A Deterministic Operator-Based Framework for Early-Warning Detection in Coupled EEG–ECG Time Series Interpretable Heart–Brain Isostasis Monitoring via Triadic Phase Embeddings

Cardiac and neural systems form a coupled regulatory unit whose dysregulation can precede acute events such as arrhythmia or seizure-associated autonomic instability. We present a deterministic, operator-based monitoring framework that embeds EEG and ECG/HRV time series into a triadic representation $\psi(t)=t+i\phi(t)+j\chi(t)$, where $\chi(t):=\partial_t \phi(t)$ serves as a sensitive marker of nonstationary regime transitions. A preregistered instability functional $\Delta\Phi(t)$ aggregates spectral and morphological deviation, information-theoretic deviation, and cross-modal coupling deviation under fixed, transparent weights and thresholds. The framework is explicitly positioned as an interpretable signal-analysis and prospective validation protocol. It does not assert new biophysical laws of physiological time and does not prescribe therapeutic intervention or closed-loop control. We define null-test baselines, modality ablations (EEG-only, ECG-only, and coupled), and validation metrics including lead-time distributions and false-alarm rates. The resulting methodology is suitable for preregistered prospective studies and device-level decision support in coupled heart--brain monitoring systems.