Feedback-Coupled Memory Systems in Continuous Time

[Submitted on 24 Jun 2026]

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Abstract:The Feedback-Coupled Memory Systems (FCMS) architecture formalizes closed-loop coordination through four abstract operators, two of which – the agent update operator $f_i$ and the environmental update operator $Psi$ – are left axiomatically undefined in the original framework. To address this, $f_i$ 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 $4beta^2 < 2etamugamma^2$. This generalizes both the discrete FCMS stability condition $4etabeta^2 < gamma$ and CMGP’s physical bifurcation threshold $alpha_c = 1/K$, confirming that memory dissipation must outpace feedback gain as a universal organizing principle. Numerical simulation with $N=2$ agents and mean-field validation at $N=10^6$ confirm the stability threshold and the self-reinforcing coordination cascade that emerges when it is violated.

Submission history

From: Stefano Grassi [view email]
[v1] Wed, 24 Jun 2026 14:03:34 UTC (567 KB)