Critical_Phenomena

This paper develops a measurement framework for instability 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) — and a tolerance protocol for evaluating whether intra-agent and inter-agent instability exhibit consistent critical behavior. The paper characterizes Silent Criticality, a pre-catastrophic state where sensing-apparatus degradation produces apparent stability while hidden correlations accumulate, and proposes recovery timescale divergence as the formal catastrophe criterion. A six-step operational measurement pipeline and estimation algorithms are provided. Measurement environment constraints are explicitly bounded: direct measurement is feasible only in tool-agent environments with internal event logs. Conversational LLM settings are treated as exploratory surrogates only. Companion theoretical framework: Vector Storm Theory (VST) v4.0.