Critical_Phenomena

This paper develops an operational measurement framework for instability and maturation dynamics in adaptive multi-agent AI systems. Drawing on self-organized criticality and branching-process theory, it defines three substrate-independent observables — storm size distribution exponent (τ), storm duration exponent (α_dur), and cascade branching ratio (R) — together with a tolerance protocol for evaluating whether intra-agent and inter-agent instability exhibit consistent critical behavior. The framework characterizes Silent Criticality, a pre-catastrophic regime in which degradation of sensing capacity produces apparent stability while hidden correlations accumulate. Recovery-timescale divergence is introduced as an operational catastrophe criterion, and a six-step measurement pipeline with executable estimation procedures is provided. Beyond instability detection, the framework establishes closure-relevant observable substrates enabling empirical tracking of governance maturation dynamics without requiring direct measurement of internal control variables. Measurement applicability is explicitly bounded: direct estimation is feasible in tool-agent environments with internal event logs, while conversational LLM settings are treated as exploratory surrogate environments. Companion theoretical frameworks, including Vector Storm Theory (VST), provide mechanistic interpretation but are not required for application of the present measurement protocol.