Analysis of Six Fundamental Mathematical Problems of the Ternary Global Unified Dynamical System《元全域统一动力学体系的六大数学基础问题解析 —— 理论完备性最终证明与工程边界界定》

This document contains the complete text of Chapter 7 from Version V29 of the Ternary Steady‑State Theory, the final closing release of the theory. This chapter provides a rigorous algebraic proof for global asymptotic stability of the steady‑state solution of the 11‑dimensional global dynamical system over the valid parameter space \(\Theta_{\text{valid}}\). It introduces the resilience recovery window \(\mathcal{R}(\delta,T_{\text{rec}})\) to formulate a flexible mathematical definition for the community‑of‑shared‑future steady‑state. A full judgement system based on the four‑dimensional civilizational end‑state vector \(\Gamma_{\text{civil}}=(\Psi,\mathcal{B}_{\text{gen}},|\Omega_{\text{code}}|,\mathcal{F}_{\text{CFC}})^T\) is constructed. A permanent freeze statement for all core theoretical objects is issued, marking the formal completion of the core mathematical system of Ternary Steady‑State Theory. Mathematical notations are standardized with ambiguity removed for time‑domain expressions. All definitions, theorems and judgement rules are frozen and serve as the sole official archival reference for this theory.本文件为三元稳态论(Ternary Steady‑State Theory)收官版本 V29 第七章完整正文。本章完成 11 维全域动力学系统稳态解在合法参数空间\(\Theta_{\rm valid}\)上的全局渐近稳定性代数证明,引入韧性恢复窗\(\mathcal{R}(\delta,T_{\rm rec})\)对人类命运共同体稳态给出柔性数理定义,建立四维终局判定向量\(\Gamma_{\rm civil}=(\Psi,\mathcal{B}_{\rm gen},|\Omega_{\rm code}|,\mathcal{F}_{\rm CFC})^T\)完整判定体系,并发布全套核心理论对象永久冻结声明,标志三元稳态论核心数理体系正式理论封顶。全文严格规范数学符号表述,修正时间域记号歧义,所有定义、定理、判定规则均已冻结,作为该理论唯一正式溯源锚点。