Interpretation of Global State Vectors and Unified Ternary Global Dynamic Equations: The Closing Paper of the Complete Axiomatic Mathematical System of Ternary Steady-State Theory《全域状态向量与三元全域统一方程解译 》

This is preprint V26 of the Ternary Steady‑State Theory series, a purely axiomatic theoretical work. Based on three fundamental axioms: closed‑loop integrity, scale balance and physical bottom boundary, this paper establishes the Yang‑type global‑domain ternary unified dynamics within an 11‑dimensional framework. The Yang‑type global‑domain state vector W(t), forward life‑global mapping operator \(T_{life}\) and its inverse operator \(T_{life}^{-1}\) are defined. It proves that the Yang‑type life ternary equations (Jing‑Qi‑Shen equations from V25) and the inorganic general ternary equations are algebraic reduced forms of the global‑domain unified equations under boundary constraints. The steady‑state of global‑domain system is solved, and sufficient‑necessary conditions for global asymptotic stability are given. Dynamical behaviours including instability, oscillation and collapse when thresholds are violated are discussed. This work achieves theoretical closure across micro‑physics, life‑system and macro‑cosmos. A clear boundary is drawn between foundational axiomatic deduction and practical applications. Parameter calibration, clinical measurement and detailed social‑system modelling are reserved for future research. All derivations are mathematically self‑consistent with V23, V24 and V25.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-20
DOI
https://doi.org/10.5281/zenodo.21767151
Primary Topic
Chaos, Complexity, and Education
Type
preprint
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preprint

Interpretation of Global State Vectors and Unified Ternary Global Dynamic Equations: The Closing Paper of the Complete Axiomatic Mathematical System of Ternary Steady-State Theory《全域状态向量与三元全域统一方程解译 》

Guojun Yang
Zenodo (CERN European Organization for Nuclear Research)
Chaos, Complexity, and Education
preprint

Interpretation of Global State Vectors and Unified Ternary Global Dynamic Equations: The Closing Paper of the Complete Axiomatic Mathematical System of Ternary Steady-State Theory《全域状态向量与三元全域统一方程解译 》

Guojun Yang
preprint en

Abstract

This is preprint V26 of the Ternary Steady‑State Theory series, a purely axiomatic theoretical work. Based on three fundamental axioms: closed‑loop integrity, scale balance and physical bottom boundary, this paper establishes the Yang‑type global‑domain ternary unified dynamics within an 11‑dimensional framework. The Yang‑type global‑domain state vector W(t), forward life‑global mapping operator \(T_{life}\) and its inverse operator \(T_{life}^{-1}\) are defined. It proves that the Yang‑type life ternary equations (Jing‑Qi‑Shen equations from V25) and the inorganic general ternary equations are algebraic reduced forms of the global‑domain unified equations under boundary constraints. The steady‑state of global‑domain system is solved, and sufficient‑necessary conditions for global asymptotic stability are given. Dynamical behaviours including instability, oscillation and collapse when thresholds are violated are discussed. This work achieves theoretical closure across micro‑physics, life‑system and macro‑cosmos. A clear boundary is drawn between foundational axiomatic deduction and practical applications. Parameter calibration, clinical measurement and detailed social‑system modelling are reserved for future research. All derivations are mathematically self‑consistent with V23, V24 and V25.

Zenodo (CERN European Organization for Nuclear Research)
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Chaos, Complexity, and Education
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