Test to distinguish between the two extreme scenarios in terms of cosmic evolution of the luminosity function. Top panel: redshift cumulative distribution function of the intrinsic E_p − L correlation scenarios cut at ℱ_cut = 10⁻⁶ ph cm⁻² for k_evol = 0 in dark blue and k_evol = 2 in light blue. The k_evol = 2 scenario is sub-sampled at N_sub = 117; the 95% confidence bound is calculated from bootstrapping. Bottom panel: distribution of p-values (right) and D-statistics (left) from the K–S tests performed on the bootstrapped samples. The back dashed vertical line shows a p-value of 0.05, below which it is possible to distinguish between the two distributions at the 95% confidence level.