{"id":"7ab53067-bf19-4d06-8ca6-58ef7aa387cc","arxiv_id":"2501.07817","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":13,"one_line_summary":"A void size function from BOSS DR16 yields w = -1.263^{+0.329}_{-0.396}, Omega_m = 0.293^{+0.060}_{-0.053}, and sigma8 = 0.897^{+0.159}_{-0.192} after MCMC fitting.","lead":"Using cosmic voids detected in BOSS DR16 galaxies, the authors measure the void size function and fit a wCDM cosmology, finding w = -1.263, Omega_m = 0.293, and sigma8 = 0.897 with 20-30% errors. The result is a test of whether void abundances can serve as an independent probe of dark energy and structure growth, complementary to galaxy clustering.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The empirical VSF-to-watershed-void mapping is unvalidated at BOSS DR16 densities, and the paper's own cut-robustness tests show >1σ shifts; the quoted 1σ intervals omit this systematic.","rationale":"The analysis is internally consistent and follows the standard Vdn framework; I found no algebraic error in Eqs. (5)�(13). The concern is not that the model disagrees with current consensus, but that the empirical mapping between an excursion-set spherical-void model and VIDE watershed voids is the place where correctness risk is highest. The central claim is the set of numerical posteriors, and those posteriors are conditional on that mapping. The paper itself provides direct evidence of fragility: it explicitly labels the relation empirical, states that no theoretical framework fixes the ellipticity threshold, and reports that small changes in the minimum radius or ellipticity cuts shift parameters by more than 1 sigma. These are systematics, not statistical fluctuations, and they are absent from the quoted error bars. The mock calibration in Song et al. (2024a) is helpful but not conclusive for this dataset because the paper reports that delta_v differs between the mocks and DR16 due to galaxy number density and void size. The proposed mock test would settle whether the mapping is biased at the precision claimed. I agree with the reader's weakest_assumption and therefore recommend keeping the CONDITIONAL verdict rather than upgrading to ACCEPT. If the mock test failed, the appropriate verdict would be REJECT or UNVERDICTED for the precise central values, but that is a checkable empirical question rather than a demonstrated inconsistency.","tokens_in":16144,"tokens_out":7141,"duration_ms":76428,"concrete_test":"Run the full BOSS DR16 pipeline (VIDE with identical settings, ellipticity cut 0.15, r_min = 2.5xMGS, jackknife covariance, same wCDM likelihood and 10-sigma priors) on realistic mock catalogs that reproduce the BOSS DR16 n(z) and galaxy bias, e.g. the official BOSS DR16 mocks or OuterRim. Compare the recovered 68% contours for w, Omega_m, and sigma8 with the known input cosmology. If the true values fall outside the recovered contours (or the best-fit offset exceeds the statistical uncertainty), the empirical model-data mapping is biased and the quoted constraints should not be treated as the full uncertainty.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing link is the mapping from the Jennings et al. (2013) Vdn excursion-set model, Eqs. (5)�(9), to VIDE watershed voids selected with ellipticity <0.15. That model is derived for spherical voids, with the Bernardeau (1994) spherical mapping c_v = 1.594, while the data are non-spherical watershed zones. The paper concedes in Section 3 that this relation is empirical and that no theory fixes the ellipticity threshold. Because the same mapping determines both the fitted delta_v and the cosmological parameters, any bias in it propagates directly into w, Omega_m, and sigma8. The paper's own robustness tests quantify this fragility: lowering the minimum radius cut from ~2.5xMGS to ~2.3x or ~2.0x MGS shifts some parameters by more than 1 sigma, and ellipticity cuts outside 0.14�0.16 produce >1 sigma deviations in Omega_m. These shifts are not propagated into the quoted statistical errors. The cited mock calibration (Song et al. 2024a) is not directly transferable: Section 4 reports that the DR16 delta_v best fits differ from the mock values because of lower galaxy number density and larger void size. Thus the model-to-data mapping is unvalidated at the exact density and selection of this catalog, and a biased mapping would bias the central cosmological claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper measures the void size function (VSF) from BOSS DR16 galaxies in two redshift bins (0.2<z<0.5 and 0.5<z<0.8) using VIDE watershed voids selected by ellipticity <0.15 and a minimum radius of about 2.5 times the mean galaxy separation. It fits the Jennings et al. (2013) volume-conserving Vdn excursion-set model, with free void linear underdensity thresholds delta_v and RSD parameters B in each bin, together with wCDM parameters w, Omega_m, and A_s, using MCMC with a jackknife covariance and 10-sigma Planck Gaussian priors on A_s, h, Omega_b, and n_s. The headline results are w = -1.263^{+0.329}_{-0.396}, Omega_m = 0.293^{+0.060}_{-0.053}, and sigma8 = 0.897^{+0.159}_{-0.192}. The paper argues that the VSF provides a complementary probe to galaxy clustering, and it explicitly acknowledges that the relation between the theoretical model and the observed watershed void catalog is empirical and that no theoretical framework fixes the optimal ellipticity threshold.","tokens_in":16475,"tokens_out":7907,"duration_ms":73613,"significance":"If the model-to-data mapping were validated, this paper would be a useful demonstration that VSF measurements from spectroscopic surveys can constrain w and Omega_m with uncertainties competitive with some clustering analyses and with a complementary degeneracy direction. The analysis uses standard public tools (VIDE, CAMB, emcee), a reasonable jackknife covariance, and transparent prior choices, and the paper explicitly acknowledges several limitations. I do not share the characterization of the joint fitting of delta_v and B as circular in the statistical sense; these are nuisance parameters estimated from the data. The decisive weakness is that the mapping between the spherical excursion-set model and VIDE watershed voids is empirical and is unvalidated at the number density and selection of the BOSS DR16 catalog, and the paper's own robustness tests show >1-sigma shifts in key parameters when the selection is changed. In addition, the sigma8 result is largely prior-driven. If the authors address these systematics, the paper could be a solid contribution; in its current form, the headline 1-sigma intervals understate the model uncertainty.","major_comments":[{"comment":"The load-bearing model-to-data connection is explicitly empirical. Section 3 states that the relation between the Jennings et al. (2013) excursion-set model and the watershed-void abundance is empirical, and that no theoretical framework fixes the optimal ellipticity threshold. Since delta_v and B are fitted jointly with w, Omega_m, and A_s from the same VSF data, any bias in this mapping propagates directly into the cosmological parameters. The paper's own Section 4 notes that the DR16 delta_v best fits differ from the mock-calibrated values because of the lower galaxy number density and larger void size, so the mock validation in Song et al. (2024a) does not transfer to this catalog. The quoted 1-sigma intervals therefore omit the dominant systematic in the model-to-data connection; please add mock-based validation at the BOSS DR16 density and selection, or include an explicit systematic term and soften the central claim.","section":"Section 3, Eqs. (5)-(9); Section 4, delta_v comparison"},{"comment":"The robustness tests reported in Section 3 show that lowering the minimum radius cut from ~2.5xMGS to ~2.3x or ~2.0xMGS shifts Omega_m, w, and delta_v by more than 1 sigma, and that ellipticity cuts outside 0.14-0.16 produce >1-sigma deviations in Omega_m. These cuts define the very data vector used for the headline constraints, so the shifts are selection systematics rather than small perturbations. They are not propagated into the statistical errors in Table 2 or the abstract. The assertion that the current choice 'can provide reliable constraint results' is not supported by these tests; at minimum, the final intervals should include the selection systematic, or the analysis should be restricted to a selection with demonstrated stability.","section":"Section 3, radius- and ellipticity-robustness paragraphs"},{"comment":"The sigma8 constraint is not an independent VSF measurement. sigma8 is derived from A_s, and A_s is sampled with a 10-sigma Planck Gaussian prior N(2.105, 0.3) (Table 2). The A_s posterior, 2.181^{+0.293}_{-0.297}, is essentially the prior, so the sigma8 posterior is dominated by the Planck prior volume rather than by the void abundance data. The abstract and summary present sigma8 = 0.897^{+0.159}_{-0.192} as a headline VSF result; this should be qualified as a prior-influenced derived parameter, with w, Omega_m, and the void parameters highlighted as the directly constrained quantities.","section":"Section 4, Table 2"}],"minor_comments":[{"comment":"The text refers to the 'MSG value'; this should be 'MGS' for mean galaxy separation.","section":"Section 2.1, Table 1"},{"comment":"The infinite series and the closed-form exponential expression in Eq. (7) are not exactly equal; please state which expression is used in the fits.","section":"Eq. (7)"},{"comment":"The minimum radius cuts are described as ~2.5xMGS, but for the first redshift bin 40 h^-1 Mpc divided by MGS=15 h^-1 Mpc is 2.67, not 2.5; please reconcile the wording with the numbers.","section":"Section 3, Fig. 3"},{"comment":"The abstract emphasizes that voids are identified 'without assuming any void shape', while the VSF model assumes spherical voids and the analysis keeps only voids with ellipticity<0.15; this wording should be reconciled.","section":"Abstract; Section 3"},{"comment":"The MCMC section reports burn-in and thinning but no convergence diagnostic; reporting a Gelman-Rubin statistic would strengthen the reproducibility of the chains.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the paper is honest about its limitations, but the central claim is conditional on an empirical model mapping and selection choices that produce >1-sigma shifts. I would not support acceptance before the authors either validate the mapping with mocks at BOSS DR16 density and selection or add a systematic error term and reframe sigma8 as prior-influenced. With those changes, the paper would be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a competent extension of the established VSF pipeline to BOSS DR16. The constraints are plausible but not tighter than the earlier DR12 results, and the main caveats are stated in the paper itself.\n\nWhat is new: DR16 VSF measurements with ellipticity-selected voids, free delta_v and B per redshift bin, jackknife covariance, and a clean MCMC setup. The paper is honest about the limits of the model: it explicitly says the relation between the Jennings/SvdW excursion-set model and the VIDE watershed voids is empirical, that no theory fixes the ellipticity threshold, and it reports robustness tests for both ellipticity and radius cuts. That is the right way to write this kind of analysis.\n\nWhere it is soft: the stress-test concern lands. The model is derived for spherical voids; the data are non-spherical watershed zones with ellipticity <0.15. The paper's own tests show that lowering the minimum radius cut from ~2.5xMGS to ~2.3x or ~2.0x shifts Omega_m, w, and delta_v by more than 1 sigma. Those shifts are not propagated into the quoted errors, so the statistical intervals understate the systematic. The mock calibration from Song et al. (2024a) is not directly transferable: the paper says the DR16 delta_v best fits differ from the mock values because of lower galaxy number density and larger void size. And sigma8 is derived from A_s with a 10-sigma Planck prior, so it is partly prior-driven rather than an independent VSF measurement. None of this is fatal, but it means the result is a conditional validation, not a fresh cosmological measurement.\n\nThe analysis itself is standard and reproducible in principle, though the data availability statement says 'upon reasonable request', so no public catalogs or chains. I would not treat the 1-sigma errors as the full uncertainty story.\n\nBottom line: this deserves a serious referee. Send it to review with a request to propagate the scale-cut systematics, release the data products, and ideally test the empirical mapping with mocks at the DR16 number densities. I would bring it to a reading group as a good example of an honest VSF analysis.","headline":"A competent, honest DR16 VSF extension with constraints consistent with DR12; the caveats are the empirical model-to-void mapping and scale-cut systematics that the paper itself reports.","tokens_in":17034,"tokens_out":3737,"would_cite":true,"duration_ms":35283,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["85A40","83F05"],"pacs":["98.80.Es"],"model":"deepseek-v4-flash","headline":"Voids in BOSS DR16 constrain dark energy to $w=-1.263^{+0.329}_{-0.396}$ and matter density to $\\Omega_{\\rm m}=0.293^{+0.060}_{-0.053}$.","keywords":["cosmic voids","void size function","dark energy equation of state","matter density","sigma8","BOSS DR16","excursion-set theory","redshift space distortions"],"falsifier":"Run the identical void finder and MCMC fitter on mock galaxy catalogs with known $w$, $\\Omega_{\\rm m}$, and $\\sigma_8$ and with BOSS DR16-like geometry and density; if the recovered values depart from the truth by more than the reported 68% intervals, the empirical model-to-void mapping is biased. A simpler data-side test is to map how the best-fit parameters shift as the ellipticity threshold moves in steps of 0.01 around 0.15.","tokens_in":15952,"feed_emoji":"🌌","tokens_out":11833,"duration_ms":103050,"temperature":0.7,"pith_summary":"This paper measures the void size function—the number density of cosmic voids as a function of radius—from 1.9 million BOSS DR16 galaxies in two redshift bins ($z=0.2$–$0.5$ and $0.5$–$0.8$), and fits it with an excursion-set model. The headline result is a dark-energy equation of state $w=-1.263^{+0.329}_{-0.396}$, matter density $\\Omega_{\\rm m}=0.293^{+0.060}_{-0.053}$, and fluctuation amplitude $\\sigma_8=0.897^{+0.159}_{-0.192}$ in a $w$CDM model. A sympathetic reader should care because void counts probe large-scale structure in underdense regions, giving degeneracy directions that are nearly orthogonal to those from galaxy clustering and therefore useful for joint cosmological constraints.","feed_headline":"Void sizes from 1.9M galaxies constrain dark energy to w=-1.26","feed_subtitle":"Underdense regions give matter density 0.293 and sigma8 0.897, complementing galaxy clustering.","key_machinery":"The load-bearing object is the $V\\,\\mathrm{d}n$ void size function, $\\mathrm{d}n_v/\\mathrm{d}\\ln R_v = (3/4\\pi R_v^3)\\,F(\\nu,\\delta_v,\\delta_c)\\,\\mathrm{d}\\nu/\\mathrm{d}\\ln R_L$. The first-crossing factor $F$ is the Sheth–van de Weygaert distribution for random walks that hit the void barrier $\\delta_v$ before the collapse barrier $\\delta_c=1.686$, with significance $\\nu=|\\delta_v|/\\sigma_M(z)$. Lagrangian and Eulerian void sizes are linked by the spherical mapping $R_L\\simeq R_v(1-\\delta_v/c_v)^{c_v/3}$ with $c_v=1.594$, and observed radii are corrected by $R^{\\rm obs}_v = q_{\\rm RSD}\\,q_{\\rm AP}\\,R_v$, with one free RSD parameter $B$ per redshift bin. These pieces convert counts of watershed voids into a cosmological likelihood.","core_discovery":"The paper reports that the abundance of nearly spherical voids identified by a Voronoi-tessellation watershed algorithm in BOSS DR16 can, by itself, produce competitive cosmological constraints. Selecting voids with ellipticity $\\epsilon_v<0.15$ and excluding small voids below roughly $2.5\\times$ the mean galaxy separation, it derives void size functions in two redshift bins and jointly fits $w$, $\\Omega_{\\rm m}$, and $\\sigma_8$ together with a void linear underdensity threshold $\\delta_v$ and an RSD nuisance parameter $B$ in each bin. The fitted values are consistent with earlier BOSS DR12-based void results and the paper argues the constraints are insensitive to the width of the Planck-based priors on $h$, $\\Omega_{\\rm b}$, and $n_s$. It also finds that the best-fit $\\delta_v$ increases toward zero at higher redshift, which it interprets as more linear void evolution and a closer match between Eulerian and Lagrangian void radii.","pith_inferences":["A natural extension is to combine the VSF with weak lensing or cluster counts to shrink the broad $w$–$\\sigma_8$ plane, which this paper leaves open.","Because the ellipticity threshold is empirical and the paper itself notes that larger voids are rounder, a size-dependent ellipticity prior could reduce the largest systematic of the method.","The reported $w<-1$ could be checked with end-to-end mock catalogs of known cosmology: if the pipeline recovers wrong $w$ at the level of the 68% error bars, the model–data mapping, not the Universe, is the source."],"forward_implications":["From one spectroscopic survey, void size functions alone constrain $w$ to about $\\pm0.3$–$0.4$ and $\\Omega_{\\rm m}$ and $\\sigma_8$ to about $\\pm20$ percent.","Combining the VSF with galaxy clustering can break the $\\Omega_{\\rm m}$–$\\sigma_8$ degeneracy, because the two probes' contours are nearly orthogonal.","The same fitting pipeline can be applied to upcoming spectroscopic surveys, where void counts are expected to increase by one to two orders of magnitude.","The fitted void barrier $\\delta_v$ rises from $-0.162^{+0.022}_{-0.024}$ to $-0.123^{+0.014}_{-0.015}$ between the low- and high-redshift bins, a trend the paper attributes to more linear evolution and galaxy bias."],"supporting_citations":[{"why":"Defines the BOSS DR16 galaxy sample whose positions seed the void finder.","marker":"Dawson et al. 2013"},{"why":"Supplies the $V\\,\\mathrm{d}n$ volume-conserving void size function and the empirical $c_v=1.594$ Lagrangian-to-Eulerian mapping.","marker":"Jennings et al. 2013"},{"why":"Provides the excursion-set first-crossing distribution $F(\\nu,\\delta_v,\\delta_c)$ used in the VSF equation.","marker":"Sheth & van de Weygaert 2004"},{"why":"Implements the Voronoi tessellation and watershed void identification and the ellipticity/effective-radius measurements.","marker":"Sutter et al. 2015"},{"why":"Gives the spherical nonlinear density contrast and the $\\Delta(R_v)$ relation used in the RSD correction.","marker":"Bernardeau 1994"},{"why":"Derives the $q_{\\rm RSD}$ and $q_{\\rm AP}$ radius corrections applied to void sizes.","marker":"Correa et al. 2021"},{"why":"Earlier BOSS DR12 void size function constraints and minimum-radius selections that the paper compares with and follows.","marker":"Contarini et al. 2023"},{"why":"Prior mock-catalog work establishing the VSF fitting pipeline and showing the size dependence of void ellipticity.","marker":"Song et al. 2024a"},{"why":"Supplies the fiducial cosmology for distance conversion and the Gaussian priors on $h$, $\\Omega_{\\rm b}$, $n_s$, and $A_s$.","marker":"Planck Collaboration et al. 2020"},{"why":"Provides the MCMC sampler used for the joint cosmological and nuisance parameter constraints.","marker":"Foreman-Mackey et al. 2013"}],"fun_headline_variants":["BOSS DR16 voids give w=-1.26, Omega_m=0.293","Void size function from BOSS DR16 yields w=-1.26 and sigma8","Nearly spherical voids in BOSS DR16 constrain w=-1.26","BOSS DR16 void abundance measures dark energy: w=-1.26","Voronoi watershed voids in BOSS DR16 probe w=-1.26"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the empirical connection between the excursion-set void model and the watershed voids—with $\\delta_v$ and $B$ left free and the ellipticity cut fixed at 0.15—is accurate enough that any mismatch does not bias the recovered cosmological parameters.","fun_headline_variants_meta":{"raw":{"variants":["BOSS DR16 voids give w=-1.26, Omega_m=0.293","Void size function from BOSS DR16 yields w=-1.26 and sigma8","Nearly spherical voids in BOSS DR16 constrain w=-1.26","BOSS DR16 void abundance measures dark energy: w=-1.26","Voronoi watershed voids in BOSS DR16 probe w=-1.26"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000834,"raw_usage":{"total_tokens":3688,"prompt_tokens":1044,"completion_tokens":2644,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":660,"completion_tokens_details":{"reasoning_tokens":2539}},"tokens_in":660,"tokens_out":2644,"duration_ms":20362,"temperature":1.0,"reasoning_tokens":2539,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:34:52.690462+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the identical void finder and MCMC fitter on mock galaxy catalogs with known $w$, $\\Omega_{\\rm m}$, and $\\sigma_8$ and with BOSS DR16-like geometry and density; if the recovered values depart from the truth by more than the reported 68% intervals, the empirical model-to-void mapping is biased. A simpler data-side test is to map how the best-fit parameters shift as the ellipticity threshold moves in steps of 0.01 around 0.15.","supporting_citations":[],"review_version":1}