This preprint develops a nonlinear dynamical framework in which authority stability is treated as an endogenous bounded state variable interacting with cumulative irreversibility. The model derives a sufficient collapse inequality linking stress accumulation, irreversibility feedback, and governance reinforcement. A minimum admissible authority threshold is introduced to formalize an execution hold condition under extreme stress. Local stability is analyzed via Jacobian methods and nullcline structure. The contribution is theoretical and intended to stimulate further empirical investigation in reliability and governance-sensitive systems.

This manuscript is released as Version 1.0. The framework is theoretical and not empirically calibrated. Feedback and academic discussion are welcome. Future versions may include extended stability analysis and empirical validation.