{"id":"cfd55c63-2b7e-4df4-bcff-b436466d70e8","arxiv_id":"2601.07075","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A BAO-ratio test converts radial and transverse distance measurements into an effective matter density; DESI DR1/DR2 data are internally consistent with one constant value, as flat ΛCDM expects.","lead":"This paper builds a sound-horizon-free consistency test for flat ΛCDM by turning BAO distance ratios into an effective matter density and checking whether that density is the same everywhere. Applying it to DESI's first two data releases, the ratios agree within large uncertainties, so the standard model is not challenged.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (7) does not follow from the stated definition of R_HH; combined with Eq. (6)'s missing reciprocal in D_H=c/H(z), the radial-only ΩM^Λ values in Tables 1–2 are not reproducible from the text as written.","rationale":"I read the paper as a calibration-free internal consistency test: ratios of BAO distances are mapped to effective flat-ΛCDM ΩM values, and the claim is that these are redshift-independent. The reader identified as the weakest assumption the neglect of correlations among derived ΩM^Λ values in the Sec. 3.5 constant fits. That is a real statistical limitation, and the paper explicitly labels the fits 'descriptive' rather than a full likelihood, so I weigh it as a moderate concern rather than a fatal one. The more load-bearing problem, in my reading, is in the radial-only branch of the method itself. The text's Eq. (6) gives the Hubble distance as proportional to sqrt(ΩM(1+z)^3+1−ΩM), but physically D_H is inversely proportional to that square root. Consequently Eq. (7) is not the inversion of the ratio defined in Eq. (5); it is the inversion of the inverse ratio under the incorrect distance formula. A reader who follows the equations literally would not reproduce the positive ΩM^Λ values in Tables 1–2 for R_HH>1. This does not necessarily mean the numerical results are wrong—the provided Julia code may implement the standard formula or the inverse ratio—but the manuscript as written fails to specify a consistent derivation for the diagnostic that anchors Tables 1–2. I therefore cannot consider the central claim fully supported by the text as it stands. The proposed concrete test—an independent recomputation of the RHH columns from the standard D_H formula, compared entry-by-entry with the published tables—would settle whether this is a typographical slip or a substantive error. I also note the correlation issue raised by the reader remains worth addressing, but the equation inconsistency is more fundamental and should be resolved first. I recommend CONDITIONAL rather than REJECT because the method is simple, the code is available, and the qualitative conclusion may survive after correction; however, acceptance should require fixing Eqs. (6)–(7), rerunning the affected tables if needed, and adding the correlated constant-fit or a clear disclaimer that the quoted χ2/dof values are not significance statistics.","tokens_in":10602,"tokens_out":14902,"duration_ms":153891,"concrete_test":"Recompute every RHH entry in Tables 1 and 2 from the DESI DR1/DR2 D_H/r_d data using the correct standard formula D_H(z)=[c/H_0][1+ΩM f(z)]^{-1/2} and the correct inversion ΩM=(R^2−1)/(f(z_j)−R^2 f(z_i)), propagating the full published covariance. Compare each entry with the published values; if the 0.510/0.706 DR2 entry (0.298) and all other radial-only values match, the printed Eq. (6)/(7) are typographical and the concern is cosmetic. If they shift, rerun the Sec. 3.5 constant fits and assess whether the 'no evidence for redshift evolution' conclusion survives.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The core radial–radial diagnostic is algebraically inconsistent as printed. Standard flat ΛCDM has D_H(z)=c/H(z)=[c/H_0]·[1+ΩM f(z)]^{-1/2}, where f(z)=(1+z)^3−1. With R_HH defined in Eq. (5) as D_H(z_i)/D_H(z_j), the inversion is ΩM=(R^2−1)/(f(z_j)−R^2 f(z_i)). However, the manuscript's Eq. (6) writes D_H ∝ sqrt(1+ΩM f(z)) (no reciprocal), and Eq. (7) gives ΩM=(1−R^2)/(R^2 f(z_j)−f(z_i)). That expression is the correct solution for the inverse ratio R→1/R under the incorrect Eq. (6), or equivalently for the standard D_H with the opposite ratio convention. For a typical DESI high-redshift pair with z_i<z_j and R_HH>1, Eq. (7) as written returns a negative ΩM. The positive RHH entries in Tables 1–2 therefore cannot have been produced by literally applying Eqs. (5)–(7); either the printed equations are wrong, or the code silently used the inverse ratio without stating it. Because these entries feed directly into the Sec. 3.5 constant-ΩM fits and the abstract's claim of consistency with a redshift-independent constant, this is a load-bearing correctness/reproducibility flaw in the central diagnostic.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a calibration-free null test of spatially flat ΛCDM using ratios of BAO distances: D_H(z_i)/D_H(z_j), D_H(z_i)/D_M(z_i), and D_H(z_i)/D_V(z_j). Each ratio is mapped to an effective matter-density parameter Ω_M^Λ, defined as the value that reproduces the observed ratio in flat ΛCDM. The sound horizon and H_0 cancel in the ratios. The method is applied to DESI DR1 and DR2 BAO data with full covariance propagation via Monte Carlo. The paper concludes that the inferred Ω_M^Λ values are broadly consistent with a redshift-independent constant, providing an internal consistency check of flat ΛCDM.","tokens_in":10870,"tokens_out":5835,"duration_ms":60288,"significance":"If the result holds, this is a useful, model-dependent-but-calibration-free diagnostic that combines radial and transverse BAO information in a single framework. The ratio construction cleanly cancels r_d and H_0, and the use of the integral mean value theorem to assign effective redshifts is a transparent way to handle integrated distances. The Monte Carlo propagation of the full DESI covariance matrices is a strength, as is the public availability of the analysis code. However, the central algebraic derivation contains an error that undermines the reproducibility of the printed results.","major_comments":[{"comment":"Eq. (6) is not the standard flat-ΛCDM Hubble distance. With H(z)/H_0 = sqrt(Ω_M(1+z)^3 + 1−Ω_M), the correct relation is D_H = (c/H_0) [Ω_M(1+z)^3 + 1−Ω_M]^{-1/2}; Eq. (6) omits the reciprocal. Consequently, Eq. (7), derived from Eq. (6), gives the inversion for the inverse ratio R_HH → 1/R_HH, not for R_HH = D_H(z_i)/D_H(z_j) as defined in Eq. (5). For standard flat ΛCDM with z_i < z_j and R_HH > 1, Eq. (7) as printed yields the wrong sign. The R_HH values in Tables 1 and 2 therefore cannot be reproduced from the text as written, and the same reciprocal error propagates into the numerical inversions for R_HM and R_HV that use Eq. (6) (§2.2.2, §2.2.3). The authors should correct Eqs. (6)–(7), re-run the analysis with the correct formula, and verify that the reported tables and conclusions remain valid. This is load-bearing because the R_HH results feed into the constant-Ω_M fits and the","section":"§2.2.1, Eq. (6)–(7)"},{"comment":"The constant-Ω_M fits treat the derived Ω_M^Λ values as independent measurements with symmetrized 68% uncertainties. This is acknowledged in the text, but the quoted χ²/dof values (e.g., 1.14 for DR1 DH/DH, 1.45 for DR1 DH/DM) are not valid significance statistics because the ratios heavily reuse the same D_H and D_M data across redshift pairs, inducing strong correlations. The abstract's statement that the values are 'broadly consistent with a redshift-independent constant' rests partly on these fits. A full covariance propagation into the derived Ω_M^Λ vector is needed to claim quantitative consistency; as it stands, the qualitative conclusion is driven by the very large 68% intervals, not by the fit statistics.","section":"§3.5"},{"comment":"The within-family best-fit constants differ substantially between diagnostics: for DR1, Ω_M^Λ ≈ 0.146 for DH/DH versus ≈ 0.293 for DH/DM, with a similar spread in DR2. The paper notes 'differences between diagnostic families motivate the discussion' but does not quantify whether these differences are statistically significant. Given that the test is explicitly designed to check consistency across ratio families, the authors should either assess this cross-family tension with the full covariance or soften the claim of overall consistency in the abstract.","section":"§3.5/§4"}],"minor_comments":[{"comment":"The reference 'P. Collaboration et al. 2020' should be formatted as 'Planck Collaboration et al. 2020' for consistency with standard usage.","section":"References"},{"comment":"For the R_HV row with z_i = 0.510 and z_j = 0.295, z_j < z_i; the text does not specify whether the ratio convention requires z_i > z_j. Please clarify the ordering convention for all ratios.","section":"Table 2"},{"comment":"The notation 'Λ−→' is unconventional and visually confusing; standard arrows would improve readability.","section":"General"},{"comment":"The phrase 'relative distances' and 'Om statistic' would benefit from consistent capitalization and a brief definition of the Om variable at first use.","section":"§1"}],"recommendation":"major_revision","confidential_remarks":"The algebraic error in Eqs. (6)–(7) is the most serious issue. It is possible that the analysis code uses the correct formula (the published code is available), but the manuscript as it stands is not self-consistent. The authors should be asked to correct the equations, verify the numerical results, and either recompute the constant fits with the full covariance or explicitly state the limitations of the reported χ²/dof values. The core idea is sound and the data processing appears careful, so a major revision addressing these points is appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the central radial–radial diagnostic as printed is wrong. Eq. (6) writes the Hubble distance as proportional to sqrt(1+ΩM f(z)); but D_H = c/H, so it should be the reciprocal. Eq. (7) is the inversion for that reciprocal definition, not for the standard one. For any pair with z_i < z_j, the observed ratio is >1, and Eq. (7) returns a negative ΩM. All RHH entries in Tables 1–2 are positive, so the tables cannot have been produced by literally following Eqs. (5)–(7). I checked the stress-test note: it holds up.\n\nWhat's worth taking from the paper: the DH/DM and DH/DV ratio families are new, the integral-mean-value redshift bookkeeping is sensible, and the Monte Carlo propagation using the full DESI covariance is the right way to do it. The DH/DH ratio is just the two-point Om diagnostic in ratio form, so that part is not new. The application is careful in the sense that they use the published covariance matrices, and the qualitative conclusion – no statistically significant deviation from flat ΛCDM at current precision – is defensible from the large error bars.\n\nSoft spots: Sec. 3.5 constant fits ignore the strong correlations among derived ΩM values and symmetrize asymmetric errors; the authors admit this, but then quote χ2/dof as if it meant something. That is a moderate problem, not fatal. The code is available but without a commit hash, so reproducibility is only moderate.\n\nThe circularity concern is not a real flaw: each ΩM is a one-parameter inversion by construction, but the test is the comparison across redshift and families, which is legitimate.\n\nWho is this for? People building BAO null tests and DESI data users. The paper deserves a serious referee, but the printed equations need fixing first. I'd send it to review with a request for corrected formulas and a code check. After that, I'd cite it.","headline":"The radial–radial inversion is misprinted (Eq. 6 missing the reciprocal, Eq. 7 gives negative ΩM for all their pairs), so the tables aren't reproducible from the text; the mixed ratios and covariance treatment are still worth a referee.","tokens_in":11508,"tokens_out":7646,"would_cite":true,"duration_ms":71951,"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":"Flat ΛCDM survives a calibration-free consistency test built from ratios of BAO distances measured by DESI.","keywords":["baryon acoustic oscillations","flat LambdaCDM","consistency test","Om diagnostic","sound horizon","dark energy","DESI","distance ratios"],"falsifier":"Recompute the constant-Ω_M^Λ fits using the full covariance matrix of the derived ratios—or of the underlying BAO measurements—instead of symmetrized independent errors; if the apparent redshift constancy disappears or a family disagreement becomes statistically significant, the paper's central claim fails. Alternatively, a future BAO data release with tighter errors that shows Ω_M^Λ trending with redshift, or a clear offset between the R_HH and R_HM families, would falsify flat ΛCDM under this test.","tokens_in":10324,"feed_emoji":"🔭","tokens_out":3019,"duration_ms":35452,"temperature":0.7,"pith_summary":"This paper tries to establish a simple, calibration-free internal consistency test for the standard flat ΛCDM cosmology. The test forms ratios of BAO distances—radial, transverse, and volume-averaged—so that the unknown sound-horizon scale cancels, and then converts each observed ratio into the matter density Ω_M that a flat ΛCDM universe would need to reproduce it. Flat ΛCDM predicts that this inferred Ω_M should be the same at every redshift and for every kind of ratio. Applied to DESI Data Release 1 and Data Release 2 BAO measurements with full covariance propagation, the inferred Ω_M values are broadly consistent with a redshift-independent constant within current uncertainties. The result matters because it provides a transparent, low-assumption check that can be sharpened as future BAO data arrive.","feed_headline":"Three BAO ratios pass a calibration-free flat-LambdaCDM test","feed_subtitle":"Sound-horizon-free ratios from DESI yield one matter density across redshift—exactly what the standard model predicts.","key_machinery":"The central objects are three ratio diagnostics—R_HH, R_HM, and R_HV—each defined as a ratio of BAO distances so that the sound horizon scale cancels exactly, with the overall H_0 normalization also dropping out. Each measured ratio is mapped to an effective flat-ΛCDM matter density Ω_M^Λ by equating it to the model prediction and solving for Ω_M, analytically for the radial–radial case and numerically for the mixed ratios. For integrated distances, the integral mean value theorem supplies effective line-of-sight redshifts and conservative redshift intervals, allowing transverse and isotropic BAO information to be placed on the same footing as direct radial measurements.","core_discovery":"The central claim is that flat ΛCDM predicts a single effective matter density parameter, Ω_M^Λ, that is independent of redshift and independent of which BAO distance ratio is used, and that DESI DR1 and DR2 BAO data satisfy this prediction at current precision. Three families of ratios are constructed: a purely radial ratio D_H(z_i)/D_H(z_j), a radial–transverse ratio D_H(z_i)/D_M(z_i), and a radial–isotropic ratio D_H(z_i)/D_V(z_j). For ratios involving the integrated distances D_M and D_V, the paper uses the integral mean value theorem to associate each measurement with a well-defined effective redshift interval. All derived Ω_M^Λ values are obtained by propagating the full published BAO","pith_inferences":["The current constancy conclusion is weaker than it appears because the derived ratios heavily reuse the same underlying BAO measurements: the same D_H appears in multiple R_HH and R_HV ratios, and the same D_M anchors both R_HM and R_HV. A full covariance treatment of the derived ratios, rather than treating them as independent, could strengthen or weaken the apparent consistency.","The effective-redshift mappings depend weakly on the assumed Ω_M when assigning redshift intervals; as redshift bins become finer, the mixed ratios become more local and the test gains discriminating power.","The same ratio construction could be applied to other cosmological distance probes, or to future BAO releases, to produce an evolving 'BAO-Om ladder' that isolates redshift-dependent departures from flat ΛCDM without invoking a calibrated distance scale."],"forward_implications":["If the constancy claim holds, BAO data can check flat ΛCDM without any calibration of the sound horizon or H_0, making the test insensitive to a whole class of systematic uncertainties.","Radial and transverse BAO information can be combined in a single null test, extending the popular Om diagnostic to integrated distance measurements.","A statistically significant redshift dependence of Ω_M^Λ within a single ratio family, or a disagreement between families built from the same dataset, would signal a departure from flat ΛCDM and motivate further investigation.","The framework generalizes to extended background models such as wCDM or models with curvature, and can be combined with other late-time probes to diagnose the origin of any detected inconsistency.","Future DESI data releases and other wide-area surveys will tighten the test by providing more precise distance measurements over finer redshift bins and more ratio combinations."],"fun_headline_variants":["BAO ratios agree on one matter density - flat ΛCDM holds","Calibration-free test: DESI BAO data fit standard model","Sound-horizon-free ratios pass flat ΛCDM consistency check","Redshift-independent matter density from BAO: ΛCDM survives","Three BAO distance ratios all yield same ΛCDM density"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The conclusion that Ω_M^Λ is redshift-independent rests on constant-Ω_M fits that treat each derived value as an independent measurement with symmetrized 68% errors, even though the ratios are built from heavily overlapping BAO measurements and are therefore strongly correlated.","fun_headline_variants_meta":{"raw":{"variants":["BAO ratios agree on one matter density - flat ΛCDM holds","Calibration-free test: DESI BAO data fit standard model","Sound-horizon-free ratios pass flat ΛCDM consistency check","Redshift-independent matter density from BAO: ΛCDM survives","Three BAO distance ratios all yield same ΛCDM density"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000241,"raw_usage":{"total_tokens":1390,"prompt_tokens":805,"completion_tokens":585,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":549,"completion_tokens_details":{"reasoning_tokens":494}},"tokens_in":549,"tokens_out":585,"duration_ms":5558,"temperature":1.0,"reasoning_tokens":494,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T11:12:31.623722+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the constant-Ω_M^Λ fits using the full covariance matrix of the derived ratios—or of the underlying BAO measurements—instead of symmetrized independent errors; if the apparent redshift constancy disappears or a family disagreement becomes statistically significant, the paper's central claim fails. Alternatively, a future BAO data release with tighter errors that shows Ω_M^Λ trending with redshift, or a clear offset between the R_HH and R_HM families, would falsify flat ΛCDM under this test.","supporting_citations":[],"review_version":1}