Economic Collapse as a Threshold Dynamical System: Steady-State Bounds, Convex Hazard, and a Japan–U.S. Comparative Test

This paper develops the dynamical extension of a memory-dependent threshold framework for macroeconomic regime shifts. Building on Fragility as a Memory-Dependent System: Structural Overload and the Architecture of Threshold Regime Shift (Zenodo, 2026) and Economic Collapse as a Threshold Phenomenon: Operationalizing a Memory-Dependent Fragility Index (Zenodo, 2026), this paper embeds the collapse functional into a minimal nonlinear macro-financial dynamical system. Three results are derived: A steady-state instability boundary condition replacing purely empirical quantile thresholds with a falsifiable analytical inequality linking strain inflows to bounded release capacity. A convex escalation result showing that time-to-threshold compresses as accumulated strain rises, implying structurally accelerating collapse hazard without assuming exponential behavior. A comparative structural implication distinguishing episodic threshold crossing (acute regime shift) from persistent near-boundary compression (chronic strain), illustrated conceptually through a United States–Japan contrast. The objective is not equilibrium replacement nor crisis timing prediction. The contribution is structural: instability is formalized as a memory-dependent accumulation process governed by first-passage threshold dynamics. All mappings are to publicly available macro-financial data sources. The framework remains falsifiable and designed for cross-country empirical validation in subsequent work.