Determine the origin of the compressed-statistic offset

Determine whether the offset between the DESI value and the mock distributions of the compressed $T^2$ statistic is caused by covariance estimation and eigenmode truncation rather than by a simple mode-by-mode disagreement between DESI and the mocks.

Background

The paper compares the connected 4PCF measured from DESI Year 1 luminous red galaxies with EZmock and Abacus mock catalogs using the inverse-covariance-weighted $T^2$ statistic. Although the DESI and mock measurements are broadly consistent mode by mode, the compressed quadratic statistic can show an offset between the data and mock distributions.

The authors state that the origin of this offset is not fully determined and suggest covariance estimation and eigenmode truncation as possible explanations. Establishing the cause is relevant for interpreting the statistical significance of the measured 4PCF.