DOI：10.12201/bmr.202604.00098

A Classification Model of TCM Syndrome Based on Algebraic Moduli Space and Rigid Degeneration

• 摘要：中医证候具有动态性、模糊性与整体性特征，其分类与演化规律难以用传统统计方法完整刻画。本文提出一种基于代数几何的证候分类理论框架：将证候分布空间构造为一个代数模空间（概型），将观测症状的概率云视为该空间上的点，运用代数几何中的刚性退化方法研究证候的动态演化与等价分类。当模型参数趋向极限时，不同的证候概率云退化至模空间边界的同一极限点，该点对应于一个更本质的宏观证候状态，由此形成证候的等价类划分。本文以太阳病向阳明病传变为例构建简化模型，展示该框架的运作机制。同时，本文直面该框架面临的核心数学挑战——临床概率分布难以直接满足多项式代数约束——并论证通过信息几何嵌入与统计投射机制可使模型在原理层面保持自洽。该研究为中医辨证论治提供了一种新的形式化数学语言，并为证候的动态分类建立了代数几何阐释基础。

  关键词： 证候分类; 代数模空间; 刚性退化; 概率云; 信息几何; 辨证论治; 天人系统医学; 生生唯物运动观

   

  Abstract: Traditional Chinese Medicine (TCM) syndromes are characterized by dynamism, fuzziness, and holism, making their classification and evolution difficult to capture fully with conventional statistical methods. This paper proposes a theoretical framework for syndrome classification grounded in algebraic geometry. We construct the space of syndrome distributions as an algebraic moduli space (scheme), regard the probability cloud of observed symptoms as points in this space, and apply the method of rigid degeneration from algebraic geometry to investigate the dynamic evolution and equivalence classification of syndromes. As model parameters approach a limit, distinct syndrome probability clouds degenerate to the same limit point on the boundary of the moduli space. This limit point corresponds to a more fundamental macroscopic syndrome state, thereby yielding an equivalence class partition of syndromes. A simplified model of the progression from Taiyang disease to Yangming disease is presented to illustrate the operational mechanism of the framework. Furthermore, we directly address the core mathematical challenge facing this framework—namely, that clinically derived probability distributions seldom satisfy polynomial algebraic constraints—and argue that, in principle, self-consistency can be maintained through embedding in information geometry and statistical projection mechanisms. This research provides a novel formal mathematical language for TCM syndrome differentiation and treatment, and establishes an algebraic-geometric foundation for the dynamic classification of syndromes.

  Key words: Syndrome Classification; Algebraic Moduli Space; Rigid Degeneration; Probability Cloud; Information Geometry; Syndrome Differentiation and Treatment; Sheng-Sheng Materialist Movement View; Medicine of Heaven-Human System

  提交时间：2026-05-08

  版权声明：作者本人独立拥有该论文的版权，预印本系统仅拥有论文的永久保存权利。任何人未经允许不得重复使用。
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• 序号	提交日期	编号	操作
  1	2026-04-11	10.12201/bmr.202604.00098V1	下载

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