Epistemic Status of Tipping in Meridional Overturning Systems

This deposit presents a closed and canonical epistemic corpus devoted to the analysis of tipping phenomena in meridional overturning systems, with a specific focus on the Atlantic Meridional Overturning Circulation (AMOC), developed within the Crowd-Based Dynamics (CBD) framework. The corpus introduces and rigorously situates the Universal Dynamic Convergence Formula (UCD) as a probabilistic structural convergence operator, explicitly non-event-based and non-predictive. The objective is not to forecast tipping events, but to characterize the progressive loss of governability of complex collective systems under accumulation, memory saturation, and limited dissipation. The work is structured into four complementary documents: Document I establishes the epistemic status of the UCD formula and canonizes tipping as a structural regime rather than an event. Document II provides a formal anchoring of the UCD formula within the CBD framework, including a canonical mapping of variables and the formulation of the Tipping Zone Theorem, defining tipping as an irreversible zone in state space. Document III specifies the minimal mathematical properties of the UCD formula (boundedness, continuity, non-invertibility, memory saturation, and structural invariance), ensuring mathematical and epistemic closure. Document IV defines the conditions of use, including strict passive implementation, prohibition of predictive or decision-oriented use, and institutional and epistemic safeguards. A central result of this corpus is the strict distinction between tipping regimes and the Sterking Limit. Tipping is formalized as a structural approach to the Sterking Limit, not as the limit itself, which remains non-operational and non-quantifiable by construction. No universal thresholds, critical times, or event-based predictions are defined or implied. This work does not introduce new empirical data, new equations beyond those already published, or new causal mechanisms. Its contribution is epistemic and structural: it provides a rigorous, closed, and non-instrumental framework for interpreting tipping phenomena across domains, while remaining fully compatible with existing physical climate models. The corpus is intended for researchers working on complex systems, tipping phenomena, collective dynamics, and epistemic foundations of non-predictive modeling. It explicitly prevents misuse for alarmist, technocratic, or policy-driven decision-making and is designed to remain robust under cross-domain scrutiny.