From Orthogonal Invariance to Walsh Spectral Multipliers: Final Reproducibility Package for Lead-Conditioned Reference Geometry and Exact Attribution in 12-Lead ECG

This archive contains the final frozen reproducibility package for the study “From Orthogonal Invariance to Walsh Spectral Multipliers: Lead-Conditioned Reference Geometry and Exact Attribution for 12-Lead ECG”. The work develops a mathematically structured reference-based framework for ECG analysis in Walsh-Hadamard coordinates. A central theoretical point is the exact orthogonal invariance of full-covariance quadratic scoring: under an orthonormal Walsh-Hadamard transform, the corresponding full-covariance Mahalanobis score is identical to its time-domain representation. Consequently, genuinely Walsh-dependent modelling enters only when additional coordinate-dependent structure is imposed, including diagonal covariance, spectral/sequence conditioning, regularization, truncation, or Walsh spectral multipliers. The framework also provides an exact algebraic attribution of a quadratic Walsh-domain score. For Q(z)=z^T A z, coordinate contributions c_k=z_k(Az)_k satisfy the conservation identity Q(z)=sum_k c_k. The final empirical study uses PTB-XL v1.0.3 at 100 Hz under patient/fold-wise separation. Folds 1–8 are used for NORM reference estimation, fold 9 for validation/model selection, and fold 10 is retained as the locked confirmatory test set. The final test cohort contains 2,198 ECG records from 1,904 patients. The pre-specified primary confirmatory task is NORM versus HYP. The locked full-covariance 12-lead reference score achieves AUROC 0.841850 (95% CI 0.811266–0.870301) and AUPRC 0.667356 (95% CI 0.603465–0.732388). Secondary confirmatory analyses include NORM versus CD, STTC, and MI. The frozen comparator study evaluates full-covariance reference scoring, diagonal Mahalanobis scoring, PCA reconstruction, and Isolation Forest on the same final test cohort. For NORM versus HYP, their audited AUROC values are 0.841850, 0.860415, 0.678791, and 0.866488, respectively. These results are retained without post-hoc modification and no claim is made that the proposed full-covariance construction outperforms every generic anomaly-detection baseline. The archive LCRG_PUBLICATION_FREEZE.zip contains the locked confirmatory results, comparator outputs, paired comparisons, and publication-audit materials. The automated final audit verifies cohort sizes, locked primary results, comparator results, finite scores, and consistency of the final test cohort, and terminates with “FINAL PUBLICATION AUDIT: ALL PASS”. The PTB-XL data themselves are not redistributed. The package is intended for mathematical, methodological, and reproducibility verification and is not presented as prospective clinical diagnostic validation. The corresponding manuscript is under journal submission.