Purity-weighted quiescent fraction as a function of redshift for different richness bins, using fixed radii of 0.5 Mpc/h (left), 1.0 Mpc/h (middle), and the RMS radius (right). In the top panels, we discard all systems with negative densities, while in the bottom panels, we apply the corrections described in the text. Grayscale trend lines are reported using the pure-membership method in the same bins, for comparison. The RMS-based measurement with corrected negative densities is the method adopted in Sect. 4.2 and shown in Fig. 5.