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REVIEW 4 major objections 5 minor 1 cited by

Cosmological constraints from the Minkowski functionals of the BOSS CMASS galaxy sample

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that the Minkowski functionals of the BOSS CMASS galaxy sample, modeled through a simulation-based emulator that captures both Gaussian and non-Gaussian information, constrain key cosmological parameters up to twice as…

desk verdict First simulation-based MFs on BOSS data with genuinely strong validation, but the headline MF-vs-2PCF improvement factors are likely inflated by an overestimated emulator-error term that penalizes the 2PCF more than the MFs. read the letter →

arxiv 2501.01698 v2 pith:XST3MOJS submitted 2025-01-03 astro-ph.CO

Wei Liu , Enrique Paillas , Carolina Cuesta-Lazaro , Georgios Valogiannis , Wenjuan Fang This is my paper · ORCID
classification astro-ph.CO
keywords MinkowskifunctionalscosmologicalconstraintsBOSSCMASSgalaxyclusteringemulatornon-Gaussianinformationlarge-scalestructurehalooccupationdistribution
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Large-scale-structure cosmologists usually compress galaxy maps into the two-point correlation function, but nonlinear structure carries extra information in the shape of density contours. This paper builds the first simulation-based model of the Minkowski functionals—four morphological measures of the smoothed galaxy density field—that can be used for full-shape inference, including both Gaussian and non-Gaussian information. Applied to the BOSS CMASS galaxy sample, the model finds that the Minkowski functionals alone constrain the cold dark matter density, $\sigma_8$, and the spectral index more tightly than the two-point correlation function, and the combination improves precision by factors of 2.0, 1.9, and 1.6 respectively. The derived growth-rate combination $f\sigma_8 = 0.453 \pm 0.016$ agrees with cosmic-microwave-background and other survey results. If right, this establishes a practical route to exploit non-Gaussian information in current and future spectroscopic surveys.

What carries the argument

The load-bearing object is the four Minkowski functionals of the galaxy density field, computed by Crofton's formula from excursion sets at a sequence of density thresholds after Gaussian smoothing with scale $R_G=15\,h^{-1}{\rm Mpc}$. Hadwiger's theorem guarantees that these four functionals completely characterize the morphology of the field under the usual invariance assumptions, which is why the full threshold curves are information-rich. The machinery that makes them usable is a neural-network emulator: tens of thousands of mock galaxy catalogs built from halo occupation distribution models in high-resolution N-body simulations, projected through the survey geometry with redshift-space and Alcock–Paczynski distortions, produce a training set of Minkowski functional curves; the emulator then predicts the curves as a function of cosmological and HOD parameters. A second emulator for the 2PCF trained with the identical pipeline provides the benchmark and the cross-check.

What would settle it

Retrain the emulator using multiple independent initial-condition phases so that phase variance is absorbed into the emulator error instead of added as a separate term, then re-run the CMASS fit; if the improvement factors over the 2PCF (2.0, 1.9, 1.6) shrink toward unity, the central claim fails, and if they persist, it survives.

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Extended reading notes

Core claim

Minkowski functionals measure the volume, surface area, integrated mean curvature, and Euler characteristic of the excursion sets of a smoothed density field as the threshold is varied, and the full curves across thresholds contain information beyond Gaussian statistics. The paper's central claim is that these full-shape Minkowski functional curves, predicted by a neural-network emulator trained on forward-modeled mock galaxy catalogs that include survey geometry, redshift-space distortions, and Alcock–Paczynski distortions, constrain cosmology more strongly than the galaxy two-point correlation function. On the BOSS CMASS data, the Minkowski functionals alone give factors of 2.0, 1.7, and 1.4 tighter constraints on $\omega_{\rm cdm}$, $\sigma_8$, and $n_s$ than the 2PCF; combining both yields $\omega_{\rm cdm}=0.1172^{+0.0020}_{-0.0023}$, $\sigma_8=0.783\pm0.026$, $n_s=0.966^{+0.019}_{-0.015}$, and $f\sigma_8=0.453\pm0.016$, with the 2PCF contributing mainly to $\sigma_8$.

Load-bearing premise

The load-bearing premise is that the total noise budget (survey scatter, emulator error, and simulation sample variance) is faithfully estimated, even though the paper's own best-fit reduced chi-square values fall below one once all three terms are included.

Editorial extensions

If this is right

  • The Minkowski functionals alone constrain $\omega_{\rm cdm}$, $\sigma_8$, and $n_s$ factors of 2.0, 1.7, and 1.4 tighter than the 2PCF, so the full shape of the MFs contains non-Gaussian information that two-point statistics miss.
  • Adding the 2PCF to the MFs tightens $\sigma_8$ by 12% and $n_s$ by 18%, showing the two probes are partly complementary; the 2PCF contributes little to $\omega_{\rm cdm}$.
  • The derived $f\sigma_8=0.453\pm0.016$ at $z_{\rm eff}=0.519$ is consistent with cosmic-microwave-background results and other BOSS analyses of the growth rate, and it is 1.9 times tighter than from the 2PCF alone.
  • Under the same pipeline, the four $\Lambda$CDM extensions ($\alpha_s$, $N_{\rm eff}$, $w_0$, $w_a$) remain consistent with their fiducial values, so the extra information does not pull the model away from the standard cosmology.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the improvement factors are driven primarily by the shape of the MF curves rather than by the amplitude, then denser surveys with smaller smoothing scales—where shot noise is lower—should show even larger gains; the paper notes its own ongoing work at higher number density but does not demonstrate it.
  • The paper's appendix shows that dropping the emulator error term drastically tightens the posteriors, which suggests the current error budget is conservative; a more faithful emulator error could make the MF-vs-2PCF improvement factors larger, not smaller.
  • Because the MFs are almost insensitive to the velocity-bias parameters, anisotropic generalizations such as Minkowski tensors or non-isotropic smoothing may recover the redshift-space information lost here; the paper identifies this as future work.
  • The reduced chi-square values below one when emulator and simulation variance are included hint that some sample variance is double-counted; if that is corrected with multi-phase emulator training, the quoted absolute errors could shrink, changing comparisons with other BOSS analyses.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper presents the first simulation-based emulator for the Minkowski functionals (MFs) of galaxy clustering and applies it to the BOSS DR12 CMASS sample. The forward model uses AbacusSummit simulations, a 7-parameter HOD galaxy-halo connection, and forward-modeled RSD, AP distortions, survey geometry, veto masks, and selection effects. A neural-network emulator is trained for the four MFs and, for comparison, for the 2PCF monopole and quadrupole. The authors validate the pipeline on internal Abacus mocks and on the external Uchuu SHAM mock, then report that the MFs give tighter cosmological constraints than the 2PCF, with the combined analysis yielding omega_cdm = 0.1172 +0.0020/-0.0023, sigma_8 = 0.783 +/- 0.026, n_s = 0.966 +0.019/-0.015, and f sigma_8 = 0.453 +/- 0.016. The paper itself acknowledges that the total covariance may be overestimated and that the z=0.5 snapshot neglects evolution to z_eff=0.519.

Significance. If the headline constraints hold, this is a genuine methodological step forward: it is the first simulation-based forward model of the MFs for a spectroscopic galaxy sample, and it demonstrates that morphological statistics can be modeled end-to-end with the same pipeline used for two-point statistics. The validation is a real strength: internal Abacus mocks at several cosmologies and an external Uchuu mock built with SHAM rather than HOD are all recovered within 1-2 sigma, which argues against a circular parameter-inference problem. The claimed improvement over the 2PCF is scientifically interesting because it points to exploitable non-Gaussian information, but the paper's own error-budget analysis shows that the comparison is not yet apples-to-apples: the 2PCF covariance is dominated by emulator error on small scales, whereas the MF covariance is not. The significance of the result therefore rests on a covariance model that the manuscript itself identifies as fragile.

major comments (4)
  1. [Sec. 3.6, Eq. (3.17), Fig. 6, Table 3] The central claim that the MFs outperform the 2PCF (Table 4 and the abstract) is sensitive to an asymmetric emulator-error term. Figure 6 shows that for the 2PCF, C_emu dominates the total covariance at s <~ 10 h^-1 Mpc, while for the MFs C_emu is subdominant at essentially all thresholds. Table 3 shows reduced chi^2 values below unity once C_emu and C_abacus are added (0.52 for the 2PCF, 0.45 for MFs+2PCF), which the authors themselves interpret as an overestimate of emulator error and possible double counting. Because the small-scale 2PCF bins are heavily downweighted by an error term that is largely absent for the MFs, the quoted improvement factors of 2.0, 1.9, and 1.6 are not an apples-to-apples comparison. I request a robustness test in which C_emu is estimated only near the high-likelihood region (as in Yuan et al. 2022, ref. [112]) or the small-scale 2PCF bins are excluded, with the resulting constraints and improvement factors reported.
  2. [Sec. 3.6, Eqs. (3.13)-(3.14), Sec. 5.1] The Abacus covariance C_abacus, estimated from 1786 AbacusSmall periodic boxes with a single best-fit HOD and rescaled by one scalar factor from 25 AbacusSummit realizations, is added to C_data estimated from the Patchy mocks. Since both C_data and the rescaled C_abacus describe sample variance of the CMASS-like survey footprint, this double counts sample variance, as the paper itself suggests in Sec. 5.1. The reduced chi^2 values below unity in Table 3 are quantitative evidence of the overestimate. This is load-bearing because C enters the likelihood (Eq. 3.9) inversely and therefore controls all quoted error bars and improvement factors. Please either drop C_abacus from the baseline or justify with a test that the double counting is negligible, and show how the central values and improvement factors change in either case.
  3. [Sec. 2.1, Sec. 3.1, Sec. 7] The emulator is trained on simulation snapshots at z=0.5, while the CMASS subsample has z_eff=0.519. The paper's concluding limitation statement in Sec. 7 notes that the evolution of clustering and of the halo-galaxy connection is neglected, but no estimate of the resulting systematic shift is given. The quoted uncertainties on omega_cdm and sigma_8 are at the 1-3 percent level, and the growth factor changes by roughly a percent between z=0.5 and z=0.519, so the effect could be comparable to the reported errors. I request a quantitative estimate, for example using the Abacus lightcones cited in ref. [172], or a demonstration that the constraints are stable to a linear-evolution reweighting of the snapshot.
  4. [Sec. 3.4.1, Sec. 5.2] The causal claim that 'non-Gaussian information embedded in the MFs' drives the improvement is not directly demonstrated. The improvement is measured against the 2PCF, which differs in smoothing, scale range, and error budget. The paper does not isolate the Gaussian part of the MF signal from the non-Gaussian part; the amplitude information discussed around Eq. (3.5) is Gaussian-dominated, while the shape information is a mixture of Gaussian and non-Gaussian contributions. A direct test, such as comparing the full MFs to a Gaussian-only MF model or to a 2PCF restricted to the effective scales probed by the MFs, would make the abstract's 'including both Gaussian and non-Gaussian part' supportable. Without such a test, the improvement factors should be described as conditional on the choice of summary statistics and error budget, not as a measurement of non-Gaussian information content.
minor comments (5)
  1. [Sec. 3.4.2] The text says 'we use 241 mu bins from -1 to 1'; the symbol is not typeset in the standard way and it would be clearer to write '241 mu-bins' and to state explicitly whether they are linearly spaced.
  2. [Fig. 2 caption] The caption repeats 'first column' for the projections along z-hat, y-hat, and x-hat; these should be first, second, and third columns respectively.
  3. [Eq. (3.4)] In the expression for W2, the integrand is printed as 'k1 + k2 dA', which is ambiguous; it should be '(k1 + k2) dA'.
  4. [Sec. 6.3] The final sentence gives the MF improvement factors over the 2PCF as '2.0, 1.4, and 1.7' for h, n_s, and sigma_8, whereas the abstract and Sec. 5.2 report 2.0, 1.9, and 1.6 for omega_cdm, sigma_8, and n_s; the numbers and parameter ordering should be harmonized.
  5. [Sec. 5.1] The discussion of the 2PCF chi^2/dof = 1.53 with C_data alone would benefit from a statement about whether the large-scale underprediction at s >~ 80 h^-1 Mpc is the main driver; this is relevant for the reader's ability to assess the 2PCF benchmark.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MFs/2PCF constraints come from a forward-model likelihood and are cross-checked on an external Uchuu mock.

full rationale

The central derivation is a standard simulation-based forward model: AbacusSummit mocks with varied cosmology and HOD are used to train emulators for the MFs and 2PCF, and Eq. (3.9) evaluates a Gaussian likelihood of the CMASS data vector against emulator predictions. Cosmological parameters are therefore inferred from a likelihood, not fitted into the model by construction. Internal parameter-recovery tests (Sec. 4.2) and, crucially, the external Uchuu SHAM mock (Sec. 4.3) break any self-referential loop; the Uchuu test uses a different N-body code, halo finder, and galaxy-halo connection and still recovers the true parameters. The covariance model (Eq. 3.10) and the sub-unity reduced chi-square values in Table 3 are an error-budget limitation (the paper itself notes possible overestimation of emulator error and double counting of sample variance), but this is a statistical robustness concern rather than a circular reduction. Self-citations (e.g., refs. [80,81]) appear as background and as a Fisher-forecast comparison in Sec. 6.3; they do not supply the load-bearing prediction, which is tested against external data. The Planck theta* prior on h is explicitly disclosed in Sec. 3.6.1 and Sec. 7. No equation in the paper reduces to its input by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 11 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the fidelity of the AbacusSummit simulations, the HOD galaxy-halo connection, the emulator's interpolation accuracy, and the covariance model. No new physical entities are introduced. The HOD parameters and analysis choices (smoothing scale, number density, redshift range, threshold bins) are fitted or chosen by hand and are therefore listed as free parameters.

free parameters (11)
  • Smoothing scale RG = 15 h^-1 Mpc
    Chosen by hand to match the mean galaxy separation; sets the scales probed by the MFs.
  • Target number density nbar = 2.4e-4 h^3 Mpc^-3
    Chosen as the minimum Patchy mock density; determines shot noise and the number-density selection prior.
  • Redshift range = 0.45 < z < 0.58
    Selected to balance number density and volume; effective redshift 0.519.
  • MF threshold bins Nb = 60, 80, 100, 120 for W0-W3
    Chosen to cover the dynamic range while avoiding noisy tails; gives a data vector of length 360.
  • log10 Mcut = posterior mean 12.78 from MFs+2PCF
    HOD central occupation mass threshold; marginalized in cosmological constraints.
  • log10 M1 = posterior mean 13.60 from MFs+2PCF
    Typical halo mass hosting one satellite; marginalized nuisance parameter.
  • log10 sigma = posterior mean -1.75 from MFs+2PCF
    Width of central occupation transition; marginalized nuisance parameter.
  • alpha = posterior mean 0.84 from MFs+2PCF
    Power-law index for satellite occupation; marginalized nuisance parameter.
  • kappa = posterior mean 5.0 from MFs+2PCF
    Multiplier setting the minimum satellite host mass; marginalized nuisance parameter.
  • alpha_vel,c = posterior mean 0.19 from MFs+2PCF
    Central velocity bias parameter; weakly constrained by MFs because isotropic smoothing erases small-scale velocity information.
  • alpha_vel,s = posterior mean 1.02 from MFs+2PCF
    Satellite velocity bias parameter; marginalized in cosmological constraints.
assumptions (7)
  • domain assumption AbacusSummit simulations accurately predict the nonlinear matter distribution over the 8D cosmological parameter range.
    The emulator training set is built from these simulations; errors in the N-body predictions propagate directly into the MF model.
  • domain assumption The 7-parameter HOD model (Eqs 3.1-3.2) describes the CMASS galaxy-halo connection, and assembly bias is negligible.
    The forward model assumes this specific galaxy-halo connection; the Uchuu SHAM test checks one alternative but does not prove the HOD form is correct for CMASS.
  • domain assumption The neural network emulator interpolates smoothly and its prediction error is independent of cosmological and HOD parameters.
    The emulator covariance Cemu is estimated as a mean correction ignoring parameter dependence, as stated in Sec 3.6.
  • domain assumption The 2048 Patchy mocks reproduce the survey geometry, masks, and covariance of the CMASS sample.
    Cdata is estimated from these mocks; if they do not match the data's systematics, the error bars are miscalibrated.
  • domain assumption The likelihood is multivariate Gaussian for the MFs and 2PCF.
    Tested in Appendix A using 2048 Patchy mocks; the test supports the assumption but does not prove it at all parameter values.
  • domain assumption The Planck 2018 theta* constraint is used to set h in all training cosmologies.
    This injects an external CMB prior into the analysis; the authors acknowledge the derived h constraints must be interpreted with caution.
  • standard math Hadwiger's theorem and Crofton's formula give unbiased MF estimators for the smoothed galaxy field.
    Standard mathematical background for defining and measuring MFs; not in dispute.

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Cite this review

Pith. "Pith review of Cosmological constraints from the Minkowski functionals of the BOSS CMASS galaxy sample." pith.science (2026). https://pith.science/paper/XST3MOJS

@misc{pith2026250101698,
  author       = {Pith},
  title        = {Pith review of: Cosmological constraints from the Minkowski functionals of the BOSS CMASS galaxy sample},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XST3MOJS}},
  note         = {Machine review of arXiv:2501.01698}
}
abstract

For the first time, we develop a simulation-based model for the Minkowski functionals (MFs) of large-scale structure, which allows us to extract the full information available from the MFs (including both the Gaussian and non-Gaussian part), and apply it to the BOSS DR12 CMASS galaxy sample. Our model is based on high-fidelity mock galaxy catalogs constructed from the \textsc{Abacus}\textsc{Summit} simulations using the halo occupation distribution (HOD) framework, which include the redshift-space distortions and Alcock-Paczynski distortions, incorporate survey realism, including survey geometry and veto masks, and account for angular plus radial selection effects. The cosmological and HOD parameter dependence of the MFs is captured with a neural network emulator trained from the galaxy mocks with various cosmological and HOD parameters. To benchmark the constraining power of the MFs, we also train an emulator for the galaxy 2-point correlation function (2PCF) using the same pipeline. Having validated our approach through successful parameter recovery tests on both internal and external mocks, including non-HOD forward models of the halo-galaxy connection, we apply our forward model to analyze the CMASS data in the redshift range $0.45<z<0.58$. We find the MFs provide stronger constraints on the cosmological parameters than the 2PCF. The combination of the two gives $\omega_{\rm cdm}=0.1172^{+0.0020}_{-0.0023}$, $\sigma_8=0.783\pm 0.026$, and $n_s=0.966^{+0.019}_{-0.015}$, which are tighter by a factor of 2.0, 1.9, and 1.6 than the 2PCF alone. The derived constraint $f\sigma_8=0.453 \pm 0.016$ is also improved by a factor of 1.9, compared to the 2PCF, and agrees well with Planck 2018 predictions and other results from a series of studies in the literature.

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