{"id":"d51eb7d1-24be-4c75-9093-ca174b4d809e","arxiv_id":"2504.21509","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Weighting 2D angular correlation functions by inverse mean neighbor distance in the β-skeleton cosmic web increases the Ωm discrimination measured by Δχ² by a factor of 2-3 relative to standard 2PACF.","lead":"Galaxy clustering in thin sky slices can be made more sensitive to the universe's matter density by weighting galaxies according to their cosmic-web environment. On BOSS CMASS data and simulations, inverse neighbor-distance weighting roughly triples the statistical separation between different Ωm models, a boost that could help slitless surveys like Euclid and CSST.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 2–3× sensitivity gain is computed from one COLA mock per Ωm with heavily overlapping redshift shells and no error on r, so the gain could be noise.","rationale":"The reader's formal weakest_assumption focuses on whether COLA+SHAM mocks reproduce β-skeleton connection properties, which is a model-fidelity concern. My stress-test identifies a distinct, more directly load-bearing issue: the statistical robustness of the reported improvement factor given a single mock realization per Ωm and heavily overlapping redshift shells. The reader's rationale does mention 'each cosmology is represented by a single COLA mock' as one of several concerns, so there is partial agreement. However, the weakest_assumption as stated is about mock accuracy, not about the noise in the Δχ² estimate. The single-realization issue undermines the central quantitative claim even if the mocks are perfectly accurate, because the improvement could arise from the particular noise realization of the one mock. The proposed test—running multiple independent realizations and measuring the scatter of r—directly settles whether the 2–3× improvement is a real signal or a statistical fluctuation. This concern reinforces the reader's CONDITIONAL verdict: the paper should be accepted only if the authors provide such multiple realizations or otherwise quantify the uncertainty on r. Therefore, no change to the verdict is needed; it remains CONDITIONAL.","tokens_in":16237,"tokens_out":9163,"duration_ms":98054,"concrete_test":"Generate at least 10 independent COLA+SHAM realizations at each Ωm (0.25, 0.31, 0.4) using the same pipeline, recompute Table 1 for each realization, and report the mean and standard deviation of the relative improvement r (Eq. 17) for the 1/D_nei combination. If the mean r remains ≈2–3 with a 1σ scatter small compared to the mean (e.g., <30% of the mean), the claim is robust; if the scatter is comparable to or larger than the mean, or if the null hypothesis r=0 is within 1–2σ, the claimed boost is not significant and the conclusions must be softened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that adding the 1/D_nei-weighted angular correlation function boosts Δχ² by a factor of 2–3 relative to the unweighted 2PACF—rests on Table 1, where each Ωm is represented by a single COLA mock realization. Equation 14 averages χ² over six redshift shells, but these shells overlap by 80% (each shell is Δz=0.05 and shifts by 0.01), so they are far from independent; the effective number of independent measurements is much smaller than six. The weighted statistics are derived from the same galaxy positions and weights, and Figure 9 shows they are strongly correlated with the unweighted 2PACF. Adding a highly correlated statistic can inflate Δχ² even if it carries no additional cosmological signal, because the single-mock noise realization contributes to the quadratic form. The paper reports no uncertainty on r (Eq. 17), so an observed improvement of 229%–336% could easily be consistent with r=0 when the mock realization is varied. This is the most load-bearing weakness because the quantitative factor of 2–3 is the paper's headline result; without multiple realizations or error bars on r, this improvement is not statistically established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes mark-weighted angular correlation functions (MACFs) built from two-dimensional β-cosmic-web classifications, using connection number Ncon, mean neighbor distance Dnei, and inverse mean neighbor distance 1/Dnei as marks. The method is tested on SDSS DR12 CMASS-NGC galaxies and COLA mocks with Ωm = 0.25, 0.31, and 0.4, with covariance matrices estimated from 300 PATCHY mocks. The central claim is that combining the standard 2PACF with the 1/Dnei-weighted angular correlation statistic increases Δχ² by a factor of 2–3 relative to the unweighted 2PACF alone, as quantified in Table 1. The paper also argues that the thin-redshift-slice formulation is well suited to slitless surveys such as Euclid and CSST.","tokens_in":16442,"tokens_out":5767,"duration_ms":61476,"significance":"If the reported gain is robust, the paper provides a timely and potentially useful extension of mark-weighted statistics to 2D angular clustering, which would be valuable for photometric and slitless surveys. The paper is transparent about its proof-of-concept nature, includes a public code link for the β-skeleton construction, and applies the method to a real SDSS sample. However, the headline quantitative claim—the factor of 2–3 improvement—rests on a single COLA mock realization per cosmological model and on a covariance matrix whose fidelity for the new mark statistics is not validated. The central result therefore needs substantial additional statistical support before the claimed sensitivity gain can be considered established.","major_comments":[{"comment":"The factor-of-2–3 improvement in Δχ² is computed from one COLA mock realization per Ωm, and no uncertainty is quoted for the relative sensitivity r defined in Eq. (17). The six redshift shells entering Eq. (14) overlap by 80% (each shell has Δz = 0.05 and the central redshifts step by 0.01), so they are far from independent; averaging them does not reduce the noise by √6. Consequently the 229%–336% values in Table 1 are point estimates whose statistical error could be comparable to the claimed effect. I request multiple independent COLA realizations per Ωm, or at minimum a jackknife/bootstrap over mock realizations and data, with error bars reported on r and on the individual Δχ² values.","section":"Section 2.2, Section 4, Table 1, Eq. (17)"},{"comment":"The covariance matrix used in the χ² calculation is estimated from PATCHY mocks, but the paper does not validate that PATCHY reproduces the β-skeleton connection properties (Ncon, Dnei, 1/Dnei) or the spatial correlations of these marks. The COLA mocks are validated against standard 2PCF, 3PCF, and power spectrum in the cited work, but not against the mark statistics that are the basis of the new angular correlation functions. If PATCHY's mark statistics are inaccurate, all entries of Table 1 change. I recommend adding a validation figure comparing PATCHY mark-weighted angular correlation functions with those from COLA mocks and/or the data, or computing the covariance from the same COLA simulations used for the model predictions.","section":"Section 2.3, Eqs. (10)–(13)"},{"comment":"The text around Figure 5 states that the probability distributions of Lcon and Dnei 'lie too close to each other to reliably distinguish between different cosmological models,' yet Table 1 reports very large Δχ² differences for the Dnei- and 1/Dnei-weighted statistics. The paper should explain why statistics built from nearly identical marginal distributions can nevertheless have large discriminating power, and should demonstrate that the effect is not driven by the single-mock noise realization or by the choice of truncation threshold fcut and normalization limits a and b. As written, the apparent contradiction weakens the interpretation of the weighted-statistic gains.","section":"Section 3.1, Figure 5; Section 4, Table 1"},{"comment":"The concluding statement that weighting by Ncon 'provides minimal improvement' is not supported by Table 1: at Ωm = 0.4, the Ncon combination gives r = +88%, which is larger than the Dnei improvement at Ωm = 0.25 (+39%). The ranking of the statistics is therefore not stable across the two off-fiducial Ωm values. The paper should quantify the stability of the ranking and avoid a summary claim that depends on one of the two comparison points.","section":"Section 4, Table 1; Section 5"}],"minor_comments":[{"comment":"The relation between the angular separation θ and the comoving scale s is stated in Eq. (8) but the binning in s and θ is not given explicitly; please state the bin edges in θ for the eight bins used in the analysis.","section":"Section 3.2, Eq. (9)"},{"comment":"The notation for Δχ² is confusing: Eq. (15) defines a per-shell quantity while Eq. (16) redefines it as the difference of averaged χ² values. Using distinct symbols (e.g., Δχ²_i and an averaged \\(\\overline{\\Delta\\chi^2}\\)) would prevent ambiguity.","section":"Section 3.2, Eqs. (15)–(16)"},{"comment":"The Landy–Szalay estimator is written for the 3D quantity W(s, μ), but the actual analysis uses 2D angular correlation functions; please specify the angular estimator used for the projected shells, since this is the core methodological step.","section":"Section 3.2, Eq. (4)"},{"comment":"The sentence 'Statistically, this enhancement is equivalent to increasing our dataset by the same amount' is an overinterpretation: a λ-fold increase in Δχ² does not map directly to a λ-fold increase in survey volume unless the full covariance is rescaled in a specific way.","section":"Section 4"},{"comment":"There is a typo in the sentence 'we compute the mean Δχ² cross the six overlapping redshift bins'; 'cross' should be 'across'.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"This is a proof-of-concept paper extending a method the group has already established in 3D. The novelty is the 2D angular implementation, and the topic is within the journal's scope. The main obstacle is statistical: the headline factor-of-2–3 improvement is not supported by error bars and relies on one mock per cosmology. I believe this can be fixed with additional realizations or a careful error analysis, so I recommend major revision rather than rejection. The authors should also address the PATCHY-validation gap, as the covariance is central to all quantitative conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the first application of β-cosmic-web mark-weighted correlation functions to 2D angular clustering — a straightforward angular analogue of the 3D MCFs from Yin et al. (2024). The quantitative comparison of Ncon, Dnei, and 1/Dnei weights on CMASS angular slices is new, and the paper is honest that this is a proof-of-concept. It uses public data, links to code, and the methodology is clearly described: Landy–Szalay estimator, normalization with integration limits, and a truncation cutoff for 1/Dnei. The visual agreement between the Ωm=0.31 mock and the data is supportive, and the qualitative ranking of weights (1/Dnei best, Ncon worst) is consistent with the 3D results. There is no circularity: no parameter is fitted to force agreement; Ωm discrimination is measured from simulations and data.\n\nThe soft spots are real and they sit directly under the headline result. Each cosmology is represented by a single COLA mock, so the Δχ² values in Table 1 are point estimates with no error bars. The six redshift shells overlap by 80% (Δz=0.05, shifted by 0.01), so the averaging in Eq. 14 does not give six independent measurements — the effective sample is much smaller. Figure 9 shows the weighted statistics are strongly correlated with the unweighted 2PACF, and adding a correlated statistic can inflate Δχ² even if it carries no new signal. The covariance from PATCHY mocks is not validated for these β-skeleton marks. And the best weight was chosen after looking at the same data. Any one of these would be a footnote; together they mean the claimed 229–336% improvement could easily be consistent with no real gain once mock noise is accounted for.\n\nThis is not a fatal flaw in the concept — the idea is sound and worth testing properly. But the paper, as written, overstates the confidence in the sensitivity boost. The abstract's 'boosting Δχ² by a factor of 2–3' should be softened to a preliminary ranking unless the authors add multiple realizations per Ωm, propagate an uncertainty on r, or validate the covariance for the mark statistics.\n\nWho should read it: LSS cosmologists working on photometric or slitless surveys (Euclid, CSST) who want a starting point for marked angular statistics. It deserves a serious referee — the novelty is legitimate and the community needs to know whether this trick works — but the referees should insist on a robustness analysis before the quantitative claim is accepted.","headline":"A legitimate but statistically under-powered proof-of-concept that β-cosmic-web marks can be applied to 2D angular clustering, though the headline 2–3× sensitivity gain is not yet established.","tokens_in":17080,"tokens_out":1696,"would_cite":true,"duration_ms":19728,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that weighting the angular two-point correlation function with β-cosmic-web marks—especially the inverse mean neighbor distance—makes the statistic two to three times more sensitive to the matter density parameter…","keywords":["β-cosmic web","mark-weighted correlation function","angular correlation function","cosmological parameter constraints","matter density parameter","CMASS galaxies","slitless surveys","large-scale structure"],"falsifier":"Run the same $1/\\bar{D}_{\\rm nei}$ weighting on an independent set of mocks with known $\\Omega_m$ values (for example, the mocks used for covariance estimation, or a full N-body simulation set) and check whether the weighted statistic still separates $\\Omega_m = 0.25$ and $0.4$ from $0.31$ by roughly 2-3 times more $\\Delta\\chi^2$ than the unweighted angular correlation function; if the gain disappears, the enhancement is a property of the mock family rather than of the statistic.","tokens_in":15998,"feed_emoji":"🌌","tokens_out":14072,"duration_ms":122748,"temperature":0.7,"pith_summary":"This paper tries to establish that the standard angular two-point correlation function becomes a much sharper cosmological probe when it is weighted by marks derived from the β-skeleton cosmic web. On thin redshift slices of the CMASS galaxy sample and mock catalogs with $\\Omega_m = 0.25$, $0.31$, and $0.4$, the authors measure how well each statistic separates these cosmologies through the average $\\Delta\\chi^2$ over six redshift bins. Weighting by mean neighbor distance improves the average $\\Delta\\chi^2$ by roughly 40%-130%, and weighting by its inverse improves it by a factor of 2-3. If correct, this gives surveys with imprecise redshifts a way to recover cosmological information that would otherwise be lost in 3D clustering analysis.","feed_headline":"Cosmic-web weights make angular clustering 2-3x sharper on Ωm","feed_subtitle":"Weighting angular correlations by inverse neighbor distance gives 2-3x larger Δχ² for matter density in clustering.","key_machinery":"The central object is the β-skeleton of the projected galaxy distribution: a graph that connects two galaxies when a lune-shaped empty region between them contains no third galaxy, with $\\beta = 3$ chosen as the baseline. From this graph each galaxy receives three marks: $N_{\\rm con}$, the number of connected neighbors; $\\bar{D}_{\\rm nei}$, the mean distance to those neighbors; and $1/\\bar{D}_{\\rm nei}$, its inverse. The mark-weighted angular correlation function is computed with the Landy–Szalay pair-count estimator, weighted by these marks, normalized by the integral of the monopole over separations from 10 to 58 $h^{-1}\\,{\\rm Mpc}$, and evaluated in six overlapping thin redshift slices projected to two dimensions. The $1/\\bar{D}_{\\rm nei}$ weight emphasizes galaxies in dense regions, and the paper attributes the sensitivity gain to information carried by those environments.","core_discovery":"The reported discovery is that combining the standard two-point angular correlation function with a β-cosmic-web weighted angular correlation function is substantially more discriminating in $\\Omega_m$ than the unweighted statistic alone. The inverse mean neighbor distance weight, $1/\\bar{D}_{\\rm nei}$, raises the average $\\Delta\\chi^2$ by 229%-336% relative to the unweighted case, depending on the fiducial model, which the paper states as a factor of 2-3. The mean neighbor distance weight gives a 39%-130% improvement, while the connection-number weight gives little or no gain and even reduces sensitivity at low $\\Omega_m$. Across all statistics the minimum $\\chi^2$ falls at $\\Omega_m = 0.31$, the mock cosmology the authors find most consistent with the observed CMASS sample.","pith_inferences":["Because $1/\\bar{D}_{\\rm nei}$ upweights dense regions, the result suggests that the angular clustering of galaxies in dense environments carries non-Gaussian, small-scale information that the standard angular correlation function misses; a natural next test is whether similar gains appear for $\\sigma_8$ or the dark-energy equation of state.","The gain is measured with one family of fast mock catalogs; applying the same weighting to an independent set of mocks, or to an observational sample with a known $\\Omega_m$ from other probes, would show whether the improvement survives outside that mock family.","The paper combines only one weighted statistic at a time with the standard angular correlation function; combining several weighted statistics in a single covariance vector could push the 2D gain toward the larger improvements seen in 3D marked statistics.","Other 2D marks, such as powers of local density or density-gradient weights, are suggested by the authors but untested; these could extend the method further if the dense-region signal is as informative as the paper argues."],"forward_implications":["The $1/\\bar{D}_{\\rm nei}$-weighted statistic combined with the standard angular correlation function raises average $\\Delta\\chi^2$ by 229%-336%, which the paper equates to the sensitivity gain of a substantially larger dataset.","The estimator works in thin angular slices, so it can be applied to slitless and wide-band photometric surveys where redshift errors degrade full 3D clustering.","The mean neighbor distance weight improves $\\Delta\\chi^2$ by 40%-130% while the connection-number weight gives little or no improvement, indicating that environmental density rather than raw connectivity drives the gain.","The minimum $\\chi^2$ at $\\Omega_m = 0.31$ appears in every statistic, so weighting sharpens a discrimination that the unweighted angular correlation function already makes, rather than changing which cosmology fits."],"supporting_citations":[{"why":"introduced the β-cosmic-web mark weights $N_{\\rm con}$, $\\bar{D}_{\\rm nei}$, and $1/\\bar{D}_{\\rm nei}$ for 3D marked correlation functions; this paper adapts them to 2D angular statistics.","marker":"Yin et al. 2024"},{"why":"supplied the fast mock galaxy catalogs used for the $\\Omega_m$ comparison and validated them against standard clustering statistics.","marker":"Ding et al. 2024"},{"why":"provided the mock realizations from which the covariance matrices are estimated.","marker":"Kitaura et al. 2016"},{"why":"defined the hybrid simulation method underlying the mock catalogs.","marker":"Tassev et al. 2013"},{"why":"first applied β-skeleton construction to cosmic-web analysis, providing the geometric basis for the marks.","marker":"Fang et al. 2019"},{"why":"supplied the pair-count estimator used to compute the correlation functions.","marker":"Landy & Szalay 1993"},{"why":"set the fiducial cosmological parameters used in the mock catalogs.","marker":"Planck Collaboration et al. 2016"}],"fun_headline_variants":["Inverse-neighbor weighting improves Ωm constraints 2-3x","Cosmic-web weighted angular correlations sharpen Ωm 2-3x","2D β-weighted clustering improves Ωm by factor 2-3","Thin-slice cosmic-web weights tighten Ωm 2-3x for slitless surveys","Cosmic-web weighted angles deliver 2-3x gain on Ωm from SDSS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The mock galaxy catalogs reproduce not only standard clustering statistics but also the β-skeleton connection properties of the real galaxy sample, so the differences between the different matter-density models are cosmological rather than simulation artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Inverse-neighbor weighting improves Ωm constraints 2-3x","Cosmic-web weighted angular correlations sharpen Ωm 2-3x","2D β-weighted clustering improves Ωm by factor 2-3","Thin-slice cosmic-web weights tighten Ωm 2-3x for slitless surveys","Cosmic-web weighted angles deliver 2-3x gain on Ωm from SDSS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00104,"raw_usage":{"total_tokens":4391,"prompt_tokens":977,"completion_tokens":3414,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":593,"completion_tokens_details":{"reasoning_tokens":3309}},"tokens_in":593,"tokens_out":3414,"duration_ms":24156,"temperature":1.0,"reasoning_tokens":3309,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:01:21.649296+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same $1/\\bar{D}_{\\rm nei}$ weighting on an independent set of mocks with known $\\Omega_m$ values (for example, the mocks used for covariance estimation, or a full N-body simulation set) and check whether the weighted statistic still separates $\\Omega_m = 0.25$ and $0.4$ from $0.31$ by roughly 2-3 times more $\\Delta\\chi^2$ than the unweighted angular correlation function; if the gain disappears, the enhancement is a property of the mock family rather than of the statistic.","supporting_citations":[{"cited_title":"2024, Phys","cited_arxiv_id":null,"evidence_quote":"introduced the β-cosmic-web mark weights $N_{\\rm con}$, $\\bar{D}_{\\rm nei}$, and $1/\\bar{D}_{\\rm nei}$ for 3D marked correlation functions; this paper adapts them to 2D angular statistics."},{"cited_title":"2024, ApJS, 270, 25 4, 5","cited_arxiv_id":null,"evidence_quote":"supplied the fast mock galaxy catalogs used for the $\\Omega_m$ comparison and validated them against standard clustering statistics."},{"cited_title":"2016, MNRAS, 456, 4156 4, 6","cited_arxiv_id":null,"evidence_quote":"provided the mock realizations from which the covariance matrices are estimated."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defined the hybrid simulation method underlying the mock catalogs."},{"cited_title":"2019, MNRAS, 485, 5276 2, 9","cited_arxiv_id":null,"evidence_quote":"first applied β-skeleton construction to cosmic-web analysis, providing the geometric basis for the marks."},{"cited_title":"D., & Szalay, A","cited_arxiv_id":null,"evidence_quote":"supplied the pair-count estimator used to compute the correlation functions."}],"review_version":1}