Authority Dynamics v1.0: Deterministic Phase Mechanics, Structural Stability, and Regime Compilation under Governance Constraints

This work introduces Authority Dynamics v1.0, a deterministic nonlinear framework in which authority stability is modeled as a bounded state variable governed by a stress–governance inequality. The model formalizes authority as a dynamic system subject to irreversibility intensity, uncertainty amplification, and governance reinforcement. We prove invariance of the authority domain, collapse inequalities, Lyapunov-based global stability, absorbing HOLD regions, structural robustness under bounded perturbations, and contraction-based deterministic convergence. A formal OPEN / CLOSING / LOCKED regime classification is derived from a phase boundary defined by the inequality between effective stress and governance capacity. The framework integrates a deterministic regime compiler that maps mathematical conditions directly to operational governance states. Unlike probabilistic risk models, authority collapse is shown to be a deterministic phase transition triggered by parameter inequality crossing. The model connects nonlinear stability theory, control systems, structural bifurcation analysis, and safety-critical design principles within a unified governance mechanics framework. Version 1.0 (SSOT). Deterministic formulation only. Future extensions may include stochastic perturbation analysis and entropy-based authority measures.