Independence, Completeness and Unified Mathematical Expression of Three Meta-Axioms in Ternary Steady-State Theory 《三元稳态论的三条元公理:独立性、完备性与统一数学表达》

Abstract

Current classical physics, cybernetics and ecological theories can only describe evolutionary rules of single-domain and local-scale systems, lacking unified fundamental meta-rules for long-term steady-state survival of full-scale open dissipative systems. This paper originally proposes three meta-axioms: closed-loop axiom, scale axiom and physical bottom-line axiom, conducts formal mathematical proofs of axiom independence and completeness, and constructs two unified mathematical models including continuous time-delay reaction-diffusion ternary PDE system and discrete Euler iterative equations. The core contributions are as follows: standardized verbal definitions, dimensionless formulas and Popper falsifiability criteria of three meta-axioms are established; three groups of dynamic counterexamples are constructed to strictly prove pairwise independence without logical implication; core system indicators including efficiency, fairness, entropy reduction, robustness and innovation are reduced to coupled derivatives of the three axioms, verifying the ternary set as the minimal complete axiom system for open dissipative systems. A three-dimensional normalized axiom state vector is defined, embedding time-delay terms, scale stress constraints and irreversible step operators, and the necessary and sufficient steady-state conditions are derived to deduce degradation paths of classical theories. This axiomatic framework applies universally to micro-cells, fluid chemistry, celestial bodies, ecological groups and human social systems, with full reproducibility. Open-source discrete simulation codes and standardized parameter templates are archived publicly. This manuscript belongs to the Ternary Steady-State Theory paper series, and the full series collection is archived at DOI: 10.5281/zenodo.20549663, providing fundamental mathematical paradigms for cross-disciplinary system dynamics deduction and numerical verification.经典物理、控制论与生态学理论仅能刻画单一领域、局部尺度系统演化规律,缺乏适用于全尺度开放耗散系统稳态存续的统一底层元规则。本文原创提出闭环、尺度、物理底线三条元公理,完成公理独立性与完备性形式化数学证明,构建连续时滞反应 - 扩散三元偏微分方程组、离散欧拉迭代方程组两套统一数理模型。研究核心工作:给出三公理标准化文字定义、无量纲表达式与波普尔可证伪判据;构造三组动力学反例,严格证明三公理两两独立、无逻辑蕴含关系;将效率、公平、熵减、鲁棒性、创新等系统核心概念归约为三公理耦合衍生量,验证三元集合为刻画开放耗散系统的最小完备公理集;定义三维归一化公理状态向量,嵌入时滞、尺度约束、不可逆阶跃算子,推导系统稳态充要条件并还原经典理论退化路径。该公理框架统一适配微观细胞、流体化学、天体、生态集群、人类社会等全域耗散系统,具备跨尺度普适性与可复现性。配套离散仿真开源代码与标准化参数模板已开源归档,本文属于三元稳态论系列论文,完整系列合集归档 DOI:10.5281/zenodo.20549663,可为跨学科系统动力学理论推演、数值验证提供底层数理范式支撑。