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REVIEW 2 major objections 5 minor 82 references

Cutting nonlinear scales with BNT leaves KiDS-Legacy S8 unchanged, so nonlinear feedback is not biasing the result at current precision.

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2026-07-11 19:33 UTC pith:HSXJ6DXE

load-bearing objection Solid first BNT k-cut on real KiDS-Legacy data: TDC recovers the official S8 with no nonlinear bias at current precision; ODC trend is a useful pipeline diagnostic, not a cosmology claim. the 2 major comments →

arxiv 2607.04384 v1 pith:HSXJ6DXE submitted 2026-07-05 astro-ph.CO

KiDS-Legacy: The consistency test of the large-scale structure with Bernardeau-Nishimichi-Taruya transform

Shiming Gu , Ziang Yan , Ludovic van Waerbeke , Francis Bernardeau , Hendrik Hildebrandt , Angus H. Wright , Maciej Bilicki , Christos Georgiou
show 5 more authors
Shun-Sheng Li Laila Linke Lauro Moscardini Robert Reischke Benjamin St\"olzner
This is my paper
classification astro-ph.CO
keywords cosmic shearKiDS-LegacyBNT transformk-cutS8weak lensingpseudo-Cℓnonlinear systematics
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 applies a physical-scale cut to the full KiDS-Legacy cosmic-shear catalogue for the first time. The cut is made possible by the Bernardeau–Nishimichi–Taruya (BNT) transform, which re-weights tomographic redshift bins so that each new kernel is localised in redshift; an angular multipole cut then becomes a nearly clean cut in physical wave-number k. When modes with k ≥ 0.33 Mpc⁻¹ are removed and the Gaussian covariance is built from the theory prediction, the inferred amplitude of structure S8 equals 0.798 ± 0.045—statistically identical to both the official KiDS-Legacy result and the same analysis without any k-cut. That agreement implies that nonlinear astrophysical feedback is not pulling S8 low at the precision of the survey. When the same covariance is instead built from the observed data vector, a mild scale-dependent drift appears (larger scales prefer lower S8, max 1.8σ). Mock tests show the drift is not produced by the data vector or the covariance alone, but by their joint use. The authors therefore present BNT k-cuts as both a practical shield against nonlinear systematics and a sensitive diagnostic of the inference pipeline itself.

Core claim

Removing k ≥ 0.33 Mpc⁻¹ from the KiDS-Legacy pseudo-Cℓ vector, with the Gaussian covariance evaluated on the theoretical prediction, yields S8 = 0.798 ± 0.045, which agrees with the fiducial KiDS-Legacy band-power result and with the authors’ own no-cut posterior to within 0.1σ. The paper therefore concludes that nonlinear astrophysical feedback does not introduce a significant bias at KiDS-Legacy precision.

What carries the argument

The Bernardeau–Nishimichi–Taruya (BNT) transform: a linear re-weighting of tomographic bins that produces more localised lensing kernels; combined with an angular multipole cut it isolates a chosen physical k-band while preserving most of the cosmological information in that band.

Load-bearing premise

The mapping from a chosen physical k-band to the retained multipole range, controlled by a single uniform fractional-tolerance threshold of 10 percent, cleanly isolates the targeted scales for every tomographic pair without residual leakage that could still shift S8.

What would settle it

Re-run the identical BNT pipeline on an independent Stage-III or Stage-IV shear catalogue (or on a suite of mocks that inject controlled baryonic feedback) and check whether the TDC k < 0.33 Mpc⁻¹ posterior still recovers the full-scale S8 to within ~0.1σ; a systematic offset larger than that would falsify the “no significant nonlinear bias” claim.

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

If this is right

  • At KiDS-Legacy precision, nonlinear modelling uncertainties need not be the dominant systematic driving any residual S8 tension.
  • Future analyses can adopt BNT k-cuts as a standard robustness test that simultaneously mitigates small-scale systematics and flags covariance–data-vector inconsistencies.
  • When the Gaussian covariance is built from the observed spectra, large-scale cosmic-variance fluctuations can weight the likelihood and produce an artificial preference for lower S8.
  • The same localisation machinery can be used to reconstruct the linear matter power spectrum on ultra-fast timescales for pipeline validation.

Where Pith is reading between the lines

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

  • The ODC versus TDC discrepancy suggests that any Stage-IV analysis that uses the data vector to estimate its own covariance should at least report a parallel TDC run as a null test.
  • Because BNT kernels tighten the redshift window, residual photo-z or multiplicative-bias errors that are sub-dominant in conventional tomography may become more visible once the data are sliced by physical scale.
  • A controlled injection of baryonic feedback into the same pseudo-Cℓ pipeline would quantify how large a feedback strength is still compatible with the observed 0.1σ stability.

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

2 major / 5 minor

Summary. The paper presents the first BNT k-cut cosmic shear analysis of KiDS-Legacy using a pseudo-Cℓ pipeline. With a theoretical-data-vector Gaussian covariance (TDC) and the cut k < 0.33 Mpc⁻¹, it obtains S₈ = 0.798 ± 0.045, consistent to ~0.1σ with both the fiducial KiDS-Legacy bandpower result and the authors’ own no-k-cut pseudo-Cℓ posterior, indicating no significant nonlinear-feedback bias at KiDS-Legacy precision. When the Gaussian covariance is instead built from the observed data vector (ODC), the same cut yields a lower S₈ = 0.717^{+0.047}_{-0.046} and a mild scale-dependent trend (maximum low- vs high-k deviation 1.80σ). Mock tests show that neither the data vector nor the covariance prescription alone produces the ODC trend, so the authors interpret it as an interplay diagnostic of the inference pipeline. The work therefore positions BNT k-cuts as both a mitigation tool for nonlinear systematics and a consistency test of weak-lensing pipelines.

Significance. If the TDC result holds, the paper supplies a clean, scale-localised demonstration that KiDS-Legacy cosmic shear is not materially biased by nonlinear astrophysical feedback at current precision—an important null result for the S₈ discussion. The simultaneous ODC diagnostic is a useful methodological contribution: it shows that BNT k-cuts can expose data–covariance interplay that standard analyses may miss. Strengths include the public sampling code, the explicit validation against the official KiDS-Legacy bandpower result (Fig. 3), the internal stability of TDC posteriors across multiple k-cuts (Figs. 4, 6), and the controlled mock tests (Fig. 5) that isolate the ODC anomaly. The analysis re-uses the authors’ earlier BNT formalism but applies it for the first time to the full KiDS-Legacy catalogue with an independent pseudo-Cℓ estimator, so the central S₈ measurements are new.

major comments (2)
  1. Section III.C, Eqs. (29)–(31): the continuous Boolean weight V(ℓ; k_cuts, T_FD) with a single uniform T_FD = 0.1 is the load-bearing step that converts a physical k-band into an ℓ-mask for every tomographic pair. The mapping is approximate and cosmology-dependent (the paper itself notes that BNT does not require the true cosmology, yet the ratio R is evaluated at a fixed Π_0). A short robustness check—repeating the main TDC k < 0.33 Mpc⁻¹ chain at T_FD = 0.05 and 0.15, or quantifying residual power outside the target k-band after the cut—would strengthen the claim that residual leakage cannot shift S₈ beyond the reported 0.1σ agreement. Without it the “no significant nonlinear bias” conclusion rests on an untested tolerance choice.
  2. Section IV.B and Fig. 6: the ODC scale-dependent trend (maximum 1.80σ between k < 0.33 and 0.33 < k < 3.3) is presented as a diagnostic of data–covariance interplay, yet the paper does not quantify how much of the shift is driven by the sample-variance term versus noise or calibration residuals. A brief decomposition (e.g., replacing only the Gaussian sample-variance piece of the ODC matrix with its TDC counterpart while keeping the observed data vector) would make the claimed “interplay” concrete and would help readers judge whether the effect is expected to grow or shrink for Stage-IV surveys.
minor comments (5)
  1. Abstract and Section IV.B: the ODC error bar is written S₈ = 0.717_{-0.046}^{+0.047} while the TDC result is quoted symmetrically; a uniform convention (or an explicit statement that the posterior is mildly asymmetric) would improve readability.
  2. Figure 2 caption: the colour scale and the cyan/green cut boundaries are hard to distinguish in greyscale; adding line-style differentiation or a clearer legend would help.
  3. Section III.A: the BNT matrix (Eq. 16) is given for the TBC cosmology; a one-sentence note that the matrix is recomputed for each sampled cosmology (or held fixed) would remove ambiguity.
  4. Table I: the prior on T_AGN is listed but the main text never shows its posterior or discusses whether baryonic feedback is constrained by the k-cuts; a brief remark would be useful.
  5. References: the arXiv numbers for the companion KiDS-Legacy papers (Wright et al. 2025, Stölzner et al. 2025) appear as 2503.xxxxx; once the journal versions are available they should be updated.

Circularity Check

1 steps flagged

Minor self-citation of authors' prior BNT pipeline and consistency-test framework; central S8 measurements and TDC/ODC comparison remain independent empirical results.

specific steps
  1. self citation load bearing [Introduction, paragraph discussing prior BNT work; also Sec. II.C Scale Cuts]
    "In our previous works [42, 45], we developed a BNT-based cosmic shear analysis pipeline, demonstrated that the BNT transform can serve as a targeted solution for nonlinear systematics, and proposed a BNT-based consistency test for modelling uncertainties within the posterior sampling process. ... We adopt the methodology introduced in Paper I [42] and further developed in Paper II [45], which provides a framework to identify the ℓ-range ... corresponding to a given physical k-band interval ..."

    The k-cut diagnostic framework and the precise definition of the continuous Boolean weight V(ℓ;k_cuts,T_FD) are taken from the authors' own preceding papers rather than re-derived from first principles here. This is a self-citation of method, not of the target S8 result; the actual posteriors are new measurements, so the circularity is only minor and non-load-bearing.

full rationale

The paper's derivation chain is an application of the BNT transform (originally Bernardeau et al. 2014) plus a k-to-ℓ mapping (R ratios and Boolean weight V with user-chosen T_FD) to a new pseudo-C_ℓ data vector extracted from KiDS-Legacy. The resulting S8 posteriors under TDC and ODC covariances, the 0.1σ agreement of the k<0.33 TDC cut with the fiducial bandpower and no-cut results, and the mild ODC scale trend are all obtained by direct likelihood sampling of the observed (or mock) data vector; none of these numbers is forced by construction from the inputs. The only self-referential element is the reuse of the authors' own earlier pipeline papers for the BNT matrix construction and the diagnostic philosophy; that reuse is normal methodological continuity and is not load-bearing for the numerical claims, which are externally falsifiable against Planck and the official KiDS-Legacy bandpower. No fitted parameter is renamed a prediction, no uniqueness theorem is imported to forbid alternatives, and the Boolean cut V is an explicit approximation whose residual leakage is already quantified by the paper's own multi-cut consistency tests. Score 2 therefore reflects only the minor, non-load-bearing self-citation.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard weak-lensing projection, the published BNT construction, the official KiDS-Legacy catalogue and priors, and a small set of analysis choices (TFD, ℓ-range, covariance split) that are stated but not derived from first principles.

free parameters (4)
  • TFD (fractional deviation threshold) = 0.1
    User-chosen tolerance that defines which ℓ-modes survive a given k-cut (Eq. 30); set uniformly to 0.1 for all tomographic pairs.
  • k-cut boundaries = 0.33 Mpc^{-1} (primary)
    Chosen physical-scale edges (0.1, 0.33, 1.0 Mpc⁻¹ and the three k-band intervals) that define the data-vector truncations whose S8 values are compared.
  • ℓ-binning and range = 50–3000
    30 log-spaced bins from ℓ=50 to 3000 (or the validation cut 100<ℓ<1500) used for the pseudo-Cℓ data vector.
  • IA amplitude A_IA and baryonic TAGN = sampled
    Nuisance parameters sampled with flat priors taken from the KiDS-Legacy analysis; they absorb residual astrophysical freedom.
axioms (5)
  • domain assumption Limber projection of the 3-D matter power spectrum yields the angular shear power spectra (Eq. 3).
    Standard weak-lensing approximation used throughout the modelling section.
  • domain assumption The BNT linear combination of tomographic kernels localizes the lensing efficiency sufficiently that an ℓ-cut maps to a k-cut at the chosen TFD accuracy.
    Core premise of the method, taken from Bernardeau et al. (2014) and the authors’ Papers I/II.
  • domain assumption Gaussian + one-halo non-Gaussian + SSC covariance (Eq. 33) adequately describes the pseudo-Cℓ errors for the adopted scale cuts.
    Standard Stage-III covariance model; non-Gaussian terms fixed to the KiDS-Legacy cosmology.
  • domain assumption NLA intrinsic-alignment model with η_TA=0 is sufficient for the residual IA signal after BNT.
    Adopted for consistency with the official KiDS-Legacy analysis.
  • domain assumption Spatially flat ΛCDM background geometry (K=0).
    Stated explicitly after Eq. 4.

pith-pipeline@v1.1.0-grok45 · 36041 in / 3075 out tokens · 29421 ms · 2026-07-11T19:33:02.328553+00:00 · methodology

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read the original abstract

We perform the first $k$-cut cosmic shear analysis of the KiDS-Legacy survey. This method uses the Bernardeau-Nishimichi-Taruya (BNT) transform to construct weak-lensing kernels that are more localised than conventional ones, and remove information from selected physical scales while retaining the constraining power of the targeted range. Removing the scale of $k \geq 0.33~\mathrm{Mpc}^{-1}$ from the KiDS-Legacy pseudo-$C_\ell$ data vector, and using a covariance matrix whose Gaussian component is computed from the theoretical data vector, we find $S_8 = 0.798 \pm 0.045$. This agrees with both the fiducial KiDS-Legacy bandpower result and our no-$k$-cut pseudo-$C_\ell$ posterior to within $0.1\sigma$, indicating no significant bias from nonlinear astrophysical feedback at the precision of KiDS-Legacy. We also study the case in which the Gaussian covariance is computed from the observed data vector. In this setup, the same scale cut of $k < 0.33~\mathrm{Mpc}^{-1}$ gives a much lower $S_8=0.717_{-0.046}^{+0.047}$. Further $k$-cut tests reveal a mild scale-dependent trend, with larger physical scales preferring lower $S_8$ values and a maximum low- versus high-$k$ deviation of $1.80\sigma$. Mock tests show that this behaviour is not produced by the covariance prescription or data vector alone, but may arise from their interplay. These results show that BNT $k$-cuts provide both a mitigation strategy for nonlinear systematics and a diagnostic of weak-lensing inference pipelines.

Figures

Figures reproduced from arXiv: 2607.04384 by Angus H. Wright, Benjamin St\"olzner, Christos Georgiou, Francis Bernardeau, Hendrik Hildebrandt, Laila Linke, Lauro Moscardini, Ludovic Van Waerbeke, Maciej Bilicki, Robert Reischke, Shiming Gu, Shun-Sheng Li, Ziang Yan.

Figure 1
Figure 1. Figure 1: FIG. 1. Panel 1 of 3: The redshift distribution of the KiDS [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Ratio of the data vector with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Constraints in the (Ω [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Constraints in the (Ω [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Left: The contribution to the total [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

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