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

DOI: 10.12201/bmr.202604.00098

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  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

  Submit time: 8 May 2026

  Copyright: The copyright holder for this preprint is the author/funder, who has granted biomedRxiv a license to display the preprint in perpetuity.
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• ID	Submit time	Number	Download
  1	2026-04-11	10.12201/bmr.202604.00098V1	Download

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