The Persistence Principle

The Persistence Principle establishes a necessary and sufficient condition for system viability across any domain describable as a stock with inflows and outflows. The core result: any system whose long-run average net flow is persistently negative will collapse in finite time. This is not a probabilistic claim or a scenario-dependent projection. It is a mathematical consequence of the system dynamics, formally proved and applicable at any scale. The theorem is applied to four critical global systems currently in violation of the persistence condition: global freshwater availability, agricultural yield capacity, atmospheric carbon stability, and sovereign fiscal capacity. Collapse horizons are derived from public empirical data. The four systems are structurally coupled — failure in one accelerates failure in the others — and their collapse horizons converge between 6 and 80 years depending on the system and unit of analysis. The corrective framework developed in response to these findings is Contributionism, described in the companion white paper. The Portland Willamette Systems Demonstration is the first proposed real-world test of its core mechanisms.