🤖 AI Summary
This study addresses the lack of a systematic framework linking geometric properties of reconstructed cardiovascular attractors to physiological quantities, which has led to ad hoc feature selection and difficulty interpreting negative results. The authors propose Attractor Domain Theory (ADT), which uniquely partitions attractor information into three non-redundant domains—geometric, ergodic, and variational—each supporting artifact rejection, stability estimation, and hemodynamic inference, respectively. They establish the necessity and sufficiency of this tripartite division through a Domain Sufficiency Theorem. Validated on 176,742 PPG segments using Takens embedding, an SCSI verification framework, and nonlinear dynamical features, the geometric domain yields an AUC of 0.757 (negative predictive value: 0.966) after bias correction. Ablation experiments identify the nonlinear correlation dimension \(C_{NL}\) as critical, with its removal reducing AUC by 0.413.
📝 Abstract
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.