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

arXiv: https://arxiv.org/abs/2604.23876 · HTML: https://mlsanity.com/paper/2604.23876/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 47 references that are in the map.
- First posted on arXiv 26 Apr 2026.

## Builds on (most cited first, 4 of 4)

- [Rethinking Multimodality: Optimizing Multimodal Deep Learning for Biomedical Signal Classification](https://mlsanity.com/paper/2508.00963/) (2025)
- [When Should a Model Change Its Mind? An Energy-Based Theory and Regularizer for Concept Drift in Electrocardiogram (ECG) Signals](https://mlsanity.com/paper/2602.22294/) (2026)
- [Complementarity-Preserving Generative Theory for Multimodal ECG Synthesis: A Quantum-Inspired Approach](https://mlsanity.com/paper/2603.26695/) (2026)
- [ECG Classification on PTB-XL: A Data-Centric Approach with Simplified CNN-VAE](https://mlsanity.com/paper/2603.07558/) (2026)

## Built on by (most cited first, 4 of 4)

- [Attractor-Vascular Coupling Theory: Formal Grounding and Empirical Validation for AAMI-Standard Cuffless Blood Pressure Estimation from Smartphone Photoplethysmography](https://mlsanity.com/paper/2605.10871/) (2026)
- [A Nonlinear Complexity Index for Wearable PPG Cardiovascular Stability: Multiscale Validation, Systematic Evaluation Correction, and Bayesian Parameter Optimization](https://mlsanity.com/paper/2605.18802/) (2026)
- [Attractor Domain Theory: A Mathematical Framework for Cardiovascular Attractor Analysis with Wearable Photoplethysmography (PPG) Validation](https://mlsanity.com/paper/2606.22039/) (2026)
- [Property-Specific Recoverability from Contact PPG to Camera rPPG under Heterogeneous Observation Conditions](https://mlsanity.com/paper/2608.27392/) (2026)

## Abstract (arXiv)

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.