Comprehensive Verification, Steady-State Analysis and Standardization of Global Application Boundaries for Ternary Unified Mathematical System —The Final Closing Paper No.27 of Yang's Mathematical Trilogy《三元全域统一数理体系综合核验、稳态分析与全域应用边界标准化界定》

This paper is the 27th and ultimate closing final paper of Yang’s Mathematical Trilogy, completing the final verification, standardization and closed-loop finalization of the entire ternary steady-state theoretical system. The complete theoretical system adopts a three-stage hierarchical progressive construction logic: V1–V6 constitutes the core framework of ternary basic axioms, which completes the rigorous mathematical demonstration of the three fundamental axioms of closed-loop, scale and bottom line, and lays the ultimate theoretical foundation for the whole system; V7–V22 is the extended system of ternary axioms, which realizes interdisciplinary theoretical derivation, scene expansion and pre-research deduction based on the basic axiom system, forming a complete extended theoretical reserve; Papers V23–V27 are the final optimization and finalization series of the whole system. On the basis of the systematic theoretical achievements accumulated from V1 to V22 and the core research results of No.23–26 papers, this paper takes the 11-dimensional global unified dynamic system and three-layer nested vector theoretical framework as the core research carrier, and carries out three key standardized finalization works. Firstly, this paper conducts a full-system self-consistency re-verification of the 11-dimensional global state vector, global coupling matrix and hierarchical degradation equations, supplements the complete Lyapunov global stability proof of the full-scale 11-dimensional system, and systematically deduces the mathematical criteria for global phase space steady-state attractors, critical bifurcation boundaries and irreversible collapse absorption states. Secondly, it sorts out the three-stage inheritance and development context of the full set of theories from basic axioms, extended derivation to final system integration, fully calibrates the dimensional mapping rules, parameter specification standards and unified symbol system of all serial papers, eliminates cross-version logical ambiguities and format differences, and forms a permanent unified standard specification for the ternary theoretical system. Thirdly, it standardizes the rigid boundary between basic theoretical research and interdisciplinary empirical application, constructs a standardized framework for global application expansion, and puts forward unified implementation norms for subsequent derivative research by global scholars. This paper further deepens the mathematical interpretation of the Community with a Shared Future for Mankind based on the full 11-dimensional global vector, constructs a complete steady-state discrimination index system for planetary-scale giant dissipative systems, and strictly distinguishes theoretical framework deduction and real data quantitative fitting. All mathematical derivation processes in this paper adopt pure axiom deduction without empirical fitting parameters or artificial simplified assumptions, completely inheriting the original mathematical paradigm of the localized Chinese ternary steady-state theory. Meanwhile, this paper systematically sorts out the full-set original ownership, unified naming norms of all Yang’s mathematical models, complete open-source copyright clauses and academic citation standards of the whole series No.21–27, forming a closed-loop standardized management system for academic achievements. Through full-dimensional stability verification, cross-paper standard unification and application boundary normalization, this paper completely finishes the construction of the self-consistent, complete, replicable and expandable localized ternary mathematical theoretical system, forming the ultimate closed-loop achievement of Yang’s mathematical trilogy.