Geometric Cybernetics & GCST A Five-Dimensional Framework for Stability, Information, and Cognitive Dynamics

Abstract This paper proposes a unified modeling framework that integrates Global Complexity–Stability Theory (GCST) with elements of geometric and cybernetic system analysis. The framework introduces an extended state space in which physical, informational, and cognitive variables are jointly represented. We define a five-dimensional manifold: 𝑀= (x, y, z, t, I) where ( I ) denotes an informational state variable. Unlike conventional treatments of information as a derived quantity, this work treats ( I ) as a primary modeling dimension that influences system structure and dynamics. Within this formulation: ● Physical observables are interpreted as projections of underlying informational states ● Cognitive processes are modeled as trajectories over structured informational configurations ● Belief is introduced as an operator that modifies informational stability under uncertainty A generalized stability functional is defined to capture system behavior across physical and cognitive domains. This enables a unified interpretation of: ● system evolution as gradient-driven optimization ● cognition as structured state transition ● decision-making under uncertainty as entropy reduction The framework also suggests an alternative interpretation of artificial general intelligence (AGI) as a system capable of stability-oriented adaptation within high-dimensional informational spaces. The goal of this work is not to replace existing domain-specific models, but to provide a common formal layer that allows interactions between physical, cognitive, and control processes to be analyzed within a single structure.