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REVIEW 3 major objections 5 minor 123 references

The linear point—the mean of the BAO peak and the preceding dip in the galaxy correlation function—can measure cosmological distances without template fitting, and after a sample-dependent damping correction it agrees with DESI DR1/DR2 BAO

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 06:21 UTC pith:FPD6QPE3

load-bearing objection First DESI linear-point measurements are done carefully, but the LP–BAO agreement rests on a damping correction calibrated with the same BAO priors, so treat the cross-check as a consistency test rather than a fully independent result. the 3 major comments →

arxiv 2601.05967 v2 pith:FPD6QPE3 submitted 2026-01-09 astro-ph.CO

The Linear Point Standard Ruler with DESI DR1 and DR2 Data

N. Uberoi , F. Nikakhtar , N. Padmanabhan , R. K. Sheth , J. Aguilar , S. Ahlen , D. Bianchi , D. Brooks
show 40 more authors
F. J. Castander T. Claybaugh A. Cuceu A. de la Macorra A. Dey B. Dey P. Doel J. E. Forero-Romero E. Gazta\~naga S. Gontcho A Gontcho G. Gutierrez K. Honscheid C. Howlett M. Ishak R. Joyce D. Kirkby T. Kisner O. Lahav C. Lamman M. Landriau L. Le Guillou M. Manera P. Martini A. Meisner R. Miquel S. Nadathur W. J. Percival C. Poppett F. Prada I. P\'erez-R\`afols G. Rossi L. Samushia E. Sanchez D. Schlegel M. Schubnell J. Silber D. Sprayberry G. Tarl\'e B. A. Weaver H. Zou
This is my paper
classification astro-ph.CO PACS 98.80.-k95.36.+x
keywords linear pointbaryon acoustic oscillationsstandard rulerDESIgalaxy clusteringcorrelation functiondensity-field reconstructioncosmological distances
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 argues that the linear point can serve as an alternative standard ruler that avoids template-based fitting. Using DESI DR1 and DR2 galaxy samples, it shows that linear-point distances, converted to the dimensionless parameter α_iso,LP, agree with the isotropic BAO dilation parameter α_iso,BAO after applying a sample-dependent correction for nonlinear smearing, particularly in reconstructed fields. The correction matters because at sub-percent precision the linear point is not immune to damping; without it, mock measurements are biased by roughly 0.5–1%. If the claim holds, cosmologists gain a template-free cross-check on the BAO distances that currently anchor dark-energy measurements.

Core claim

The central claim is that the linear point can be used as an alternative isotropic distance ruler whose measurements match template-based BAO results once the smearing of the linear-theory signal by nonlinear structure is accounted for. The authors define α_iso,LP as the ratio of the fiducial linear point to the measured one, where the fiducial value is computed from the unsmeared linear-theory correlation function. In mock catalogs, the raw α_iso,LP is systematically offset from α_iso,BAO by roughly 0.5–1%, more so pre-reconstruction than post-reconstruction. They attribute this offset to isotropic damping and correct the fiducial linear point by convolving the linear correlation function w

What carries the argument

The load-bearing object is the linear point, s_LP = (s_peak + s_dip)/2, located by a centered and scaled quintic polynomial fit to the correlation-function monopole over 70–115 h⁻¹ Mpc. The argument runs through the dimensionless ratio α_iso,LP = s_fid_LP / s_LP, the linear-point analogue of the BAO dilation parameter. To correct for nonlinear smearing, the authors convolve the linear-theory correlation function with an isotropic Gaussian kernel of width Σ_iso (Eq. 3.8), recompute the fiducial linear point with Σ_iso sampled from the DESI BAO damping priors, and use this 'corrected' fiducial value in α_iso,LP. Standard reconstruction enters by reducing Σ_iso and sharpening the feature, which

Load-bearing premise

The correction assumes that a Gaussian smoothing of the linear-theory correlation function, with a width taken from the DESI BAO damping priors, fully captures how nonlinear structure formation moves the linear point; if Σ_iso is mis-calibrated or the convolution is an incomplete model, the corrected α_iso,LP is biased and the agreement with BAO is partly manufactured.

What would settle it

Compute corrected α_iso,LP on mock catalogs generated with a cosmology different from the fiducial one while keeping the fiducial Σ_iso priors fixed; if the corrected values no longer recover the true input distances—or if varying Σ_iso by ±1σ within its quoted prior changes α_iso,LP by more than the claimed agreement—then the correction is absorbing model error rather than removing physical smearing.

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

If this is right

  • At sub-percent precision, the linear point is not fully model-independent: a sample-dependent, cosmology-dependent correction for damping is required to match template-based BAO results.
  • Post-reconstruction linear-point measurements are more precise (15–60% smaller uncertainties in mocks) and agree more closely with BAO measurements.
  • The linear point can serve as a cross-check on template-based BAO distances, which are currently used to infer dark-energy properties.
  • A purely geometric ruler can be extracted with a simple polynomial fit over a narrow region of the correlation function, requiring no BAO template shape.
  • Uncertainty in the damping scale Σ_iso propagates into α_iso,LP, inflating errors by up to roughly 48% in mocks when the correction is applied.

Where Pith is reading between the lines

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

  • A decisive, still-missing test is to compare corrected linear-point distances against distance measurements that do not rely on the BAO template, such as supernova-calibrated distances; the paper itself stops at comparing to α_iso,BAO.
  • Because the correction is calibrated using the same damping priors that enter the BAO template fits, the agreement could partly reflect shared assumptions; a test on mocks built with a different cosmology would separate physical smearing from model absorption.
  • The Laguerre deconvolution route, if the degeneracy with the smearing kernel can be tamed with independent priors, could restore the model-independence that the explicit correction gives up.
  • With DR2's smaller errors, the linear point could be extended to full cosmological parameter inference, such as H0 and Ωm, which the paper leaves for future work.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper measures the linear point (LP) in the monopole of the two-point correlation function for the DESI DR1 and DR2 BGS, LRG, and ELG samples, and converts it to a dimensionless parameter α_iso,LP analogous to the isotropic BAO dilation parameter. Using 25 Abacus-2 DR1 mock catalogs, the authors find that LP measurements are 15–60% more precise post-reconstruction than pre-reconstruction, and that raw LP measurements are systematically offset from template-based α_iso,BAO measurements. They attribute this offset to nonlinear smearing and introduce a sample-dependent correction to the fiducial linear point, computed by convolving the linear-theory correlation function with an isotropic Gaussian kernel whose width Σ_iso is taken from the DESI BAO damping priors. After this correction, they report 'excellent agreement' between α_iso,LP and α_iso,BAO, particularly post-reconstruction, and discuss the implications for using the LP as an alternative standard ruler.

Significance. If the central claim holds, the linear point would provide a useful complementary distance-scale measurement with different systematics from template-based BAO fitting. The raw polynomial-fit LP measurement is genuinely independent of BAO templates, and the paper is careful in several respects: it uses 25 Abacus-2 mocks for validation, reports χ² values and failure rates, discusses the DR2 mock unavailability explicitly, and includes detailed appendices on parameter choices, poor signal-to-noise cases, and error analyses. However, the headline agreement after correction is not yet established as an independent cross-check: the correction relies on the same Σ_iso damping parameters used inside the DESI BAO template fits, and the agreement is not quantified with any tension statistic. The paper is transparent about the compromise to strict model-independence, but the strength of the claim in the abstract exceeds what the current analysis demonstrates.

major comments (3)
  1. [Sec. 5.1–5.2, Figs. 5, 6, 8] The central claim of 'excellent agreement' between corrected α_iso,LP and α_iso,BAO is never quantified. No χ², Δ/σ, or probability-to-exceed is reported for any of the DR1 or DR2 tracers. This matters especially because the LP and BAO measurements are made on the same correlation functions, so their errors are correlated; ignoring these correlations can make agreement look better than it is. Please add a quantitative comparison, ideally with a conservative treatment of the LP–BAO covariance, and state the resulting tension for each tracer and for the combined sample.
  2. [Sec. 3.2.1, Table 3] The 'corrected' fiducial linear point is computed by convolving the linear-theory correlation function with Σ_iso drawn from Table 2, and Table 2 lists the same Gaussian damping priors used in the DESI BAO template fits (Sec. 2.2.3). The mock validation in Sec. 4 also uses the same Abacus-2 mocks that informed these priors. The post-correction agreement is therefore partly built in: it tests consistency with the BAO damping model, not independence from it. The raw, uncorrected LP measurement is independent, but the corrected comparison is not. Please provide a sensitivity test, e.g., varying Σ_iso by ±1σ and showing the effect on the LP–BAO residual, or calibrating Σ_iso from an independent source; otherwise the abstract's claim should be softened.
  3. [Sec. 4, Table 4] The mock comparison does not include the α_iso,BAO values in Table 4, so the reader cannot directly assess the offset before and after correction. Moreover, several corrected mock values remain far from the BAO values or from unity — e.g., BGS pre-reconstruction 1.016±0.012, LRG1 pre 1.006±0.008, ELG2 post 0.994±0.004 — yet no test is shown for whether these residuals are consistent with noise. Please report the mock α_iso,BAO values and a quantitative residual statistic for each tracer.
minor comments (5)
  1. [Table 3] The quoted uncertainty for BGS pre-reconstruction (0.03 h⁻¹ Mpc) is anomalously smaller than for LRGs (0.44) and ELGs (0.12) despite a comparable Σ_iso uncertainty (0.9 h⁻¹ Mpc). Please check this value and explain the non-monotonic behavior; it affects the error bars on the corrected α_iso,LP values in Table 4 and Figure 6.
  2. [Table 4] The table would be much more informative if it listed the mean α_iso,BAO values for each tracer next to the uncorrected and corrected α_iso,LP values, rather than only showing them in figures.
  3. [Eq. (3.8)] The convolution formula is hard to read: the integrand includes 'r3s(rs)3/2 e...' which appears to contain typographical errors or undefined notation. Please write the integrand and the modified spherical Bessel function i0 explicitly.
  4. [Sec. 5.1, Appendix B] The failure to measure a pre-reconstruction BGS linear point is an important limitation, and it is appropriately discussed. However, the abstract and conclusion should state more prominently that the 'excellent agreement' claim does not cover this tracer/regime.
  5. [Figs. 5 and 8] The axis ranges differ between the DR1 and DR2 comparison figures, which makes visual comparison of scatter and offsets difficult. Consider using identical ranges when the data allow.

Circularity Check

1 steps flagged

LP–BAO agreement is partly built in: the LP smearing correction uses the same DESI BAO damping priors that feed α_iso,BAO.

specific steps
  1. fitted input called prediction [Sec. 3.2.1 (Eq. 3.8, Table 3), applied in Secs. 4–5]
    "Mean values and standard deviations of the Gaussian priors for the nonlinear BAO damping parameters across and along the line of sight (Σ⊥ and Σ∥, respectively) used in the DESI BAO fitting pipeline ... We generate 1000 realizations of Σiso sampled from the Gaussian priors mentioned in Table 2; for each value, we generate a nonlinear correlation function ξNL(s) using Eq. 3.8. ... We define the mean of the sample to be 'corrected' fiducial linear point."

    The corrected α_iso,LP is obtained by dividing the observed s_LP by a smeared fiducial s_LP computed with Eq. 3.8 using Σ_iso from Table 2. But Table 2 is explicitly the Gaussian damping prior used in the DESI BAO template fits that produce α_iso,BAO. Therefore the correction shifts the LP scale by exactly the nonlinear-smearing model and calibration (Abacus-2 mocks) already built into the BAO pipeline. The post-correction agreement between α_iso,LP and α_iso,BAO is thus partly an identity check of the convolution model against the template fit rather than an independent geometric cross-check. The mock validation in Sec. 4 also uses the same Abacus-2 mocks that set those priors. The raw, uncorrected LP measurement is independent; the corrected comparison is not.

full rationale

The raw linear-point measurement itself is genuinely model-independent: s_LP is obtained from a polynomial fit to a narrow range of the measured correlation function, with no BAO template. The definition α_iso,LP = s_fid_LP/s_LP is also straightforward. However, the paper's headline claim of 'excellent agreement' with α_iso,BAO depends on a 'sample-dependent correction' that convolves the linear-theory correlation function with Σ_iso taken from the same Gaussian damping priors used inside the DESI BAO template fits that define α_iso,BAO. This makes the corrected LP scale share its nonlinear-smearing input with the BAO measurement it is compared against; the agreement is therefore partly manufactured by sharing the calibration. The paper is transparent about this, but transparency does not remove the circularity in the comparison. No significant load-bearing self-citation or ansatz-smuggling was found; the central issue is the BAO-calibrated smearing correction. Thus 6/10: the central cross-check is partially circular, though the raw LP pipeline has independent content.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The paper's distance scale rests on (a) an assumed nonlinear smearing model, (b) fiducial cosmology input, (c) a polynomial approximation, and (d) damping priors borrowed from the template BAO pipeline. No new physical entities are introduced; the main external inputs are the Σ_iso priors and the fiducial linear-theory correlation function.

free parameters (3)
  • LP pipeline parameters = n=5, s∈[70,115] h^-1 Mpc, Δs=4 h^-1 Mpc
    Chosen by hand in Appendix A to optimize for DESI, replacing BOSS-optimized n=5, 60-120 h^-1 Mpc, Δs=3 h^-1 Mpc. The choice affects which peak/dip is identified.
  • Isotropic damping priors Σ_iso (per tracer, pre/post) = BGS 7.5±0.9 / 4.2±0.9; LRG 5.7±0.9 / 3.8±0.9; ELG 5.6±0.9 / 3.8±0.9 h^-1 Mpc
    Taken from the DESI BAO template pipeline (Table 2); used to generate corrected s_fid_LP via Eq 3.8. These are fitted/calibrated quantities, not derived in this paper.
  • Effective correction to s_fid_LP = ~92.0-92.5 h^-1 Mpc depending on tracer/regime (Table 3)
    Equivalent to multiplicative corrections BGS 1.01/1.006, LRG/ELG 1.009/1.005; chosen to undo smearing and bring α_iso,LP into line with α_iso,BAO.
axioms (6)
  • domain assumption Gaussian convolution (Eq 3.8) with isotropic kernel Σ_iso accurately describes nonlinear smearing of the correlation function on BAO scales.
    Used to compute corrected s_fid_LP in Sec 3.2.1; if the convolution model is wrong, the correction factors are miscalibrated.
  • domain assumption The fiducial Planck 2018 ΛCDM cosmology and CLASS linear-theory correlation function at z=0 give the true unsmeared linear point s_fid_LP=93.01 h^-1 Mpc.
    All α_iso,LP values are ratios to this number (Eq 3.7); errors in the fiducial model propagate into all results.
  • ad hoc to paper A quintic polynomial in 70-115 h^-1 Mpc identifies the BAO peak and preceding dip.
    Adopted in Sec 3.2/Appendix A; fails for pre-recon BGS DR1 (Appendix B), so the assumption is not universally valid.
  • domain assumption Abacus-2 DR1 mocks reproduce the nonlinear clustering, survey geometry, and fiber assignment of DESI DR1.
    Used for validation and systematic-shift estimates; DR2 mocks were not available (Sec 2.1), so DR2 results rely on transfer of DR1 validation.
  • domain assumption iFFT RecSym reconstruction removes nonlinear smearing down to residual damping described by Table 2 priors.
    Post-recon LP analysis and correction rely on this residual damping picture.
  • domain assumption The inverse-volume-distance ratio y_LP is nearly cosmology-independent (Eq 3.4).
    Quoted y_LP values and Hubble-diagram interpretation depend on this relation from prior LP literature.

pith-pipeline@v1.3.0-alltime-deepseek · 37027 in / 14018 out tokens · 138140 ms · 2026-08-04T06:21:27.776523+00:00 · methodology

0 comments
read the original abstract

The linear point, a purely geometric feature in the monopole of the two-point correlation function, has been proposed as an alternative standard ruler. Compared to the peak in the correlation function, it is more robust to late-time nonlinear effects at the percent level. In light of improved simulations and high quality data, we revisit the robustness of the linear point and use it as an alternative to template-based fitting approaches typically used in BAO analyses. We present the linear point measurements on galaxy samples from the first and second data releases (DR1 and DR2) of the DESI survey. We convert the linear point into a dimensionless parameter $\alpha_{iso,LP}$, defined as the ratio of the linear point in the fiducial cosmology and the observed value, analogous to the isotropic BAO scaling parameter $\alpha_{iso}$ used in previous BAO measurements. Using the 2nd generation of AbacusSummit mock catalogs, we find that linear point measurements are more precise when calculated in the post-reconstruction regime with 15-60% smaller uncertainties than those pre-reconstruction. We find a systematic shift in the linear point measurements compared against the isotropic BAO measurements in mocks; we attribute this to the isotropic damping parameter responsible for smearing the linear point in the nonlinear regime. We propose a sample-dependent correction that mitigates the impact of late-time nonlinear effects. While this introduces a cosmology dependence in an otherwise model-independent measurement, this is necessary given the sub-percent precision dictated by current cosmological surveys. Comparing $\alpha_{iso,LP}$ with isotropic BAO measurements made on the DESI DR1 and DR2 galaxy samples, we find excellent agreement after applying this correction, particularly post-reconstruction. We discuss future scope regarding cosmological inference with linear point measurements.

discussion (0)

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