Distance to Admissibility: A Unified Functional Framework for Tipping Points

This paper introduces Distance to Admissibility as a unified functional framework for tipping points in complex systems. Rather than classifying tipping by mechanism, the approach treats tipping as the loss of admissibility itself—the disappearance of the margin that allows meaningful system evolution to persist. Bifurcation-induced, noise-induced, and rate-induced tipping are shown to arise as projections of a single admissibility-based functional, providing a common geometric interpretation across decades of tipping-point theory. The framework is developed at a foundational level and illustrated through a non-empirical template for the Atlantic Meridional Overturning Circulation (AMOC), demonstrating how admissibility margin can be operationalized without reducing the theory to mechanism-specific diagnostics.