Surface-Aware Interpretable Geometry for ECG-AI Trust Boundaries, with Calibrated Abstention

This preprint presents a first-principles, orthogonally invariant eigenvalue-spectral ECG metric layer for grounding, auditing, and triangulating cardiac AI, evaluated retrospectively on public de-identified ECG datasets. Multilead segments are summarized through covariance-state features computed on the eigenvalue spectrum of windowed, delay-embedded covariance matrices on the symmetric positive-definite cone; because these features depend only on the eigenvalue distribution, they are invariant to the orthogonal (heartbeat-driven) rotation of the covariance eigenvectors. A surface-aware metric-family router selects, per (ECG-surface x cardiac-condition) cell, from a heterogeneous registry of geometric metric families, with an explicit calibrated- abstention path when comparable saved evidence is unavailable. A between-subject five-family ellipsoid battery across five PTB-XL conditions (patient-level permutation nulls, family-wise correction) shows the winning metric family changes by condition, so no single universal metric dominates — the empirical motivation for routing. The manuscript states its evidence ceiling plainly: the reported routing gain is an oracle ceiling rather than a held-out result, the abstention gate is an evidence-availability filter without a measured operating characteristic, the headline atrial-fibrillation AUC rests on a small positive cohort (41 positives), and the work does not claim a cleared device, a clinically validated router, or restored dwell-time performance. It is framed as a biomedical-informatics methods paper supporting a trust-layer, routing/abstention architecture, and validation agenda — not solved clinical alerting.