Attractor Domain Theory: A Mathematical Framework for Cardiovascular Attractor Analysis with Wearable Photoplethysmography (PPG) Validation

Researchers introduce Attractor Domain Theory (ADT), a mathematical framework that partitions cardiovascular attractor information into three non-redundant domains for analyzing heart dynamics from wearable PPG sensors. Validation across 176,742 PPG segments demonstrates strong performance (AUC=0.757, NPV=0.966), providing a principled approach to feature selection in cardiac signal analysis that has lacked theoretical grounding for three decades.

Attractor Domain Theory addresses a fundamental gap in nonlinear cardiac dynamics research. For 30 years, scientists have extracted Lyapunov exponents, recurrence statistics, and entropy metrics from reconstructed cardiac attractors without a coherent theoretical framework explaining which properties measure which physiological quantities. This ambiguity transformed feature selection into an unprincipled search problem, making negative results difficult to interpret.

ADT solves this by proving that cardiac attractor information partitions into exactly three mutually non-redundant domains: Geometry Domain (artifact rejection via delay embedding), Ergodic Domain (stability estimation via asymptotic invariants), and Variational Domain (hemodynamic inference via Lyapunov exponents). The Domain Sufficiency Theorem establishes mathematical necessity and sufficiency, providing the theoretical justification previously missing from the field.

The validation results carry practical significance for wearable health technology. Testing across four datasets yielded AUC=0.757 with NPV=0.966 after correcting three systematic evaluation artifacts—a methodological rigor that itself advances the field. Ablation analysis identified C_NL as the dominant Geometry Domain component, reducing feature space complexity.

For biomedical device developers and health tech companies, ADT enables more robust PPG-based cardiovascular monitoring. The framework transforms cardiac signal analysis from empirical feature engineering into principle-driven domain selection, reducing overfitting risk and improving generalization across diverse patient populations. Academic researchers gain theoretical clarity for designing future cardiac dynamics studies.

• →Attractor Domain Theory provides the first principled mathematical framework for selecting cardiac dynamics features from wearable PPG signals.
• →Three non-redundant information domains (Geometry, Ergodic, Variational) are proven both necessary and sufficient for complete cardiovascular attractor characterization.
• →Validation achieved AUC=0.757 and NPV=0.966 across 176,742 PPG segments after correcting systematic evaluation artifacts.
• →Ablation studies confirm C_NL as the dominant Geometry Domain component, enabling feature space simplification.
• →Framework transition from empirical to principle-driven approach addresses 30-year gap in nonlinear cardiac dynamics methodology.