Deduction and Reduction of the Ternary‑System Equations: From Three Meta‑Axioms to Dissipative Structures, Allometric Scaling and Autopoiesis Theory (V24‑rev01)《三元方程的推演还原:从三公理到耗散结构、异速生长律与自创生理论》(V24‑rev01)

The ternary equation serves as the standardized unified mathematical carrier of three indigenous fundamental meta-axioms, namely the closed-loop axiom, scale axiom and physical bottom-line axiom. The logical self-consistency and global universality of an original axiom framework can be rigorously verified via the deduction-reduction criterion. If the universal full-scale ternary equation can degenerate into well-established classical fundamental theories under specified mathematical boundary constraints without empirical fitting terms, the axiom system is fully logically compatible with existing physics, biology and system science frameworks. Failure of such parameter-free theoretical degeneration indicates inherent irreconcilable logical flaws within the axiom set. Based on two standard models — the full-space time-delay reaction-diffusion ternary partial differential equation system and discrete Euler iterative equation system, this paper imposes hierarchical boundary constraints and completes rigorous reduction proofs for three landmark interdisciplinary classical theories. First, the Prigogine non-equilibrium dissipative structure theory is fully reconstructed on the basis of the closed-loop axiom; analytical solution of steady-state orderliness and Hopf bifurcation critical criterion are derived to fill the theoretical blank of sufficient and necessary conditions for long-term ordered persistence in classical dissipative theory. Second, Kleiber’s 3/4 allometric scaling law is deduced purely from the scale axiom. Topological analysis verifies that fractal transport network is the only evolutionary configuration satisfying the rigid scale stress boundary for living systems, and quantitative dynamics of ecosystem carrying capacity is further established. Third, the autopoiesis theory is reconstructed by closed survival manifolds in phase space grounded on the physical bottom-line axiom. The conserved quantity of system persistence is defined following Noether’s theorem, and multi-layer quantitative criteria for irreversible biological collapse are constructed.Furthermore, this paper realizes unified underlying logical projection of the three meta-axioms within thermodynamics, quantum mechanics and relativistic cosmology. The covariant ternary equation systematically resolves three long-standing fundamental theoretical puzzles: the anthropic window, fidelity decay in quantum measurement, and local negative entropy of living systems. All derivations in this paper contain no empirical fitting coefficients or artificial extra assumptions. Every evolutionary criterion and critical threshold can be directly calculated from the original ternary equation, forming a complete closed-loop verification of the self-consistency of the meta-axiom system.