Cardiac Stability Theory: An Axiomatically Grounded Framework for Continuous Cardiac Health Monitoring via Smartphone Photoplethysmography

We present Cardiac Stability Theory (CST), an axiomatically grounded framework formally defining cardiovascular health as a stability margin around a cardiac dynamical attractor. From four axioms we derive the Cardiac Stability Index (CSI), a composite scalar in [0,1] integrating the largest Lyapunov exponent, recurrence determinism, and signal entropy via time-delay embedding. The ECG-based model (CSISurrogateV2, CNN-Transformer) achieves R2=0.8788, MAE=0.0234 on PTB-XL (21,799 recordings). We extend CSI to smartphone PPG via Complementary Domain Transfer (CDT): CSISurrogateV2 generates pseudo-labels for the BUT PPG dataset (48 recordings, 12 subjects), training TinyCSINet (122,849 parameters), achieving MAE=0.0557, ρ=0.660 on the held-out test set (n=1065 windows) at <30 ms mobile latency. CDT is validated on BIDMC, Welltory, and RWS-PPG. Paired validation on 5,035 BIDMC windows yields r=0.454 (ρ=0.485, p<10-295), confirming correlated cardiac stability across modalities. CSI is negatively correlated with age (slope = -0.000225 CSI/year, PTB-XL), discriminates atrial fibrillation from normal sinus rhythm (AUROC=0.89), and is robust under Perturbation Invariance Training (max AUC drop 1.65%). We derive HeartSpan, a longitudinal stability metric relative to population age norms, enabling continuous non-invasive cardiac monitoring from commodity smartphones for longevity tracking and cardiac risk stratification.