Pith. sign in

REVIEW 2 major objections 5 minor 91 references

Diffhalos generates cosmological lightcones of dark matter halos, subhalos, and mass assembly histories that match N-body statistics.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-14 11:53 UTC pith:3HOLU33Z

load-bearing objection Solid, usable JAX light-cone generator that couples HMF sampling, subhalos, and DiffmahNet MAHs; the engineering is real and the soft spots are openly stated. the 2 major comments →

arxiv 2607.10419 v1 pith:3HOLU33Z submitted 2026-07-11 astro-ph.GA astro-ph.CO

Diffhalos: A Generative Model of Cosmological Lightcones of Dark Matter Halos

Georgios Zacharegkas , Andrew P. Hearin , Alan Pearl , Matthew R. Becker , Florian K\'eruzor\'e , Sara Ortega-Martinez This is my paper
classification astro-ph.GA astro-ph.CO
keywords dark matter haloslightconeshalo mass functionsubhalosmass assembly historynormalizing flowsdifferentiable cosmologymock catalogs
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Cosmology surveys need realistic populations of dark matter structures across redshift, but full N-body lightcones are expensive. Diffhalos builds those populations by sampling host halos from a differentiable mass function, painting subhalos from a conditional mass-ratio model, and assigning each object a mass assembly history drawn from a normalizing flow trained on merger trees. The resulting catalogs reproduce the statistical distributions of simulated lightcones, while automatic differentiation yields direct gradients of the mass functions with respect to cosmological parameters. Because the generators also support lightweight quasi-Monte Carlo grids, the same framework can produce both large mock catalogs and small, abundance-weighted samples for calibrating galaxy–halo models.

Core claim

Diffhalos produces Monte Carlo and quasi-Monte Carlo lightcones of host halos, subhalos, and their mass assembly histories whose joint distributions in mass, redshift, and assembly closely approximate those measured in N-body simulations, while remaining fully differentiable with respect to cosmological parameters.

What carries the argument

A three-stage generative pipeline: inverse-transform sampling of a cumulative, differentiable halo mass function; sampling of a conditional cumulative subhalo mass function in the mass ratio µ; and DiffmahNet, a normalizing flow that maps (M_obs, t_obs) to Diffmah mass-assembly parameters.

Load-bearing premise

The model treats the conditional subhalo mass function as independent of redshift and trains the assembly-history flow on merger trees from only one cosmology.

What would settle it

Generate a Diffhalos lightcone at a cosmology and redshift range outside the training set and compare its host and subhalo mass functions and assembly-history distributions against an independent high-resolution N-body lightcone; systematic mismatches would falsify the claimed statistical fidelity.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper introduces Diffhalos, a JAX-based generative pipeline for cosmological lightcones of dark matter host halos, subhalos, and their mass assembly histories (MAHs). Hosts are drawn by inverse-transform sampling of a cumulative HMF (either Halox/Tinker or a sig-slope MLP emulator of N_halo(>m,z)); subhalos are drawn from a conditional cumulative subhalo mass function N_sub(>μ|M_host) calibrated to Discovery/Bolshoi-style fits; MAHs are assigned by DiffmahNet, a normalizing flow that samples Diffmah parameters conditioned on observed mass and time. Monte Carlo and memory-efficient quasi-Monte Carlo generators are provided. Component-wise comparisons to Colossus, SMDPL, and Discovery show percent-to-10% agreement on mass functions and MAH means/variances (Figs. 1–4, 6–9), autodiff gradients of the HMF match finite differences (Fig. 2), and an example application computes cosmological derivatives of the halo and subhalo mass functions. The authors discuss intended use with galaxy–halo models (Diffsky/DiffstarPop) and list planned extensions (cosmology-dependent CSHMF/MAHs, density-field coupling).

Significance. If the claimed statistical fidelity holds for joint lightcone populations, Diffhalos supplies a practical, differentiable, and publicly available alternative to full N-body lightcones for calibrating galaxy–halo connection models and generating abundance-weighted mocks. Strengths include the autodiff implementation (enabling gradient-based inference), the dual MC/QMC generators that address memory limits, open code, and transparent component-wise validation against established libraries and public merger trees. The work is a useful proof-of-concept infrastructure paper rather than a new precision emulator; its main value is the modular pipeline that can be upgraded with existing high-accuracy HMF emulators and multi-cosmology merger-tree suites.

major comments (2)
  1. §6 explicitly states that the CCSHMF is taken independent of redshift (“we neglect the weak redshift dependence”) and is calibrated only versus host mass; Fig. 6 shows total host+sub mass functions at several redshifts, but the joint (M_sub, z) distribution across a full lightcone is not validated against a simulated lightcone. Because a lightcone spans z=0–5, residual redshift evolution of the unevolved subhalo mass function can bias high-z satellite abundances. A quantitative residual plot (or an explicit upper bound drawn from Jiang & van den Bosch 2016 / Discovery) of N_sub(>μ|M_host,z) versus the redshift-independent model is needed to support the Abstract claim of statistical fidelity for lightcone populations.
  2. §7 trains DiffmahNet exclusively on SMDPL (one cosmology). The Abstract and §8 advertise cosmology-dependent lightcones and gradients of the HMF/subhalo MF (Fig. 2), yet MAH diversity is frozen to the SMDPL cosmology. Piecewise recovery of SMDPL MAH means/variances (Fig. 9) does not guarantee that the joint (M,z,θ_MAH) distribution remains accurate when θ_cosmo is varied. Either restrict the cosmology-variation claims to the HMF stage alone, or supply a cross-check (even on a second public box) quantifying MAH bias under modest Ω_m/σ_8 shifts.
minor comments (5)
  1. Fig. 3 caption and text claim “10% or better” accuracy for the MLP emulator; the bottom residual panels show excursions approaching or exceeding 10% at the high-mass end for some redshifts. Soften the wording or quote the actual max residual.
  2. Notation: m_halo ≡ log10 M_halo is introduced in §2.1 but occasionally mixed with M_halo in figure labels and axis titles; a single consistent convention would improve readability.
  3. The updated 5-parameter Diffmah model (including t_peak) is only referenced via Alarcon et al. 2025 Appendix A; a one-sentence definition of the five parameters in §7 would make the paper self-contained.
  4. §5 QMC description is brief; stating the typical N_grid and the precise weight normalization used for summary statistics would aid reproducibility.
  5. Typos / style: “lighcone” (p. 3), “Diffhaloscan” / “Diffhalosto” spacing artifacts in the Abstract and §1, and occasional missing spaces after periods.

Circularity Check

0 steps flagged

No significant circularity: generative sampling recovers fitted analytic models and training simulations by design of inverse-transform and density estimation, with only minor non-load-bearing self-citations to prior libraries.

full rationale

The paper constructs Diffhalos as a three-stage Monte Carlo / quasi-Monte Carlo generator (host HMF via Halox or MLP emulator of cumulative N_halo, conditional subhalo mass function via sig-slope kernel, MAHs via DiffmahNet normalizing flow). Component-wise validation (Figs. 4, 6–9) shows that samples recover the analytic HMF/CSHMF by construction of inverse-transform sampling and recover the mean/variance of SMDPL MAHs by construction of a trained density estimator; these are standard checks for a generative model, not circular reductions of a claimed first-principles derivation. Calibrations of the CSHMF and DiffmahNet use external public N-body products (Discovery, SMDPL/Rockstar/ConsistentTrees, Jiang & van den Bosch fitting functions) and are reported as such. Self-citations to Diffmah (H21) and Halox supply reusable libraries whose internal accuracy is independently demonstrated against Colossus/Tinker; they do not supply a uniqueness theorem or force the central statistical-fidelity claim. Assumptions such as redshift-independent CSHMF and single-cosmology DiffmahNet training are limitations of scope, not circular steps. Score 1 reflects only the presence of ordinary co-author library citations that are not load-bearing for the result.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 2 invented entities

The central claim rests on standard CDM halo-model machinery plus a handful of fitted functional forms and a neural density estimator trained on one simulation suite. Free parameters are the coefficients of the sig-slope kernels, the MLP weights that map cosmology to those kernels, and the normalizing-flow parameters of DiffmahNet. Domain assumptions include the Tinker mass function, the Jiang & van den Bosch subhalo fitting functions, and the Diffmah parametric form itself. No new physical entities are postulated.

free parameters (4)
  • sig-slope HMF kernel parameters θ_HMF
    Coefficients of the cumulative power-law-plus-sigmoid form that is emulated by the MLP; fitted to Colossus/Tinker predictions across mass and redshift.
  • MLP weights mapping θ_cosmo → θ_HMF
    Neural-network parameters trained on a grid of Ωm–σ8 cosmologies; accuracy quoted at ~10 %.
  • CCSHMF sig-slope parameters
    Coefficients of the conditional cumulative subhalo mass function, tuned to Discovery simulation measurements and Jiang & van den Bosch forms.
  • DiffmahNet normalizing-flow parameters
    Weights of the flow that approximates P(θ_MAH | M_obs, t_obs); trained on SMDPL Rockstar/ConsistentTrees merger trees.
axioms (4)
  • domain assumption The Tinker et al. (2008) fitting formula for f(σ) accurately describes the halo mass function to ~10–20 %.
    Used throughout §4 and as the training target for the MLP emulator; accuracy ceiling acknowledged by the authors.
  • domain assumption The unevolved conditional subhalo mass function has negligible redshift dependence.
    Explicitly adopted in §6 after citing Jiang & van den Bosch (2016); load-bearing for the light-cone generator.
  • domain assumption Halo mass assembly histories are well approximated by the five-parameter Diffmah functional form.
    Foundation of DiffmahNet (§7); inherited from Hearin et al. (2021) and Alarcon et al. (2025).
  • domain assumption Standard ΛCDM linear power spectrum and spherical-collapse mass variance (Eqs. 1–2).
    Inherited via Halox/jax-cosmo; used for all analytic HMF gradients.
invented entities (2)
  • Diffhalos generative pipeline independent evidence
    purpose: End-to-end Monte-Carlo / quasi-Monte-Carlo light-cone generator that couples HMF, CSHMF and MAH sampling in JAX.
    The software framework itself is the paper’s primary contribution; it is a computational construct, not a new physical object.
  • DiffmahNet independent evidence
    purpose: Normalizing-flow density estimator for Diffmah parameters conditioned on observed mass and time.
    New trained model released with the paper; independent evidence is the public code and the SMDPL training set.

pith-pipeline@v1.1.0-grok45 · 22109 in / 2945 out tokens · 38068 ms · 2026-07-14T11:53:17.866517+00:00 · methodology

0 comments
read the original abstract

We present a generative model of cosmological lightcones of dark matter halos, Diffhalos. In our model, we draw Monte Carlo samples of the halo mass function in a lightcone with a JAX-based implementation of the halo model, Halox, and we generate samples of subhalos by drawing from a model for the conditional subhalo mass function. We generate mass assembly histories (MAHs) using a normalizing flow trained on merger trees in cosmological N-body simulations. We show that Diffhalos can generate samples of halos, subhalos, and their MAHs with a statistical distribution that accurately approximates populations in simulated lightcones. As an example application, we use Diffhalos to calculate gradients of the halo and subhalo mass functions with respect to cosmological parameters. We conclude with a discussion of ongoing work using Diffhalos together with models of the galaxy--halo connection to make theoretical predictions for cosmological populations of galaxies, and to generate mock galaxy catalogs.

Figures

Figures reproduced from arXiv: 2607.10419 by Alan Pearl, Andrew P. Hearin, Florian K\'eruzor\'e, Georgios Zacharegkas, Matthew R. Becker, Sara Ortega-Martinez.

Figure 1
Figure 1. Figure 1: — Comparison between HMF predictions from Halox (solid) and Colossus (dashed) for two different cosmologies: Planck 2018 on the top and a low S8 cosmology on the bottom. Below each panel we also show the fractional differences between the two models. Predictions are compared for redshifts ranging from z = 0 (purple) to z = 5 (yellow). model in jax (K´eruzor´e & Moreau 2025). Halox sup￾ports cosmology depen… view at source ↗
Figure 2
Figure 2. Figure 2: — Comparison between predictions of HMF gradients with respect to the cosmological parameters Ωm (top) and σ8 (bot￾tom) using Halox (solid gray) and Colossus (dashed orange). to K´eruzor´e & Moreau (2025) for further discussion of Halox. 4.2. Emulator-based calculation The halo model calculation outlined in §4.1 is a flex￾ible technique for capturing the cosmology-dependence of the HMF, but using this tech… view at source ↗
Figure 5
Figure 5. Figure 5: — Example halo lightcones, presented by the redshift distribution dnhalo/dz of the halos, generated by Monte Carlo (MC) vs quasi-Monte Carlo (QMC) techniques in the redshift range z ∈ [0, 5]. In the MC method, the entire halo population in the lightcone volume is generated; the QMC lightcone is a fast and lightweight alternative based on a weighted grid. See §5 for de￾tails. tion of MC-generated halos agre… view at source ↗
Figure 4
Figure 4. Figure 4: — Comparison between the Monte Carlo realizations (solid) of the HMF and the analytical model predictions (dashed). Different panels correspond to different cosmologies, while different colored lines represent different redshifts ranging from z = 0 to z = 5, as indicated in the legend [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: — Comparison of the total mass function of host halos and subhalos between N-body simulations (solid) and the Diffhalos approximation (dashed). Different colored curves show compar￾isons at different redshifts in the range 0 < z < 4. parameterized model for the conditional cumulative sub￾halo mass function (CCSHMF). Conditioned on mhalo, this model predicts the expected cumulative abundance of subhalos per… view at source ↗
Figure 8
Figure 8. Figure 8: — Comparison between the Monte Carlo (MC) and quasi￾Monte Carlo (QMC) subhalo generator, presented as the distribu￾tion of subhalos in µ, for lightcone realizations at different redshifts in each panel. halo Mobs ≡ Mhalo(tobs) at the time of observation tobs. DiffmahNet is a Python library that produces samples of MAHs for halos, all of which satisfy the above con￾dition that at tobs their mass is Mobs. In… view at source ↗
Figure 9
Figure 9. Figure 9: — Comparison of the mass assembly histories (MAHs) of halos in the SMDPL N-body simulation vs. DiffmahNet. Each set of curves corresponds to the MAHs of a population of halos identified at time tobs to have mass mobs = log10 Mhalo(tobs)/M⊙. The left panel shows halos identified at tobs = 13.8 Gyr, and the right panel halos identified at tobs = 6.42 Gyr. Each panel has three sets of curves corresponding to … view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

91 extracted references · 14 canonical work pages · 2 internal anchors

  1. [1]

    P., Becker, M

    Alarcon, A., Hearin, A. P., Becker, M. R., et al. 2025, arXiv:2510.27604, arXiv:2510.27604, doi:10.48550/arXiv.2510.27604

    Pith/arXiv arXiv doi:10.48550/arxiv.2510.27604 2025

  2. [2]

    E., Zennaro, M., Contreras, S., et al

    Angulo, R. E., Zennaro, M., Contreras, S., et al. 2021, Mon. Not. Roy. Astron. Soc., 507, 5869, doi:10.1093/mnras/stab2018

    doi:10.1093/mnras/stab2018 2021

  3. [3]

    Becker, M. R. 2015, arXiv:1507.03605, arXiv:1507.03605. https://arxiv.org/abs/1507.03605

    Pith/arXiv arXiv 2015

  4. [4]

    H., Hearin, A

    Behroozi, P., Wechsler, R. H., Hearin, A. P., & Conroy, C. 2019, MNRAS, 488, 3143, doi:10.1093/mnras/stz1182

    doi:10.1093/mnras/stz1182 2019

  5. [5]

    S., Wechsler, R

    Behroozi, P. S., Wechsler, R. H., & Wu, H.-Y. 2013a, ApJ, 762, 109, doi:10.1088/0004-637X/762/2/109

    doi:10.1088/0004-637x/762/2/109

  6. [6]

    S., Wechsler, R

    Behroozi, P. S., Wechsler, R. H., Wu, H.-Y., et al. 2013b, ApJ, 763, 18, doi:10.1088/0004-637X/763/1/18

    doi:10.1088/0004-637x/763/1/18

  7. [7]

    D., Pope, A., Alarcon, A., et al

    Beltz-Mohrmann, G. D., Pope, A., Alarcon, A., et al. 2025, The Open Journal of Astrophysics, 8, 74, doi:10.33232/001c.140866

    work page doi:10.33232/001c.140866 2025

  8. [8]

    J., Nadler, E

    Benson, A. J., Nadler, E. O., Du, X., & Gluscevic, V. 2026, arXiv e-prints, arXiv:2606.12137, doi:10.48550/arXiv.2606.12137

    Pith/arXiv arXiv doi:10.48550/arxiv.2606.12137 2026

  9. [9]

    A universal model for the accretion rates and formation times of dark matter halos

    Bera, A., & Diemer, B. 2026, arXiv e-prints, arXiv:2606.09997, doi:10.48550/arXiv.2606.09997

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2606.09997 2026

  10. [10]

    R., Faber, S

    Blumenthal, G. R., Faber, S. M., Primack, J. R., & Rees, M. J. 1984, Nature, 311, 517, doi:10.1038/311517a0

    doi:10.1038/311517a0 1984

  11. [11]

    Bower, R. G. 1991, MNRAS, 248, 332, doi:10.1093/mnras/248.2.332

    doi:10.1093/mnras/248.2.332 1991

  12. [12]

    G., Benson, A

    Bower, R. G., Benson, A. J., Malbon, R., et al. 2006, MNRAS, 370, 645, doi:10.1111/j.1365-2966.2006.10519.x

    doi:10.1111/j.1365-2966.2006.10519.x 2006

  13. [13]

    Bradbury, J., Frostig, R., Hawkins, P., et al. 2018

    2018

  14. [14]

    2025, arXiv:2508.10902, arXiv:2508.10902

    Brieden, S., Beutler, F., & Pellejero-Iba˜ nez, M. 2025, arXiv:2508.10902, arXiv:2508.10902. https://arxiv.org/abs/2508.10902

    arXiv 2025

  15. [15]

    2023, The Open Journal of Astrophysics, 6, 15, doi:10.21105/astro.2302.05163

    Campagne, J.-E., Lanusse, F., Zuntz, J., et al. 2023, The Open Journal of Astrophysics, 6, 15, doi:10.21105/astro.2302.05163

    Pith/arXiv arXiv doi:10.21105/astro.2302.05163 2023

  16. [16]

    E., Schaye, J., et al

    Chaves-Montero, J., Angulo, R. E., Schaye, J., et al. 2016, MNRAS, 460, 3100, doi:10.1093/mnras/stw1225

    doi:10.1093/mnras/stw1225 2016

  17. [17]

    E., & Zennaro, M

    Contreras, S., Angulo, R. E., & Zennaro, M. 2021, MNRAS, 508, 175, doi:10.1093/mnras/stab2560

    doi:10.1093/mnras/stab2560 2021

  18. [18]

    2020, ApJS, 251, 17, doi:10.3847/1538-4365/abbf51 —

    Diemer, B. 2020, ApJS, 251, 17, doi:10.3847/1538-4365/abbf51 —. 2022, MNRAS, 513, 573, doi:10.1093/mnras/stac878

    doi:10.3847/1538-4365/abbf51 2020

  19. [19]

    O., Benson, A., & Gluscevic, V

    Driskell, T., Nadler, E. O., Benson, A., & Gluscevic, V. 2024, arXiv:2410.11680, arXiv:2410.11680. https://arxiv.org/abs/2410.11680

    Pith/arXiv arXiv 2024

  20. [20]

    E., et al

    Evrard, A. E., et al. 2002, Astrophys. J., 573, 7, doi:10.1086/340551

    doi:10.1086/340551 2002

  21. [21]

    Fosalba, P., Crocce, M., Gazta˜ naga, E., & Castander, F. J. 2015, Mon. Not. Roy. Astron. Soc., 448, 2987, doi:10.1093/mnras/stv138

    doi:10.1093/mnras/stv138 2015

  22. [22]

    2008, Mon

    Fosalba, P., Gaztanaga, E., Castander, F., & Manera, M. 2008, Mon. Not. Roy. Astron. Soc., 391, 435, doi:10.1111/j.1365-2966.2008.13910.x

    doi:10.1111/j.1365-2966.2008.13910.x 2008

  23. [23]

    2022, MNRAS, 512, 4909, doi:10.1093/mnras/stac257 Garc´ ıa, R., Salazar, E., Rozo, E., et al

    Garaldi, E., Kannan, R., Smith, A., et al. 2022, MNRAS, 512, 4909, doi:10.1093/mnras/stac257 Garc´ ıa, R., Salazar, E., Rozo, E., et al. 2023, MNRAS, 521, 2464, doi:10.1093/mnras/stad660

    doi:10.1093/mnras/stac257 2022

  24. [24]

    Ruderman, J. T. 2025, Phys. Rev. D, 112, 063531, doi:10.1103/f3tj-r882

    doi:10.1103/f3tj-r882 2025

  25. [25]

    2023.https://arxiv.org/abs/2305.11935

    Hadzhiyska, B., et al. 2023.https://arxiv.org/abs/2305.11935

    Pith/arXiv arXiv 2023

  26. [26]

    2025, ApJ, 982, L44, doi:10.3847/2041-8213/adbe5e

    Hahn, C., & Melchior, P. 2025, ApJ, 982, L44, doi:10.3847/2041-8213/adbe5e

    work page doi:10.3847/2041-8213/adbe5e 2025

  27. [27]

    Hahn, O., List, F., & Porqueres, N. 2024, J. Cosmology Astropart. Phys., 2024, 063, doi:10.1088/1475-7516/2024/06/063

    work page doi:10.1088/1475-7516/2024/06/063 2024

  28. [28]

    2023, MNRAS, 521, 1741, doi:10.1093/mnras/stad456

    Benson, A. 2023, MNRAS, 521, 1741, doi:10.1093/mnras/stad456

    doi:10.1093/mnras/stad456 2023

  29. [29]

    P., Chaves-Montero, J., Becker, M

    Hearin, A. P., Chaves-Montero, J., Becker, M. R., & Alarcon, A. 2021, The Open Journal of Astrophysics, 4, 7, doi:10.21105/astro.2105.05859

    Pith/arXiv arXiv doi:10.21105/astro.2105.05859 2021

  30. [30]

    P., & Watson, D

    Hearin, A. P., & Watson, D. F. 2013, MNRAS, 435, 1313, doi:10.1093/mnras/stt1374

    work page doi:10.1093/mnras/stt1374 2013

  31. [31]

    2014, Astrophys

    Heitmann, K., Lawrence, E., Kwan, J., Habib, S., & Higdon, D. 2014, Astrophys. J., 780, 111, doi:10.1088/0004-637X/780/1/111

    doi:10.1088/0004-637x/780/1/111 2014

  32. [32]

    2021, ApJS, 252, 19, doi:10.3847/1538-4365/abcc67

    Heitmann, K., Frontiere, N., Rangel, E., et al. 2021, ApJS, 252, 19, doi:10.3847/1538-4365/abcc67

    work page doi:10.3847/1538-4365/abcc67 2021

  33. [33]

    Henriques, B. M. B., White, S. D. M., Thomas, P. A., et al. 2015, MNRAS, 451, 2663, doi:10.1093/mnras/stv705

    doi:10.1093/mnras/stv705 2015

  34. [34]

    2019.https://arxiv.org/abs/1906.08355

    Hollowed, J. 2019.https://arxiv.org/abs/1906.08355

    Pith/arXiv arXiv 2019

  35. [35]

    2025, MNRAS, doi:10.1093/mnras/staf1785

    Horowitz, B., & Luki´ c, Z. 2025, MNRAS, doi:10.1093/mnras/staf1785

    doi:10.1093/mnras/staf1785 2025

  36. [36]

    Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90, doi:10.1109/MCSE.2007.55 10 Zacharegkas et al

    doi:10.1109/mcse.2007.55 2007

  37. [37]

    2023, Astronomy & Astrophysics, 677, A123

    Izquierdo-Villalba, D., Colpi, M., Volonteri, M., et al. 2023, Astronomy & Astrophysics, 677, A123

    2023

  38. [38]

    2021, Monthly Notices of the Royal Astronomical Society, 502, 621, doi:10.1093/mnras/staa4034

    Jiang, F., Dekel, A., Freundlich, J., et al. 2021, Monthly Notices of the Royal Astronomical Society, 502, 621, doi:10.1093/mnras/staa4034

    doi:10.1093/mnras/staa4034 2021

  39. [39]

    Jiang, F., & van den Bosch, F. C. 2016, MNRAS, 458, 2848, doi:10.1093/mnras/stw439

    doi:10.1093/mnras/stw439 2016

  40. [40]

    2001-2016, http://www.scipy.org

    Jones, E., Oliphant, T., Peterson, P., et al. 2001-2016, http://www.scipy.org

    2001

  41. [41]

    halox: Dark matter halo properties and large-scale structure calculations using JAX

    Kannan, R., Garaldi, E., Smith, A., et al. 2022, MNRAS, 511, 4005, doi:10.1093/mnras/stab3710 K´ eruzor´ e, F., & Moreau, L. A. 2025, arXiv e-prints, arXiv:2509.22478, doi:10.48550/arXiv.2509.22478

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stab3710 2022

  42. [42]

    2016, MNRAS, 457, 4340, doi:10.1093/mnras/stw248

    Klypin, A., Yepes, G., Gottl¨ ober, S., Prada, F., & Heß, S. 2016, MNRAS, 457, 4340, doi:10.1093/mnras/stw248

    doi:10.1093/mnras/stw248 2016

  43. [43]

    A., Trujillo-Gomez, S., & Primack, J

    Klypin, A. A., Trujillo-Gomez, S., & Primack, J. 2011, ApJ, 740, 102, doi:10.1088/0004-637X/740/2/102

    doi:10.1088/0004-637x/740/2/102 2011

  44. [44]

    2021, Mon

    Knabenhans, M., et al. 2021, Mon. Not. Roy. Astron. Soc., 505, 2840, doi:10.1093/mnras/stab1366 Kodi Ramanah, D., Charnock, T., Villaescusa-Navarro, F., &

    doi:10.1093/mnras/stab1366 2021

  45. [45]

    Wandelt, B. D. 2020, MNRAS, 495, 4227, doi:10.1093/mnras/staa1428

    doi:10.1093/mnras/staa1428 2020

  46. [46]

    O., Mansfield, P., & Benson, A

    Kong, D., Yu, H.-B., Nadler, E. O., Mansfield, P., & Benson, A. 2025, J. Cosmology Astropart. Phys., 2025, 074, doi:10.1088/1475-7516/2025/10/074

    work page doi:10.1088/1475-7516/2025/10/074 2025

  47. [47]

    1993, MNRAS, 262, 627, doi:10.1093/mnras/262.3.627

    Lacey, C., & Cole, S. 1993, MNRAS, 262, 627, doi:10.1093/mnras/262.3.627

    doi:10.1093/mnras/262.3.627 1993

  48. [48]

    Lagos, C. d. P., Tobar, R. J., Robotham, A. S. G., et al. 2018, MNRAS, 481, 3573, doi:10.1093/mnras/sty2440

    doi:10.1093/mnras/sty2440 2018

  49. [49]

    2022, arXiv e-prints, arXiv:2211.09958, doi:10.48550/arXiv.2211.09958

    Li, Y., Lu, L., Modi, C., et al. 2022, arXiv e-prints, arXiv:2211.09958, doi:10.48550/arXiv.2211.09958

    Pith/arXiv arXiv doi:10.48550/arxiv.2211.09958 2022

  50. [50]

    2025, arXiv e-prints, arXiv:2510.05206, doi:10.48550/arXiv.2510.05206

    List, F., Hahn, O., Fl¨ oss, T., & Winkler, L. 2025, arXiv e-prints, arXiv:2510.05206, doi:10.48550/arXiv.2510.05206

    Pith/arXiv arXiv doi:10.48550/arxiv.2510.05206 2025

  51. [51]

    C., Lee, M

    Lovell, C. C., Lee, M. E., Roper, W. J., et al. 2026, arXiv:2604.17981, arXiv:2604.17981. https://arxiv.org/abs/2604.17981

    Pith/arXiv arXiv 2026

  52. [52]

    2024, ApJ, 970, 178, doi:10.3847/1538-4357/ad4e33

    Mansfield, P., Darragh-Ford, E., Wang, Y., et al. 2024, ApJ, 970, 178, doi:10.3847/1538-4357/ad4e33

    doi:10.3847/1538-4357/ad4e33 2024

  53. [53]

    2018, MNRAS, 480, 5113, doi:10.1093/mnras/sty2206 Mart´ ın-Navarro, I., Vazdekis, A., Peralta de Arriba, L., et al

    Marinacci, F., Vogelsberger, M., Pakmor, R., et al. 2018, MNRAS, 480, 5113, doi:10.1093/mnras/sty2206 Mart´ ın-Navarro, I., Vazdekis, A., Peralta de Arriba, L., et al. 2026, arXiv e-prints, arXiv:2605.24093, doi:10.48550/arXiv.2605.24093

    Pith/arXiv arXiv doi:10.1093/mnras/sty2206 2018

  54. [54]

    I., Baugh, C

    Merson, A. I., Baugh, C. M., Helly, J. C., et al. 2013, Monthly Notices of the Royal Astronomical Society, 429, 556

    2013

  55. [55]

    R., Heitmann, K., Lawrence, E., et al

    Moran, K. R., Heitmann, K., Lawrence, E., et al. 2023, Mon. Not. Roy. Astron. Soc., 520, 3443, doi:10.1093/mnras/stac3452

    doi:10.1093/mnras/stac3452 2023

  56. [56]

    P., Naab, T., & White, S

    Moster, B. P., Naab, T., & White, S. D. M. 2018, MNRAS, 477, 1822, doi:10.1093/mnras/sty655

    doi:10.1093/mnras/sty655 2018

  57. [57]

    2019, Computational Astrophysics and Cosmology, 6, 1, doi:10.1186/s40668-019-0029-9

    Mustafa, M., Bard, D., Bhimji, W., et al. 2019, Computational Astrophysics and Cosmology, 6, 1, doi:10.1186/s40668-019-0029-9

    doi:10.1186/s40668-019-0029-9 2019

  58. [58]

    O., Banerjee, A., Adhikari, S., Mao, Y.-Y., & Wechsler, R

    Nadler, E. O., Banerjee, A., Adhikari, S., Mao, Y.-Y., & Wechsler, R. H. 2021, ApJ, 920, L11, doi:10.3847/2041-8213/ac29c1

    doi:10.3847/2041-8213/ac29c1 2021

  59. [59]

    O., Mao, Y.-Y., Wechsler, R

    Nadler, E. O., Mao, Y.-Y., Wechsler, R. H., Garrison-Kimmel, S., & Wetzel, A. 2018, ApJ, 859, 129, doi:10.3847/1538-4357/aac266

    work page doi:10.3847/1538-4357/aac266 2018

  60. [60]

    O., Mansfield, P., Wang, Y., et al

    Nadler, E. O., Mansfield, P., Wang, Y., et al. 2023, ApJ, 945, 159, doi:10.3847/1538-4357/acb68c

    doi:10.3847/1538-4357/acb68c 2023

  61. [61]

    P., Pillepich, A., Springel, V., et al

    Naiman, J. P., Pillepich, A., Springel, V., et al. 2018, MNRAS, 477, 1206, doi:10.1093/mnras/sty618

    doi:10.1093/mnras/sty618 2018

  62. [62]

    2018, MNRAS, 475, 624, doi:10.1093/mnras/stx3040

    Nelson, D., Pillepich, A., Springel, V., et al. 2018, MNRAS, 475, 624, doi:10.1093/mnras/stx3040

    doi:10.1093/mnras/stx3040 2018

  63. [63]

    Somerville, R. S. 2025, arXiv:2507.10652, arXiv:2507.10652. https://arxiv.org/abs/2507.10652

    arXiv 2025

  64. [64]

    Nguyen, T., Modi, C., Yung, L. Y. A., & Somerville, R. S. 2024, MNRAS, 533, 3144, doi:10.1093/mnras/stae2001

    doi:10.1093/mnras/stae2001 2024

  65. [65]

    2025, Phys

    Pandey, S., Salcido, J., To, C.-H., et al. 2025, Phys. Rev. D, 111, 043529, doi:10.1103/PhysRevD.111.043529

    work page doi:10.1103/physrevd.111.043529 2025

  66. [66]

    L., Makinen, T

    Pandya, V., Bryan, G. L., Makinen, T. L., et al. 2026, arXiv e-prints, arXiv:2604.06318, doi:10.48550/arXiv.2604.06318

    Pith/arXiv arXiv doi:10.48550/arxiv.2604.06318 2026

  67. [67]

    2011, Journal of Machine Learning Research, 12, 2825 P´ erez, F., & Granger, B

    Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011, Journal of Machine Learning Research, 12, 2825 P´ erez, F., & Granger, B. E. 2007, Computing in Science and Engineering, 9, 21, doi:10.1109/MCSE.2007.53

    doi:10.1109/mcse.2007.53 2011

  68. [68]

    2010, Monthly Notices of the Royal Astronomical Society, 401, 705

    Pichon, C., Thi´ ebaut, E., Prunet, S., et al. 2010, Monthly Notices of the Royal Astronomical Society, 401, 705

    2010

  69. [69]

    2018, MNRAS, 473, 4077, doi:10.1093/mnras/stx2656 Planck Collaboration, Ade, P

    Pillepich, A., Springel, V., Nelson, D., et al. 2018, MNRAS, 473, 4077, doi:10.1093/mnras/stx2656 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2014, A&A, 571, A16, doi:10.1051/0004-6361/201321591

    doi:10.1093/mnras/stx2656 2018

  70. [70]

    B., Mutch, S

    Poole, G. B., Mutch, S. J., Croton, D. J., & Wyithe, S. 2017, MNRAS, 472, 3659, doi:10.1093/mnras/stx2233

    work page doi:10.1093/mnras/stx2233 2017

  71. [71]

    H., & Schechter, P

    Press, W. H., & Schechter, P. 1974, ApJ, 187, 425, doi:10.1086/152650

    doi:10.1086/152650 1974

  72. [72]

    2014, in American Geophysical Union Fall Meeting Abstracts, Vol

    Ragan-Kelley, M., Perez, F., Granger, B., et al. 2014, in American Geophysical Union Fall Meeting Abstracts, Vol. D7

    2014

  73. [73]

    J., Gonzalez, E

    Ramakrishnan, S., Castander, F. J., Gonzalez, E. J., et al. 2025, arXiv e-prints, arXiv:2512.13801. https://arxiv.org/abs/2512.13801

    arXiv 2025

  74. [74]

    M., Wechsler, R

    Reddick, R. M., Wechsler, R. H., Tinker, J. L., & Behroozi, P. S. 2013, ApJ, 771, 30, doi:10.1088/0004-637X/771/1/30

    doi:10.1088/0004-637x/771/1/30 2013

  75. [75]

    Richardson, T. R. G., St¨ ucker, J., & Angulo, R. E. 2026, A&A, 707, A117, doi:10.1051/0004-6361/202556846

    work page doi:10.1051/0004-6361/202556846 2026

  76. [76]

    M., Enke, H., et al

    Riebe, K., Partl, A. M., Enke, H., et al. 2013, Astronomische Nachrichten, 334, 691, doi:10.1002/asna.201211900

    doi:10.1002/asna.201211900 2013

  77. [77]

    2026, The Open Journal of Astrophysics, 9, 55306, doi:10.33232/001c.155306

    Robertson, A., & Benson, A. 2026, The Open Journal of Astrophysics, 9, 55306, doi:10.33232/001c.155306

    doi:10.33232/001c.155306 2026

  78. [78]

    2022, MNRAS, 514, 3692, doi:10.1093/mnras/stac1569

    Dujovne, D. 2022, MNRAS, 514, 3692, doi:10.1093/mnras/stac1569

    work page doi:10.1093/mnras/stac1569 2022

  79. [79]

    2015, MNRAS, 449, 49, doi:10.1093/mnras/stv264 Rodr´ ıguez-Puebla, A., Behroozi, P., Primack, J., et al

    Rodriguez-Gomez, V., Genel, S., Vogelsberger, M., et al. 2015, MNRAS, 449, 49, doi:10.1093/mnras/stv264 Rodr´ ıguez-Puebla, A., Behroozi, P., Primack, J., et al. 2016, MNRAS, 462, 893, doi:10.1093/mnras/stw1705

    doi:10.1093/mnras/stv264 2015

  80. [80]

    2021, JCAP, 02, 047, doi:10.1088/1475-7516/2021/02/047

    Sgier, R., Fluri, J., Herbel, J., et al. 2021, JCAP, 02, 047, doi:10.1088/1475-7516/2021/02/047

    work page doi:10.1088/1475-7516/2021/02/047 2021

Showing first 80 references.