Marked statistics across the cosmic web: Environmental dependent clustering in modified gravity simulations

Joaquin Armijo; Lucas Da Costa

REVIEW 3 major objections 5 minor 1 references

This paper claims that weighting galaxy pairs by cosmic-web environment—especially nodes and filaments—roughly doubles, and up to quadruples, the sensitivity of marked correlation functions to f(R) modified gravity relative to measuring the

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2026-08-03 11:29 UTC pith:UXZDT3WI

load-bearing objection Environmental splitting of marked statistics is a sensible idea with credible qualitative plots, but the headline 'factor of 2.3/4.1 information gain' rests on an undefined chi2_nu and an uncontrolled baseline. the 3 major comments →

arxiv 2601.05934 v2 pith:UXZDT3WI submitted 2026-01-09 astro-ph.CO

Marked statistics across the cosmic web: Environmental dependent clustering in modified gravity simulations

Joaquin Armijo , Lucas Da Costa This is my paper

classification astro-ph.CO

keywords modified gravityf(R) gravitymarked correlation functioncosmic webgalaxy clusteringlarge-scale structurecosmic filamentschameleon screening

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.

This paper tries to establish that the cosmic web provides a new lever arm for testing modified gravity. Using marked correlation functions—pair-counting statistics in which each galaxy is weighted by local density or host halo mass—the authors split a large f(R)-gravity simulation into nodes, filaments, walls, and voids, and compare with general relativity. They find that the f(R) signal is strongest for galaxies in nodes and filaments, and that combining environment-split measurements raises the discriminating power by about a factor of two over the standard all-galaxy marked correlation function, with the node-plus-filament combination exceeding it by a factor of four. If the claim holds, survey analyses need not rely only on overall clustering; splitting by environment is a cheap way to sharpen constraints on deviations from general relativity.

Core claim

On its own terms, the paper claims that the environmental structure of the cosmic web is not just a source of nuisance but a carrier of signal for modified gravity. In f(R) gravity with a present-day scalaron amplitude of |f_R0| = 10^-5, the fifth force is screened in high-density nodes but active in lower-density environments, and the simulations show that this leaves measurable imprints in the marked correlation function: deviations from GR of up to about 20 percent for galaxies in nodes and filaments on scales of roughly 1 to 20 Mpc/h. The decisive quantitative claim is that measuring the marked correlation function separately for nodes, filaments, walls, and voids, then concatenating the

What carries the argument

The workhorse is the marked correlation function, M(r) = (1 + W(r))/(1 + ξ(r)), where ξ is the standard two-point correlation function and W is the same pair count weighted by a mark per galaxy. The marks used are local density contrast raised to the power p = 0.5 and host halo mass raised to the power p = 0.5. Environment labels are assigned by sorting the eigenvalues of the Hessian of a smoothed density field into nodes (all positive), filaments (two positive), walls (one positive), and voids (all negative), thereby selecting the regions where the f(R) fifth force is unscreened. The ratio form matters because it suppresses galaxy-bias and selection effects while retaining the environmental

Load-bearing premise

The entire information-gain claim hangs on how the quoted chi-square values are defined and normalized, and the paper never gives that definition; under the standard definition of reduced chi-square, the reported factors of 2.3 and 4.1 would be hard to reconcile with the smaller per-environment values.

What would settle it

Take the quoted per-environment reduced chi-square values and the quoted combined values, and check whether the combined value is a weighted average of the components divided by the total number of bins. If the reduced chi-square is defined in the standard way, a concatenated data vector cannot exceed every component; finding that it does would show the gain is an artifact of bin counting rather than information content.

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

If this is right

Environment-split marked correlation functions raise the expected signal-to-noise for low- and high-redshift LRG-like mocks by about a factor of two over the all-galaxy marked correlation function; combining nodes and filaments alone exceeds it by a factor of four.
Filaments, not just voids, are a primary carrier of f(R) information at non-linear scales (roughly 1 to 5 Mpc/h), while voids contribute mainly at large scales beyond about 20 Mpc/h.
Both density-based and host-halo-mass-based marks separate the F5 model from GR, with relative residuals up to about 20 percent for nodes and filaments at small separations.
The constraining power in a higher-redshift, higher-number-density LRG-like sample is about four times larger than in a lower-redshift, lower-density sample.
The environment classification is meaningful in both GR and f(R) simulations, and galaxies in unscreened environments are systematically more massive in the f(R) model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The quoted factor-of-2.3 and 4.1 comparisons rely on the unreported definition of the reduced chi-square statistic; until the degrees-of-freedom accounting is specified, the gain should be read as a comparison of the plotted summary values rather than a proven information-theoretic result.
The same environment-splitting strategy could be exported to other screening mechanisms and to other statistics, such as marked power spectra or density-split clustering; a filament-specific gain there would corroborate that the web environment, rather than the choice of mark, is the active ingredient.
A sharper test would recompute the environment-split marked correlation function using covariance from many independent simulation realizations rather than jackknife subvolumes; if the factor-of-two gain survives that covariance treatment, the forecast is on firmer ground.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Environmental splitting of marked statistics is a sensible idea with credible qualitative plots, but the headline 'factor of 2.3/4.1 information gain' rests on an undefined chi2_nu and an uncontrolled baseline.

read the letter

First thing to know: this paper has a genuinely useful qualitative result buried under a quantitative claim that cannot be audited. The environment-split marked correlation functions do show a consistent F5/GR pattern — nodes and filaments deviate more than walls and voids — and the authors did real work building HOD mocks matched in number density and clustering, using the Arnold et al. f(R) simulations and pycosmommf classification. If the question is whether cosmic-web environment changes the response of marked statistics to f(R) gravity, the figures answer yes, and I see no reason to doubt that. That part deserves credit.

The soft spot is the headline. Section 5.3 says they compute the individual reduced chi-square (chi2_nu) but never gives the formula, the number of degrees of freedom, or how the covariance of a combined data vector is assembled. Figure 7 reports values like 400 and 800 for the DESI-like sample. A reduced chi-square with maybe a few dozen bins cannot be 400 unless the model is catastrophically wrong; what is plotted looks like raw chi2 or (S/N)^2 without per-dof normalisation. If that is the case, the factors 2.3 and 4.1 quoted in the abstract mostly reflect the fact that concatenating four data vectors adds up raw sums, not that there is four times more physical information. The baseline is also uncontrolled: the all-galaxies curve is cited to Armijo et al. 2018, but the paper does not say it recomputed that benchmark with the same jackknife covariance, binning, mark definition, and HOD mocks. The stress-test note is right that a combined reduced chi-square can exceed every component when cross-environment covariance is non-zero, so the reader's simplistic weighted-average objection is not decisive on its own. That cuts both ways: because the covariance blocks are not shown or described, we cannot tell whether the improvement is real or a normalization artifact. This is the central claim, so it has to be fixed before the paper is usable.

Smaller issues: F5 curves in Figures 4 and 5 have no error bars, so visual deviations up to 20% are not quantified; and the abstract and conclusions compare against slightly different baselines. Both are secondary.

Bottom line: this is a sensible, competent measurement paper that currently overstates what it demonstrates. I would send it to a referee rather than desk reject, because the idea is timely and the qualitative signal is credible. The referee should require an explicit definition of chi2_nu, the dof, the jackknife covariance construction for combined vectors, and a same-pipeline all-galaxies baseline. Until then I would not cite the information-gain numbers.

Referee Report

3 major / 5 minor

Summary. This paper uses two large N-body simulations, GR and Hu-Sawicki f(R) gravity with |f_R0|=10^-5, classifies the cosmic web into nodes, filaments, walls, and voids with pycosmommf, populates haloes with HOD parameters matched to CMASS- and DESI-like number densities and clustering, and computes density- and mass-marked correlation functions in each environment at z=0 and z=1. The main claim is that environmental splitting, especially filaments and nodes, enhances sensitivity to f(R) gravity, and that combining environmental data vectors raises the reduced chi-square by a factor of 2.3 relative to the all-galaxy measurement, with node+filament giving a factor of 4.1. These factors, taken from Fig. 7, are the quantitative basis for the abstract and conclusions.

Significance. If substantiated, the result would be practically important: it suggests that a cheap post-processing step—splitting galaxy samples by cosmic web environment—can roughly double the constraining power of marked correlation functions for modified gravity, and that filaments are not just the largest-volume environment but also carry the most additional information. The paper has clear strengths: it uses well-defined simulation pairs, matches HOD mocks to the two-point clustering, provides jackknife covariance information in Appendix A, and the qualitative differences between GR and F5 in Figures 4 and 5 are visually credible. However, the central quantitative claim about factor 2.3 and 4.1 improvements rests entirely on an undefined reduced chi-square, so the headline numbers are not currently auditable. The paper would be significantly stronger if the metric were precisely defined and the all-galaxy baseline recomputed in the same pipeline.

major comments (3)

[§5.3, Eq. (16), Fig. 7] The quantity χ2ν is never defined. Eq. (16) defines (S/N)^2, but the text then states that 'the individual reduced chi-square (χ2ν)' is calculated without giving the data vector, the number of degrees of freedom, or the covariance matrix used for individual versus combined vectors. The abstract's headline factors of 2.3 and 4.1 come entirely from Fig. 7. A reduced chi-square for a concatenated vector can exceed the component reduced chi-squares when cross-environment covariance is included, so the quoted behavior is not by itself impossible; however, without the formula and the combined covariance blocks, the reader cannot tell whether the factors reflect physical information or simply the larger number of bins/parameters in the combined vector. Please state the exact formula for χ2ν, report the degrees of freedom, and show the covariance matrix for each combined vector; also give the eq
[§5.3, all-galaxy benchmark] The baseline values in Fig. 7 are quoted as 'results of (Armijo et al. 2018)' rather than recomputed with the same mocks, binning, mark definitions, and jackknife covariance used for the environment-split measurements. Since this baseline appears in the denominator of the headline 'factor of two / factor of four' claims, any difference in pipeline can create an apparent gain. The all-galaxy χ2ν must be recomputed with the identical pipeline and compared on equal footing.
[§5.3, Fig. 7, conclusions] The interpretation of χ2ν as 'information content' is problematic. A reduced chi-square is a goodness-of-fit statistic, not a detection significance or Fisher information. The values in Fig. 7 are hard to interpret without degrees of freedom: χ2ν=800 for the DESI-like node+filament combination could be an extremely strong detection if ν is small, or a poor fit if ν is large. The paper should report a detection statistic with fixed degrees of freedom (e.g., Δχ2 between F5 and GR, or the S/N from Eq. 16) and state explicitly whether the quoted factors are in Δχ2, χ2ν, or S/N.

minor comments (5)

[§3.2 and §4] The cell size used for the density field is L_cell=2.19 Mpc/h in §3.2 but L_cell=2 Mpc/h in §4. Please use one consistent value and explain the difference if intentional.
[§3.4] The sentence 'whereas the can also have an impact in the error bars' is incomplete; it should refer to the random seed uncertainty.
[§3.4] The mock samples are at z=0 and z=1 while CMASS and DESI LRG samples have effective redshifts of about 0.5 and 0.8. This is acknowledged, but the forecasts should be labeled as approximate and the mismatch discussed quantitatively.
[Throughout] Several placeholder citations appear as '(cite)' or '(cites)' (e.g., §3.3, §3.4). These need to be resolved.
[Appendix A] The appendix shows correlation coefficients for HOD2 only; for reproducibility, include the actual covariance matrices (or a link to them) for all samples and for the combined vectors used in Fig. 7.

Circularity Check

0 steps flagged

No significant circularity: the environmental marked-correlation measurements are empirical forward-model outputs; the undefined chi2_nu and self-cited inputs are reproducibility concerns, not demonstrated circularity.

full rationale

The central claim is an empirical comparison of marked correlation functions measured in N-body simulations, not a derivation from assumptions. The chain is: f(R) and GR simulations (Arnold et al. 2019b) -> CIC density fields -> pycosmommf environment classification -> HOD mocks matched to observed n_gal and xi(r) -> marked correlation function M(r) -> S/N and chi2_nu statistics. Nowhere is the environment-split M defined in terms of the claimed outcome, nor is any parameter fitted to the final chi2_nu and then renamed a prediction. The HOD parameters are imported from Armijo et al. (2024b) and the mark index p=0.5 from Armijo et al. (2018), but these are prior inputs; the paper explicitly states it matches xi(r) 'to isolate the effect of MG in the studied environments' and to find 'dependence in higher-order moments', so the M differences are not forced by the two-point fit. The main audit issue is Section 5.3/Figure 7: the formula and degrees of freedom for the quoted chi2_nu are never given, and the all-galaxies benchmark is described as 'results of (Armijo et al. 2018)', so the 2.3x/4.1x ratios cannot be fully verified from the text and could in principle be normalization artifacts. However, the paper does provide jackknife covariance matrices, and without the missing formula one cannot exhibit an equation-level identity or a fitted-parameter-renamed-as-prediction. A missing definition is a correctness/reproducibility concern, not a demonstrated circular step. No self-citation is invoked to forbid alternatives or to define the conclusion, and the central environmental-split measurement has independent empirical content.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The analysis rests on standard cosmological and f(R) assumptions, on calibrated HOD mocks, and on a covariance estimator; the main additional burden is the unstated statistic used to quantify information content.

free parameters (3)

HOD parameters (log M_min, log M_0, log M_1, σ_logM, α) per model and sample = GR HOD1: 13.117, 13.152, 13.953, 0.220, 0.935; F5 HOD1: 13.142, 13.239, 14.028, 0.239, 1.028; GR HOD2: 12.700, 13.800, 1
Fitted so the mock galaxy samples reproduce the observed number density and two-point clustering of CMASS/DESI LRG samples (§3.4, Table 1). These fits absorb MG-induced clustering differences before the marked statistic is applied.
Mark power index p = 0.5 (both density and mass marks)
Chosen from previous marked-correlation studies (Armijo et al. 2018; Hernández-Aguayo et al. 2018), not optimized here (§2.3, §5). Affects the weight given to high/low density galaxies and hence the magnitude of M.
Environmental cell size L_cell = 2 Mpc/h (also used for density field grid cells of 2.19 Mpc/h for CIC density)
Chosen to define environment at a nonlinear scale similar to Sunseri et al. (2025); the classification into nodes/filaments/walls/voids depends on this scale (§4).

axioms (5)

domain assumption Hu-Sawicki f(R) with chameleon screening produces the modified Poisson equations and fifth force; background expansion matches ΛCDM by construction
Used as the gravity model throughout; parameters n=1 and |f_R0|=1e-5 adopted from prior literature (§2).
domain assumption HOD prescription (Zheng et al. 2007) with five free parameters adequately describes galaxy occupancy of halos in both GR and f(R)
Used to construct CMASS- and DESI-like mocks (§3.4).
domain assumption NEXUS+/pycosmommf Hessian eigenvalue criteria define physical environments (nodes, filaments, walls, voids)
The environment classification that drives the whole analysis is taken from this algorithm; the physical meaning of the split is assumed (§4).
domain assumption Jackknife resampling with 512 subvolumes of the simulation box provides an unbiased covariance for M(r)
Used for S/N and χ2; the authors acknowledge it may bias small scales (§5.3, Appendix A).
domain assumption Calibrating the F5 HOD to reproduce GR's two-point clustering is a valid way to isolate higher-order information
By construction, the mocks erase the 2-pt MG difference; the marked correlation function then probes residual environment-dependent differences (§5 intro).

pith-pipeline@v1.3.0-alltime-deepseek · 15632 in / 16394 out tokens · 145192 ms · 2026-08-03T11:29:44.109474+00:00 · methodology

0 comments

read the original abstract

We study environment-dependent clustering using the marked correlation function applied to Hu-Sawicki $f(R)$ modified gravity simulations. This gravity theory enriches the structure formation by enhancing gravity in a scale-dependent form. By employing a multi-scale cosmic structure finder algorithm, we define the cosmic environments divided in: nodes, filaments, walls and voids. We find a stronger impact of modified gravity in nodes and filaments, which together dominate the information content by more than a factor of four relative to other environments. Combining environmental information further enhances the expected signal-to-noise ratio for CMASS- and DESI-like mock samples, particularly in configurations including filaments. Overall, marked correlation functions that incorporate environmental structure increase the information content by about a factor of two compared to standard density-based marks applied to the full galaxy sample. These results demonstrate the importance of environmental information, especially from filaments, in improving the sensitivity of galaxy clustering tests to deviations from GR in the $f(R)$ scenario.

Figures

Figures reproduced from arXiv: 2601.05934 by Joaquin Armijo, Lucas Da Costa.

**Figure 2.** Figure 2: Histogram d𝑛/𝑑 log 𝜌 of density values 𝜌𝑖 in both GR (solid lines) and F5 (dashed lines) simulations. We separate the 𝜌𝑖 values by their respective cosmic structure as defined by pycosmommf: Nodes (red), filaments (green), walls (blue), voids (grey). where 𝑓𝑅0 is the present-day value of the scalaron.With these choices, the model free parameters are two: 𝑛 and 𝑓𝑅0. These can be constrained using late-time… view at source ↗

**Figure 3.** Figure 3: Left: Histogram of HOD galaxy density values d𝑛gal/𝑑 log 𝜌 as function of log 𝜌/𝜌¯ for the same cosmic structures of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Left: Density-marked correlation function M as function of galaxy distance 𝑟 for GR (purple) and F5 (orange) simulations with 𝑚 = 𝜌 0.5 . We analyse results for HOD1 (solid) and HOD2 (dashed) samples in a range of distance between 1 < 𝑟/(Mpc/ℎ −1 ) < 70. We provide error bars for GR simulation as shaded region for HOD1 (light purple shade) and HOD2 (dark purple shade). A bottom subpanel showing the relativ… view at source ↗

**Figure 5.** Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: signal-to-noise ratio as function of distance 𝑟 calculated using Equation 16. We estimate these for different cosmic structures using same colour scheme than [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: Reduced chi-square statistic 𝜒 2 𝜈 of M for different cosmic structures (same colour scheme as [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

discussion (0)

Reference graph

Works this paper leans on

1 extracted references · 1 linked inside Pith

[1]

P., et al., 2017a, ApJ, 848, L12 Abbott B

Abbott B. P., et al., 2017a, ApJ, 848, L12 Abbott B. P., et al., 2017b, ApJ, 848, L13 Anderson L., et al., 2012, MNRAS, 427, 3435 Appleby S., Battye R., 2007, Physics Letters B, 654, 7 Aragón-CalvoM.A.,vandeWeygaertR.,JonesB.J.T.,2010,MNRAS,408, 2163 Armijo J., Cai Y.-C., Padilla N., Li B., Peacock J. A., 2018, MNRAS, 478, 3627 ArmijoJ.,BaughC.M.,PadillaN...

Pith/arXiv arXiv 2012

[1] [1]

P., et al., 2017a, ApJ, 848, L12 Abbott B

Abbott B. P., et al., 2017a, ApJ, 848, L12 Abbott B. P., et al., 2017b, ApJ, 848, L13 Anderson L., et al., 2012, MNRAS, 427, 3435 Appleby S., Battye R., 2007, Physics Letters B, 654, 7 Aragón-CalvoM.A.,vandeWeygaertR.,JonesB.J.T.,2010,MNRAS,408, 2163 Armijo J., Cai Y.-C., Padilla N., Li B., Peacock J. A., 2018, MNRAS, 478, 3627 ArmijoJ.,BaughC.M.,PadillaN...

Pith/arXiv arXiv 2012