Temporal Scale Separation in Collapse Precursors: A Comparative Study of Variance, Transport, Topological, and Autocorrelation-Break Signals in Adaptive Agent Systems

This paper presents a comparative analysis of four collapse precursor classes across multiple temporal horizons in a synthetic adaptive-agent transport system. Rather than asking which predictor “wins,” the study investigates whether different precursor signals operate at distinct dynamical scales of the collapse process itself. Four methods are evaluated on the same dataset at horizons H = 50, 100, 200, 500, and 1000 steps: rolling standard deviation (variance amplification), rolling mean absolute deviation (transport disruption), persistent homology via sliding-window RIPS filtration, and an autocorrelation-break density signal derived from short-range temporal coupling disruption. The results reveal a clear temporal hierarchy: variance and MAD dominate at short horizons but decay rapidly, autocorrelation-break density remains weak yet comparatively stable across long horizons, and persistent homology contributes near-zero predictive information across all scales. The negative persistent-homology result is scientifically important because it constrains the collapse dynamics in these systems to local reactive processes rather than global topological restructuring. The study therefore supports a temporally layered model of collapse involving: fast reactive instability cascades, slower hysteretic susceptibility drift, and the absence of large-scale geometric bifurcation. The paper argues that collapse precursors should not be treated as competing measurements of the same event, but as signals operating at different temporal layers of adaptive-system failure dynamics.