1-cumulative density function (CDF) from sky-scrambled optimal statistic HD S/N distributions and a comparison between different methods. In the top panel, the blue histograms are for DR2full while the orange histograms are for DR2new. Vertical lines are the measured S/N_HD values reported in Table 4. The large discrepancy between the two data sets could be an indication that some remaining signal is still present after the scrambling, especially in the strong S/N regime. More checks need to be performed to assess the validity of this method. The bottom panel compares a simulated null distribution in cyan, the generalised χ² (GX2) distribution from Hazboun et al. (2023) in purple and the two proxy methods of phase shifting in orange and sky scrambling in green. At the measured value from the DR2new, the two methods differ by a factor of a few. The estimated p-values for each method are given in the legends.