标题： 量子态几何与模糊度量空间的不相容性：三个无解定理 显示英文标题

标题： On the Incompatibility of Quantum State Geometry and Fuzzy Metric Spaces: Three No-Go Theorems

摘要： 我们证明了三个结构上的不可能性结果，表明模糊度量空间无法捕捉量子态几何的本质特征。 首先，我们证明它们无法模拟由于相位不敏感而导致的概念之间的破坏性干涉。 其次，我们证明从量子态空间到任何模糊度量空间中不存在保持距离的嵌入。 第三，我们建立了模糊逻辑无法区分对称与反对称的概念组合——这是建模结构化知识的根本限制。 这些定理共同表明，模糊框架在结构上无法表示内在不确定性，而量子力学提供了一种更优且几何一致的替代方案。 显示英文摘要

摘要： We prove three structural impossibility results demonstrating that fuzzy metric spaces cannot capture essential features of quantum state geometry. First, we show they cannot model destructive interference between concepts due to phase insensitivity. Second, we prove there is no distance-preserving embedding from quantum state space into any fuzzy metric space. Third, we establish that fuzzy logic cannot distinguish symmetric from antisymmetric concept combinations -- a fundamental limitation for modeling structured knowledge. These theorems collectively show that fuzzy frameworks are structurally incapable of representing intrinsic uncertainty, where quantum mechanics provides a superior, geometrically coherent alternative.