On DESI's DR2 exclusion of $\Lambda$CDM

The DESI collaboration, combining their Baryon Acoustic Oscillation (BAO) data with cosmic microwave background (CMB) anisotropy and supernovae data, have found significant indication against the $\Lambda$CDM cosmology. This can also be interpreted as the significance of the detection of the $w_a$ parameter that measures variation of the dark energy equation of state. DESI's DR2 article quotes exclusion of $\Lambda$CDM for combinations of BAO and CMB data with each of three different and overlapping supernovae compilations (at 2.8-sigma for Pantheon+, 3.8-sigma for Union3, and 4.2-sigma for DESY5). We show that one can neither choose amongst nor average over these three different significances. We demonstrate how a principled statistical combination yields a combined exclusion significance of 3.1-sigma. Further we argue that, faced with these competing significances, the most secure inference from the DESI DR2 results is the 3.1-sigma level exclusion of $\Lambda$CDM obtained from combining DESI+CMB alone, omitting supernovae.