Planetary Civilization Synergetic Steady State Based on Ternary Global Unified Dynamic Axiom System — A Neutral Mathematical Characterization of the Community with a Shared Future for Mankind《基于三元全域统一动力学公理体系的行星文明协同稳态 —— 人类命运共同体中立数理刻画研究》

Most domestic researches on the Community with a Shared Future for Mankind adopt qualitative humanistic interpretation methods, while mainstream international quantitative global governance models are built on the underlying logic of zero-sum game and geopolitical competition, lacking indigenous quantitative analysis tools free from national and ideological bias. Based on four monographs of Ternary Steady-State Theory and 27 supporting serial papers archived open access on Zenodo over more than 20 years, this paper takes three independent and complete primitive axioms (Closed-Loop Axiom, Scale Axiom and Bottom-Line Axiom) as the theoretical foundation, constructs an 11-dimensional layered time-delay reaction-diffusion global dynamic system for closed spherical planets, and deduces the dimensionless civilizational synergy phase transition criterion \(\Psi\). Time-series big data of Roman, Maya, Chinese and modern global civilizations are used for cross-civilization case verification only to demonstrate the model’s historical explanatory power. A rigorous set-theoretic mathematical definition of the Community with a Shared Future for Mankind is proposed based on the objective evolution laws of non-equilibrium dissipative systems. The necessary and sufficient conditions for global synergetic steady state are derived forwardly, and the dynamic instability mechanisms of three development modes including bloc division, intergenerational overdraft and unrestrained resource predation are revealed reversely. All theoretical derivations, equations and historical cases in this paper originate from archived supporting monographs without additional theoretical assumptions, maintaining a neutral and objective research perspective throughout the whole text. This study constructs an original localized quantitative analysis framework, which can respond to various one-sided international interpretations and prejudices from a mathematical perspective. Only the basic theoretical framework is established in this paper, and refined parameter calibration and complete regional empirical simulation are reserved for subsequent independent research.