Critical Phenomena in Multi-Agent Systems: Self Organized Criticality, Correspondence Tests and Limits of Observation

This working paper specifies measurements and falsifiable tests for instability propagation in adaptive multi-agent systems. It distinguishes storm size, duration, observed activity growth, and model-based endogenous reproduction. Version 4.0 addresses event segmentation, finite-support tail estimation, calibration, and the coverage limits of recovery probes. Proposed tests examine constraint-dependent cutoffs, information retained by component measurements, and reference-anchor asymmetry before measured degradation. Cross-scale correspondence requires aligned definitions, identified estimators, and calibrated uncertainty. Deterministic illustrations check mathematical distinctions; neither these checks nor the reviewed external studies establish empirical validation of the complete framework.