提出心脏吸引子理论，用可穿戴设备分析心血管状态的数学框架。
Attractor Domain Theory: A Mathematical Framework for Cardiovascular Attractor Analysis with Wearable Photoplethysmography (PPG) Validation
- 将心脏吸引子分为几何、统计和变化三域，各有不同生理意义。
- 在17万段PPG数据上验证，几何域识别能力AUC达0.757，阴性预测值0.966。
- 揭示了各域对噪声抑制、稳定性评估和血流推断的专长，适合心电/脉搏研究者。
心血管系统在生理状态空间中沿有界轨迹演化，收敛至一个紧致几何对象——心脏吸引子。可穿戴光体积描记（PPG）或心电图（ECG）仅观测该吸引子的一维投影；根据Takens嵌入定理，延迟坐标可重建其完整几何结构。过去三十年的非线性心脏动力学研究提取了李雅普诺夫指数、递归统计与样本熵，但缺乏对吸引子属性与心血管指标之间对应关系的理论解释，导致特征选择成搜索问题，负面结果难以解读。本文提出吸引子域理论（ADT），证明重构吸引子的信息可划分为三个互不冗余的域：几何域（延迟嵌入；原生能力：抗干扰）、遍历域（渐近统计不变量；原生能力：稳定性估计）、变率域（有限时间李雅普诺夫指数场；原生能力：血流推断）。我们证明了域充分性定理（吸引子信息的帕塞瓦尔类比），并确立三域为必要且充分。通过SCSI框架在四个数据集共176,742段PPG信号上验证几何域，校正三种系统性评估偏差后，AUC为0.757[0.686-0.828]，阴性预测值NPV=0.966（净增0.179）。消融实验确认C_NL是几何域主导成分（Delta AUC=-0.413），并发现域内五成分存在冗余。
原文摘要 · Abstract (English)
The cardiovascular system evolves along a bounded trajectory in physiological state space that converges to a compact geometric object: the cardiac attractor. A wearable photoplethysmograph (PPG) or electrocardiograph (ECG) observes a one-dimensional projection of this attractor; by Takens' embedding theorem, delay coordinates reconstruct its full geometry. Three decades of nonlinear cardiac dynamics have extracted Lyapunov exponents, recurrence statistics, and sample entropy from reconstructed attractors, yet no principled account exists of which attractor properties capture which cardiovascular quantities, or why, leaving feature selection as a search problem and negative results uninterpretable. We introduce Attractor Domain Theory (ADT), which proves that the reconstructed attractor's information partitions into three mutually non-redundant domains: the Geometry Domain G (delay embedding; native capability: artifact rejection), the Ergodic Domain S (asymptotic statistical invariants; native capability: stability estimation), and the Variational Domain V (finite-time Lyapunov exponent field; native capability: hemodynamic inference). We prove a Domain Sufficiency Theorem (the Parseval analog for attractor information) and establish that three domains are necessary and sufficient. Geometry Domain validation via the SCSI framework across 176,742 PPG segments from four datasets yields AUC = 0.757 [0.686-0.828] and NPV = 0.966 after correcting three systematic evaluation artifacts (+0.179 net inflation). Ablation confirms C_NL as the dominant Geometry Domain component (Delta AUC = -0.413) and intra-domain redundancy across five components.
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