Colless M. et al., 2001, MNRAS, 328, 1039

Conroy C., Wechsler R. H., Kravtsov A. V., 2006, ApJ, 647, 201

Conroy C., Gunn J. E., White M., 2009, ApJ, 699, 486

de la Torre S. et al., 2013, A&A, 557, A54

DESI Collaboration et al., 2016, preprint (arXiv:1611.00036)

Dembinski H. et al., 2024, Zenodo.

Duarte M., Mamon G. A., 2015, MNRAS, 453, 3848

Dubois Y. et al., 2014, MNRAS, 444, 1453

Eisenstein D. J. et al., 2005, ApJ, 633, 560

Eisenstein D. J., Seo H.-J., Sirko E., Spergel D. N., 2007, ApJ, 664, 675

Feldman H. A., Kaiser N., Peacock J. A., 1994, ApJ, 426, 23

Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125, 306

Gao L., Springel V., White S. D. M., 2005, MNRAS, 363, L66

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Gorski K. M., Wandelt B. D., Hansen F. K., Hivon E., Banday A. J., 1999, preprint(astro-ph/9905275)

Guo H. et al., 2015, MNRAS, 453, 4368

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Ishiyama T., Nitadori K., Makino J., 2012, preprint (arXiv:1211.4406)

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Kaiser N., 1987, MNRAS, 227, 1

Kauffmann G. et al., 2003, MNRAS, 341, 33

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Klypin A., Holtzman J., 1997, preprint(astro-ph/9712217)

Klypin A., Prada F., 2018, MNRAS, 478, 4602

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Lin S. et al., 2020, MNRAS, 498, 5251

Loveday J. et al., 2012, MNRAS, 420, 1239

Marinoni C., Hudson M. J., 2002, ApJ, 569, 101

McCullagh N., Norberg P., Cole S., Gonzalez-Perez V., Baugh C., Helly J., 2017, preprint (arXiv:1705.01988)

Moustakas J. et al., 2013, ApJ, 767, 50

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Perlmutter S. et al., 1999, ApJ, 517, 565

Pillepich A. et al., 2018, MNRAS, 475, 648

Planck Collaboration XIII, 2016, A&A, 594, A13

Planck Collaboration VI, 2020, A&A, 641, A6

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Rodríguez-Torres S. A. et al., 2016, MNRAS, 460, 1173

Ross A. J., Samushia L., Howlett C., Percival W. J., Burden A., Manera M., 2015, MNRAS, 449, 835

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Zehavi I. et al., 2011, ApJ, 736, 59

Zhao C. et al., 2021, MNRAS, 503, 1149

## SUPPORTING INFORMATION

Supplementary data are available at MNRAS online.

Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

## APPENDIX A: THE EFFECT OF SCATTER IN SHAM

As discussed in Section 3.2, our SHAM model has only one free parameter $\sigma$, which roughly corresponds to the scatter in $0.1 M_r^h$ at a fixed value of our halo mass proxy, Vpeak. In practice, the value of $\sigma$ affects mainly the amplitude of the TPCF for a given volume-limited sample, results are shown in Fig. 1 for different values of the scatter. Increasing the value of $\sigma$ introduces a larger number of low-$V_{peak}$ galaxies into the volume-limited samples, which are weakly clustered (and also removes high-$V_{peak}$ galaxies, which are strongly clustered). This has the effect of decreasing the amplitude of the TPCF. The effect of scatter is consequently larger for strongly clustered volume-limited samples, becoming negligible for samples with magnitude threshold $0.1 M_r^h > -20$. In order to tune the scatter parameter, we optimize the goodness-of-fit of the TPCF monopole for the Uchuu snapshot at $z = 0.093$ to the SDSS measurements, finding an optimal value of $\sigma = 0.5$. We choose this snapshot since it is the closest to the median SDSS redshift $z = 0.1$.

This value is in agreement with previous observational estimations of the scatter using SHAM. For example, Trujillo-Gomez et al. (2011) estimate the scatter of $0.1 M_r^h$ at fixed halo circular velocity, by combining an estimate of the intrinsic scatter of the Tully-Fisher relation (Verheijen 2001) with the scatter resulting from the distribution of dust extinction corrections in SDSS, arriving precisely at a value of 0.5.
Colless M. et al., 2001, MNRAS, 328, 1039
Conroy C., Wechsler R. H., Kravtsov A. V., 2006, ApJ, 647, 201
Conroy C., Gunn J. E., White M., 2009, ApJ, 699, 486
de la Torre S. et al., 2013, A&A, 557, A54
DESI Collaboration et al., 2016, preprint (arXiv:1611.00036)
Dembinski H. et al., 2024, Zenodo.
Duarte M., Mamon G. A., 2015, MNRAS, 453, 3848
Dubois Y. et al., 2014, MNRAS, 444, 1453
Eisenstein D. J. et al., 2005, ApJ, 633, 560
Eisenstein D. J., Seo H.-J., Sirko E., Spergel D. N., 2007, ApJ, 664, 675
Feldman H. A., Kaiser N., Peacock J. A., 1994, ApJ, 426, 23
Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125, 306
Gao L., Springel V., White S. D. M., 2005, MNRAS, 363, L66
Gelman A., Rubin D. B., 1992, Stat. Sci., 7, 457
Gorski K. M., Wandelt B. D., Hansen F. K., Hivon E., Banday A. J., 1999, preprint(astro-ph/9905275)
Guo H. et al., 2015, MNRAS, 453, 4368
Guzzo L. et al., 2008, Nature, 451, 541
Hartlap J., Simon P., Schneider P., 2007, A&A, 464, 399
Hayashi E., Navarro J. F., Taylor J. E., Stadel J., Quinn T., 2003, ApJ, 584, 541
Howlett C., Ross A. J., Samushia L., Percival W. J., Manera M., 2015, MNRAS, 449, 848
Ishiyama T., Fukushige T., Makino J., 2009, PASJ, 61, 1319
Ishiyama T., Nitadori K., Makino J., 2012, preprint (arXiv:1211.4406)
Ishiyama T. et al., 2021, MNRAS, 506, 4210
Ivezić Ž. et al., 2019, ApJ, 873, 111
Kaiser N., 1987, MNRAS, 227, 1
Kauffmann G. et al., 2003, MNRAS, 341, 33
Kennicutt R. C., Jr, 1998, ARA&A, 36, 189
Klypin A., Holtzman J., 1997, preprint(astro-ph/9712217)
Klypin A., Prada F., 2018, MNRAS, 478, 4602
Kravtsov A. V., Berlind A. A., Wechsler R. H., Klypin A. A., Gottlöber S., Allgood B., Primack J. R., 2004, ApJ, 609, 35
Kroupa P., 2001, MNRAS, 322, 231
LSST Science Collaboration et al., 2009, preprint (arXiv:0912.0201)
Laureijs R. et al., 2011, preprint (arXiv:1110.3193)
Leslie S. K., Kewley L. J., Sanders D. B., Lee N., 2016, MNRAS, 455, L82
Lin S. et al., 2020, MNRAS, 498, 5251
Loveday J. et al., 2012, MNRAS, 420, 1239
Marinoni C., Hudson M. J., 2002, ApJ, 569, 101
McCullagh N., Norberg P., Cole S., Gonzalez-Perez V., Baugh C., Helly J., 2017, preprint (arXiv:1705.01988)
Moustakas J. et al., 2013, ApJ, 767, 50
Peebles P. J. E., 1980, The large-scale structure of the universe, Princeton University Press, Princeton, United States.
Perlmutter S. et al., 1999, ApJ, 517, 565
Pillepich A. et al., 2018, MNRAS, 475, 648
Planck Collaboration XIII, 2016, A&A, 594, A13
Planck Collaboration VI, 2020, A&A, 641, A6
Reddick R. M., Wechsler R. H., Tinker J. L., Behroozi P. S., 2013, ApJ, 771, 30
Riess A. G. et al., 1998, AJ, 116, 1009
Rodríguez-Torres S. A. et al., 2016, MNRAS, 460, 1173
Ross A. J., Samushia L., Howlett C., Percival W. J., Burden A., Manera M., 2015, MNRAS, 449, 835
Safonova S., Norberg P., Cole S., 2021, MNRAS, 505, 325
Salim S. et al., 2007, ApJS, 173, 267
Schaye J. et al., 2015, MNRAS, 446, 521
Seljak U., McDonald P., 2011, J. Cosmol. Astropart. Phys., 2011, 039
Shu Y., Bolton A. S., Schlegel D. J., Dawson K. S., Wake D. A., Brownstein J. R., Brinkmann J., Weaver B. A., 2012, AJ, 143, 90
Skibba R. A., Sheth R. K., 2009, MNRAS, 392, 1080
Smith A., Cole S., Baugh C., Zheng Z., Angulo R., Norberg P., Zehavi I., 2017, MNRAS, 470, 4646
Smith A. et al., 2019, MNRAS, 484, 1285

Smith A., Cole S., Grove C., Norberg P., Zarrouk P., 2022a, MNRAS, 516, 1062

Smith A., Cole S., Grove C., Norberg P., Zarrouk P., 2022b, MNRAS, 516, 4529

Springel V. et al., 2018, MNRAS, 475, 676

Stiskalek R., Desmond H., Holvey T., Jones M. G., 2021, MNRAS, 506, 3205

Swanson M. E. C., Tegmark M., Hamilton A. J. S., Hill J. C., 2008, MNRAS, 387, 1391

Szewciw A. O., Beltz-Mohrmann G. D., Berlind A. A., Sinha M., 2022, ApJ, 926, 15

Takada M. et al., 2014, PASJ, 66, R1

Taruya A., Nishimichi T., Saito S., 2010, Phys. Rev. D, 82, 063522

Taylor E. N. et al., 2011, MNRAS, 418, 1587

Trujillo-Gomez S., Klypin A., Primack J., Romanowsky A. J., 2011, ApJ, 742, 16

Vale A., Ostriker J. P., 2004, MNRAS, 353, 189

Verheijen M. A. W., 2001, ApJ, 563, 694

Wechsler R. H., 2001, PhD thesis, University Of California, Santa Cruz

Wechsler R. H., Tinker J. L., 2018, ARA&A, 56, 435

Wechsler R. H., Zentner A. R., Bullock J. S., Kravtsov A. V., Allgood B., 2006, ApJ, 652, 71

White M., 2015, MNRAS, 450, 3822

White M., Tinker J. L., McBride C. K., 2014, MNRAS, 437, 2594

York D. G. et al., 2000, AJ, 120, 1579

Zehavi I. et al., 2005, ApJ, 630, 1

Zehavi I. et al., 2011, ApJ, 736, 59

Zhao C. et al., 2021, MNRAS, 503, 1149

## SUPPORTING INFORMATION

Supplementary data are available at MNRAS online.

Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

## APPENDIX A: THE EFFECT OF SCATTER IN SHAM

As discussed in Section 3.2, our SHAM model has only one free parameter $\sigma$, which roughly corresponds to the scatter in $0.1 M_r^h$ at a fixed value of our halo mass proxy, Vpeak. In practice, the value of $\sigma$ affects mainly the amplitude of the TPCF for a given volume-limited sample, results are shown in Fig. 1 for different values of the scatter. Increasing the value of $\sigma$ introduces a larger number of low-$V_{\text{peak}}$ galaxies into the volume-limited samples, which are weakly clustered (and also removes high-$V_{\text{peak}}$ galaxies, which are strongly clustered). This has the effect of decreasing the amplitude of the TPCF. The effect of scatter is consequently larger for strongly clustered volume-limited samples, becoming negligible for samples with magnitude threshold $0.1 M_r^h > -20$. In order to tune the scatter parameter, we optimize the goodness-of-fit of the TPCF monopole for the Uchuu snapshot at $z = 0.093$ to the SDSS measurements, finding an optimal value of $\sigma = 0.5$. We choose this snapshot since it is the closest to the median SDSS redshift $z = 0.1$.

This value is in agreement with previous observational estimations of the scatter using SHAM. For example, Trujillo-Gomez et al. (2011) estimate the scatter of $0.1 M_r^h$ at fixed halo circular velocity, by combining an estimate of the intrinsic scatter of the Tully-Fisher relation (Verheijen 2001) with the scatter resulting from the distribution of dust extinction corrections in SDSS, arriving precisely at a value of 0.5.
<figure><img src="image_20.png" /></figure>

**Figure B1.** Difference in the magnitude and stellar mass distributions between SDSS and the Uchuu mock. The plot shows $(f_i^{\text{SDSS}} - f_i^{\text{Uchuu}})/f_i^{\text{av}}$, where $f_i$ is the fraction of galaxies in each bin of redshift and magnitude (or stellar mass) from SDSS or Uchuu, and $f_i^{\text{av}}$ is the average of these. Blue indicates there are more galaxies in the mock, while red indicates that there are more galaxies in SDSS. In bins where there are many galaxies, the differences are small. Some vertical features can be seen, due to large-scale structure in the catalogues.

## APPENDIX B: THE DIFFERENCE BETWEEN THE UCHUU AND SDSS MAGNITUDE DISTRIBUTIONS

To highlight the differences between the Uchuu mock and the SDSS data in terms of the distribution of properties (magnitudes, stellar masses) as a function of redshift, we show the residuals in Fig. B1.

The difference between the frequency of galaxies in each bin for SDSS and Uchuu ($f_i^{\text{SDSS}}$ and $f_i^{\text{Uchuu}}$ respectively), normalized by the average density of the two samples, is very small except for the regions of the very low density of points.

This paper has been typeset from a TeX/LA TeX file prepared by the author.
<figure><img src="image_21.png" /></figure>

**Figure B1.** Difference in the magnitude and stellar mass distributions between SDSS and the Uchuu mock. The plot shows $(f_i^{SDSS} - f_i^{Uchuu})/f_i^{av}$, where $f_i$ is the fraction of galaxies in each bin of redshift and magnitude (or stellar mass) from SDSS or Uchuu, and $f_i^{av}$ is the average of these. Blue indicates there are more galaxies in the mock, while red indicates that there are more galaxies in SDSS. In bins where there are many galaxies, the differences are small. Some vertical features can be seen, due to large-scale structure in the catalogues.

## APPENDIX B: THE DIFFERENCE BETWEEN THE UCHUU AND SDSS MAGNITUDE DISTRIBUTIONS

To highlight the differences between the Uchuu mock and the SDSS data in terms of the distribution of properties (magnitudes, stellar masses) as a function of redshift, we show the residuals in Fig. B1.

The difference between the frequency of galaxies in each bin for SDSS and Uchuu ($f_i^{SDSS}$ and $f_i^{Uchuu}$ respectively), normalized by the average density of the two samples, is very small except for the regions of the very low density of points.

This paper has been typeset from a TeX/LATEX file prepared by the author.