Upper panel: Histograms of normalized residuals for the best-fit AvERA-625k and flat ΛCDM models, fit to the Pantheon+ SN Ia data (Scolnic et al. 2022). The red curve represents the standard normal distribution expected for the true model underlying the data. Lower panel: Histograms of AD-test log₁₀p values for half a million realizations sampled from the joint posterior distributions. The dashed vertical line marks the significance threshold of p = 0.05 (log₁₀p = −1.301) for consistency with the null hypothesis of being the true model. While none of the realizations reach this level, the preference for the AvERA model is clearly evident.