New FCMS paper proves memory dissipation must outpace feedback gain in AI systems

Stefano Grassi's latest paper, "Feedback-Coupled Memory Systems in Continuous Time," tackles a fundamental gap in the FCMS architecture by defining two previously axiomatically undefined operators: the agent update operator f_i and the environmental update operator Ψ. The author grounds f_i in Mechanism-Based Intelligence (MBI), where agents update locally via a decentralized price mechanism and economic principles. The environment Ψ is modeled by the Coupled Memory Graph Process (CMGP), a non-Markovian framework where the physical substrate records and responds to trajectory history coherently without external forcing. This continuous-time instantiation achieves Lyapunov global dissipativity governed by the threshold 4β² < 2ημγ², which generalizes both the discrete FCMS stability condition and CMGP's physical bifurcation threshold.

Numerical simulations with N=2 agents and mean-field validation at N=10⁶ confirm the stability threshold and reveal a self-reinforcing coordination cascade when the condition is violated. The work formalizes a universal organizing principle: memory dissipation must outpace feedback gain to maintain stability in multi-agent AI systems. By bridging discrete and continuous formulations, Grassi provides a rigorous foundation for scaling decentralized AI agents, with implications for swarm robotics, economic simulations, and distributed learning systems. The paper, 19 pages with 4 figures, builds on arXiv:2603.11560 and includes open-source code.