Feedback-Coupled Memory Systems in Continuous Time

• URL: http://arxiv.org/abs/2607.09714v1
• Date: Wed, 24 Jun 2026 14:03:34 GMT
• Title: Feedback-Coupled Memory Systems in Continuous Time
• Abstract summary: We show that memory dissipation must outpace feedback gain as a universal organizing principle in FCMS architecture.<n>This generalizes both the discrete FCMS stability condition $42 $ and CMGP's physical bifurcation threshold $_c = 1/K$.<n> 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $Ψ$ - 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 $Ψ$ 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 $4β^2 < 2ημγ^2$. This generalizes both the discrete FCMS stability condition $4ηβ^2 < γ$ and CMGP's physical bifurcation threshold $α_c = 1/K$, 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.

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