The Emergence of Relationships: Why Knowledge Modeling Must Avoid Creating Relations - Vector Modeling of the Five Elements under Wittgenstein’s Logical Form and the Natural Emergence of the Golden Ratio

This project presents a mathematical reconstruction of the Five Elements (Wu Xing) theory using vector space geometry and group theory. We prove that "Generation" and "Overcoming" relationships emerge naturally from a regular pentagonal structure, without any explicit rule creation. KEY DISCOVERY: The relationship strengths (cos 72° = 0.309, cos 144° = -0.809) correspond precisely to the Golden Ratio φ, revealing that the Five Elements system possesses an intrinsic "minimality and optimality" property at the ontological level. 本项目从向量空间几何与群论的角度重构五行理论。我们证明"相生"与"相克"关系从正五边形结构中自然涌现，无需任何显式规则创建。 核心发现：关系强度（cos 72° = 0.309, cos 144° = -0.809）精确对应黄金分割率φ，揭示五行系统在本体论层面具有"极简与最优"的内禀属性。