Exact local attribution after covariance-spectrum compression

This record contains the preprint and supporting research materials for “Exact Local Attribution after Covariance-Spectrum Compression” by Surya Tallavarjula and Seyed Ali Rastegar. The paper studies statistical attribution when a complex-valued data matrix is compressed to the unordered eigenvalues of its sample covariance matrix. Near a white proper-complex Gaussian model, it derives the exact finite-dimensional local geometry of two mechanisms that affect the observed covariance spectrum: trace-preserving covariance shape and fourth-order entry-law non-Gaussianity. The principal results include: • explicit covariance-spectral scores depending only on Tr(XX*) and Tr{(XX*)²}; • the exact Fisher-information matrix coupling covariance shape and non-Gaussianity; • a sharp identifiability transition, with the two mechanisms distinguishable exactly when the number of snapshots n is greater than one; • the pointwise one-snapshot identity Uₚ,₁ = pVₚ,₁; • one-sided differentiability in quadratic mean, replicated local asymptotic normality, and boundary likelihood-ratio inference; • a physical rank-one source embedding connecting the spectral experiment to source-symbol excess kurtosis; and • exact score-mean formulas showing how dependent source dynamics enter through normalized block-energy variance. The fourth-order statistic is globally unbiased for complex excess kurtosis over standardized proper iid entry distributions with finite fourth moment and is locally efficient along the canonical minimum-information tangent. The authors retain the frozen machine-readable protocols, random seeds, package-version records, generated summary tables, complete figure-generation code, and additional exact-likelihood and fresh-block audit materials used in preparing the manuscript and supplement. These materials can be supplied to researchers upon reasonable request. This work extends the authors’ earlier study of non-Gaussianity after covariance-spectrum compression, available at: https://zenodo.org/records/21546124.