Feedback-Coupled Memory Systems in Continuous Time

The Feedback-Coupled Memory Systems (FCMS) architecture formalizes closed-loop coordination through four abstract operators, two of which - the agent update operator fi and the environmental update operator Psi - are left axiomatically undefined in the original framework. To address this, fi is defined by Mechanism-Based Intelligence (MBI), where agents update locally through a decentralized price mechanism and economic principles, and Psi is defined by the Coupled Memory Graph Process (CMGP), a non-Markovian framework where the environment is treated as a physical substrate that records and responds to trajectory history coherently without external forcing. The resulting continuous-time FCMS instantiation achieves Lyapunov global dissipativity governed by the computable threshold 4β2 < 2ημγ2. This generalizes both the discrete FCMS stability condition 4ηβ2 < γ and CMGP's physical bifurcation threshold αc = 1/K, confirming that memory dissipation must outpace feedback gain as a universal organizing principle. Numerical simulation with N=2 agents and mean-field validation at N=106 confirm the stability threshold and the self-reinforcing coordination cascade that emerges when it is violated.