Provenance and Covariance Sensitivity in a Summary-Level Comparison of Sound-Horizon-Free Hubble-Constant Measurements

This technical note presents a reproducible, summary-level audit of covariance assumptions and source provenance in a published compilation of 88 sound-horizon-free Hubble-constant (H₀) measurements, comprising 30 distance-ladder estimates and 58 comparison estimates. The analysis first reproduces inverse-variance weighted means and their nominal contrast under an independence assumption. It then examines how illustrative within-group equicorrelation models affect generalized least-squares (GLS) estimates, uncertainties, and the resulting statistical contrast. The technical contributions include a closed-form, O(n) expression for equicorrelated GLS, an exact condition for the sign of individual weights, the effective-sample-size limit under equicorrelation, positive-semidefinite constraints on cross-group correlation, sensitivity of the contrast to pooled-mean correlation, and a worst-case variance bound under an entrywise correlation constraint. The study also investigates source provenance and reconstructs the 88-entry comparison table from the source paper’s appendix. It identifies a discrepancy between one tabulated H₀ estimate and its cited source, and examines how alternative dependence assumptions affect the resulting statistical contrast. The results distinguish between generic correlation structures and sign-coherent shared systematic effects. They show that the inferred contrast can depend materially on the assumed covariance structure, while emphasizing that summary-level calculations cannot establish the true joint covariance of the underlying measurements. Scope and limitations: All reported statistics are conditional on the compiled values, uncertainty conventions, and specified covariance assumptions. This work does not establish that the Hubble tension has disappeared, determine its definitive statistical significance, or recommend excluding any measurement. A companion C++17/Python library provides implementations of the analysis and supports reproducibility and independent verification.