Density distribution of the critical points as derived from the DTFE. The left and right columns refer to the Legacy MGS and LOWZ+CMASS sample, respectively. Rows are different smoothing cycles of the density field prior to filament detection. In each panel, the solid lines refer to maxima (red), bifurcations (brown), type 2 saddles (green), type 1 saddles (yellow), and minima (blue). Only the 3σ persistence threshold case is shown, except for maxima, where the 5σ persistence sample is also reported (dashed red lines). Although indicated as 5σ, the high-persistence cut for LOWZ+CMASS in the one-smoothing case has been limited to 4.5σ.