ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: Residuals are in units of σ as in Fig. B1 . Following the method used in Appendix B1 , it was verified (but not shown here) that the mass gradients towards filaments after randomization of the distances D skel in bins of distances to the nearest wall D wall are substantially reduced. Only a very weak mass gradient (at a 1σ level at most) is detected after randomization even for d skel min = 2.5 Mpc. Similarly to what was found in Section B1 , increasing this parameter does not induce any substantial reduction of the gradient. Thus this distance was chosen as the limit for the exclusion region around filaments. APPENDIX C: SMALL-SCALE DENSITY-COSMIC WEB RELATION In this Appendix, the impact of the small-scale density estimator on the mass and type/colour gradients is presented. The density used here is DTFE, i.e. the density computed at the smallest possible scale. 10 As in Section 6 , the two methods, the reshuffling and density-matching, are applied. Fig. C1 shows the differential distributions of the distances to the nearest filament, D skel (normalized by 〈 D z 〉, for the same selections as in Fig. 12 . The contribution of the nodes to the measured signal is minimized, by removing from the analysis galaxies located closer to a node than 3.5 Mpc. Star-forming and passive galaxies have been matched in mass, as described in Appendix A1 . The vertical lines indicate the medians of the distributions, whose values, together with the error bars, are listed in Table F3 . Figure C1. Top rows: As in Fig. 12 , but using the DTFE density for both methods, reshuffling (Figure a) and density matching (Figure b). The numerical values of medians, shown as vertical lines, are listed in Table F3 . When the small-scale density, DTFE in this case, is used in the reshuffling method, the randomized (dashed lines) and original signal (solid lines) are nearly identical. Similarly, all gradients are almost completely erased, as expected. Bottom rows: Residuals are in unit of σ as in Fig. 12 . (a) Reshuffling. (b) Density matching. In Figure (a), the mass and type gradients are shown before (solid lines, as in 12 ) and after (dashed lines) applying the reshuffling of galaxies in the bins of overdensity (1+δ), where the number density corresponds to the DTFE density. The result conforms to the expectations. The reshuffling does not remove the observed mass and type/colour gradients, i.e. the distributions before and after the reshuffling are almost identical, suggesting that at the small scale, traced by DTFE, the density and cosmic web are closely correlated through the small-scale processes. Figure (b) illustrates the PDFs for samples that have been matched in overdensity (1 + δ), as described in Appendix A2 , where the density considered is DTFE. The density-matching technique yields qualitatively similar result than the above used reshuffling in that almost no mass and type gradients are detected when galaxies matched in the DTFE density. Qualitatively same