and rate of change in a single dynamical law. The framework is purely theoretical and does not claim immediate predictive power or superiority over existing methods.