Comparisons of H I – (top row) and H₂- (bottom row) halo-mass relations between TNG100 and NUM for z = 0 (left panels), z = 1 (middle panels), and z = 2 (right panels). NUM and TNG100 are represented by solid and dashed lines, respectively, with shaded areas showing the bootstrapping errors; while the results of different distances to filaments are shown as different colours: blue for 0 < d_fil/h⁻¹ Mpc < 4, orange for 4 < d_fil/h⁻¹ Mpc < 8, and red for 8 < d_fil/h⁻¹ Mpc < 12. We add observational measurements in Guo et al. (2020) at z = 0 as filled circles with error bars in the top left panel.