Operational Signalling under Adaptive Interaction: Global Control Laws, Criticality, and Regime Classification

This paper establishes global laws governing operational signalling in measurement-dependent models under adaptive multi-round interaction. Unlike earlier analyses based on fixed profiles or one-step behaviour, the present work studies the full dynamical evolution of the underlying probability distribution. Previous papers in the series showed that signalling is not identifiable from finite data, that repeated interaction can nevertheless generate operational distinguishability, and that one-step amplification is governed by a precise structural coefficient. The adaptive setting introduced a Bellman-type recursion and revealed a persistent multiscale regime associated with harmonic-comparable profiles. However, a global theory of the resulting dynamics was not previously available. The present paper provides that global theory. It establishes a universal exponential control law showing that multi-round signalling capacity is governed by the cumulative one-step gain. It proves a complete classification of adaptive trajectories into three regimes: head-heavy dynamics with microscopic peeling, tail-heavy dynamics with macroscopic peeling, and a critical harmonic regime with logarithmic growth. It further shows that strong universality fails at the level of profile geometry: there is no finite family of asymptotic profile classes capturing all non-collapsing trajectories. These results demonstrate a fundamental dichotomy. Adaptive signalling is universal at the level of control behaviour, but not at the level of profile dynamics. While all systems obey the same exponential law, the underlying distributions exhibit a continuum of persistent geometries. This completes the operational signalling programme developed across six works, providing a unified description of adaptive dynamics and clarifying the limits of universality in measurement-dependent systems.