New Framework Defines Stability for Feedback-Coupled Memory Systems

The Feedback-Coupled Memory Systems (FCMS) architecture provides a theoretical framework for understanding closed-loop coordination, but its original formulation left two key operators undefined: how agents update and how the environment responds. This new research addresses these gaps by providing concrete definitions for these abstract components within a continuous-time model. The agent update operator is defined using Mechanism-Based Intelligence (MBI), where agents adjust locally through decentralized price mechanisms, drawing on economic principles. The environmental update operator is defined by the Coupled Memory Graph Process (CMGP), which treats the environment as a physical substrate that records and responds to historical trajectories in a coherent, non-Markovian manner, meaning its future state depends on its entire past, not just the immediate previous state. This continuous-time instantiation of FCMS establishes a Lyapunov global dissipativity condition, providing a computable threshold for system stability. This new condition generalizes prior discrete FCMS stability criteria and CMGP's physical bifurcation threshold. The core finding is a universal organizing principle: memory dissipation must always exceed feedback gain for the system to remain stable. Numerical simulations and mean-field validation confirm this stability threshold and illustrate the self-reinforcing coordination cascades that occur when this principle is violated.