Comparison of the observational dataset (black points) to the 2D probability histogram reconstruction algorithm (see Sect. 3.8) applied to the fiducial simulation (colored histogram). Results are shown for two resolutions, R = 64³ (top panel) and R = 512³ (bottom panel). Observations include detections of H₂ (circles) and upper limits on N(H₂) (arrows). The color code indicates the fraction of lines of sight (in logarithmic scale) contained in each bin. As a reminder, contours of the regions A, B, C, D, and E defined in Sect. 2 (see Table 1) are also displayed.