FCD-TITAN 2-C: Finite-Frame Transfer Compatibility: Exact Spectral-Mixing Residuals under Known Circular LTI Transfer

Abstract

Finite-Frame Transfer Compatibility: Exact Spectral-Mixing Residuals under Known Circular LTI Transfer Finite spectral estimation and known linear transfer do not generally commute. This work shows that the resulting spectral discrepancy is not merely an uncontrolled finite-window artifact: under a known circular LTI transfer and an exact all-origin finite-frame mixing kernel, the compatibility residual is analytically defined and quantitatively computable without fitted calibration. For an input power spectrum S, a nonnegative finite-frame mixing operator K, and power transfer a=∣H∣2, the fitted log-frequency slope of the compatibility defect is exactly the residual between ideal transfer slope and observed spectral-slope migration on a fixed frequency mask. Its pointwise depth curvature is also determined by a variance of log transfer gain under a depth-tilted spectral measure. The frozen benchmark contains 64 synthetic records and 65 nonoverlapping real-data blocks from electrocardiography, Bitcoin minute returns, and solar-wind magnetic-field data. Across 3483 retained cells, pooled R2 for ΔR4=R4−R3 ranges from 0.9891 to 0.9994 across the nine real dataset–estimator groups. After removing fixed-configuration means, R2 remains 0.6608–0.9943; across 81 fixed real configurations, the median R2 is 0.8782. The record includes the manuscript, frozen data, executed publication run, source code, dependency specification, provenance and licensing documentation, and SHA-256 manifests required to reproduce and audit the reported results. Reproducibility DOI: 10.5281/zenodo.22056027Corresponding author: gmtheory@outlook.fr Licensing is file- and source-specific. See DATA_LICENSES_AND_ATTRIBUTION.md for upstream licenses, attribution requirements, and provenance of the redistributed data.