Derivation, Steady-State Analysis and Mathematical Self-Consistency of the Essence-Qi-Spirit Dynamic Equations《精气神方程组的推导、稳态分析与数理自洽性 —— 三元生命数理论核心数学框架》

Drawing on the three meta‑axioms of Ternary Steady‑State Theory: Closed‑Loop Axiom, Scale‑Matching Axiom and Physical‑Bottom‑Line Axiom, this paper establishes coupled dynamical equations for Jing‑Qi‑Shen oriented toward living autopoietic systems and realises the standardised mathematical reconstruction of the traditional Chinese vital theory of Jing‑Qi‑Shen. First, three‑dimensional dimensionless state variables for matter (Jing), energy (Qi), and information (Shen) are constructed. A hierarchical one‑to‑one mapping between these variables and the underlying parameters of the ternary meta‑axioms is established. The traditional cyclic transformation logic “Jing generates Qi, Qi generates Shen, Shen governs Jing” is rigorously transformed into a first‑order coupled ordinary‑differential system equipped with bottom‑line step‑operator switches. Second, under constraints of the healthy‑safety regime, the unique analytical steady‑state solution of the system is fully derived (based on the revised steady‑state framework from Paper V1). A three‑dimensional Jacobian stability matrix is constructed via linearisation; the characteristic equation is solved, and necessary‑and‑sufficient conditions for global asymptotic stability of the living‑system steady‑state are provided. Third, case‑based algebraic degradation reasoning rigorously verifies full mathematical self‑consistency between the Jing‑Qi‑Shen equation set and the ternary axiomatic system. It proves that simultaneous satisfaction of all three meta‑axioms constitutes the necessary and sufficient prerequisite for long‑term ordered persistence of living organisms. Finally, phase‑space state‑deviation trajectories are mapped onto typical TCM syndromes including Jing‑depletion, Qi‑stagnation, Qi‑counterflow and Shen‑disorder. A unified quantitative analytical paradigm is built that bridges traditional vital cognition with modern non‑equilibrium thermodynamics and time‑delay‑system dynamics. All derivations contain no empirical fitted parameters; reduction steps are reversible and reproducible. This living‑system‑specific equation set can be obtained by boundary‑constraint degradation from the global ternary reaction‑diffusion equations, achieving theoretical unification across microscale‑life‑macro‑cosmological scales.