Mean Reversion or Innovation Collapse? Stability Analysis of Closed-Loop Social Communication Systems with AI-Agent Mediators

We model the Expansion--Compression (EC) loop introduced in the \textsc{DECO} series as a discrete-time closed-loop control system,with the LLM expansion operator $\E$ as a forward gain element and the LLM compression operator $\C$ as a feedback element.Using the transfer-function formalism of linear systems theory and its nonlinear extensions, we analyse the stability, convergence properties,and phase transitions of a population of $N$ such loops coupled through a shared semantic environment.

We establish four principal results.First, the single-agent EC-loop is \emph{always asymptotically stable}:the semantic state converges to a unique attractor determined by the LLM's training distribution (\emph{Attractor Theorem}).Second, for a population of $N$ agents, there exists a critical \emph{innovation injection rate} $\lc$ such that for
$\lambdaEC > \lc$ the population-level semantic state is diverse (multi-attractor regime), while for $\lambdaEC \leq \lc$ it collapses to a monoculture fixed point (\emph{Phase Transition Theorem}).Third, under bias-amplifying prompts, the system can enter an unstable regime in which small perturbations grow unboundedly, yielding \emph{semantic runaway} --- the control-theoretic formalisation of ``information bubble'' dynamics (\emph{Runaway Instability Theorem}).Fourth, we derive the \emph{Innovation Preservation Margin (IPM)},a scalar index that predicts whether a given seed idea will retain meaningful distinctiveness after $n$ iterations of the population-level EC-loop.

These findings characterise the macro-dynamic consequences of AI-mediated cognitive decoupling at the societal scale and ground the signalling inflation and ritual-evacuation analyses of Papers~3 and~4 in a rigorous dynamical framework.