Graph-Based ECG Synthesis with Activation-Consistency Certification and Diagnostics-Aware Morphology Curation

Abstract: Synthetic electrocardiogram (ECG) generation can support algorithm development and robustness evaluation, but simulated signals must preserve interpretable activation, recovery, and morphology properties. We present a graph-based ECG synthesis framework that combines activation-consistency certification with diagnostics-aware morphology curation. A unified heart graph supports an eikonal-template backend (ET) and a pseudo-diffusion reaction--eikonal backend (RE). We formulate graph Eikonal activation as a Bellman fixed-point problem and use the Bellman residual as a computable certificate for activation-time consistency. Each simulated ECG is evaluated by a two-stage diagnostics pipeline that separates metric computation from experiment-specific acceptance policies. On the cardiac graph, RE-derived activation times showed near-millisecond agreement with the Eikonal backbone and achieved $R^2=0.99876$ after causal predecessor filtering. Recovery experiments showed that endo-epicardial APD gradients determined the main T-wave morphology window, whereas the diffusion strength $κ$ provided secondary repolarization smoothing. In final balanced multi-lead curation, RE accepted 658/2000 samples versus 578/2000 for ET and increased per-model morphology coverage from 0.09248 to 0.09888. The framework provides a conservative basis for controllable and curated synthetic ECG generation.