{"id":"86b01922-297b-430d-ad10-c8f4000dbe75","arxiv_id":"2412.14704","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The BNT transform of cosmic shear data makes ℓ-space cuts behave like k-space cuts, reducing nonlinear scale leakage and preserving unbiased S8 constraints in Euclid-like forecasts.","lead":"Weak lensing surveys that cut small angular scales still leak in signals from poorly modeled nonlinear scales, which can bias cosmological parameters like S8. This paper shows that rearranging the lensing data with the Bernardeau-Nishimichi-Taruya (BNT) transform makes a cut in angular scale behave much more like a clean cut in physical scale, preserving constraining power while avoiding the bias.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The BNT method's advertised robustness to the fiducial cosmology used for the transform and for setting ℓ-cuts is asserted, not demonstrated; a wrong-Π0 test would settle whether the central claim survives.","rationale":"The reader's weakest-assumption identification is correct: the BNT transform and the ℓ-cut calibration both depend on a fiducial cosmology through the distance-redshift relation, and the paper's claim of insensitivity is asserted without a dedicated test. This is the weakest link in the central argument because the entire advantage of BNT over noBNT is the sharper k-to-ℓ mapping produced by nulled lensing kernels; if those kernels overlap due to a wrong fiducial cosmology, the ℓ-cut no longer approximates a k-cut and scale leakage persists. The concern is internal to the method, not a disagreement with external consensus, and it can be settled by a concrete numerical experiment. I also considered other limitations noted by the reader, such as the absence of intrinsic alignments, the idealized covariance, and the lack of a direct x-cut comparison; these are real caveats but they do not cut as directly against the central mechanism as the untested fiducial-cosmology assumption. The paper otherwise has genuine strengths: the formalism is coherent, the calculations use public tools (CCL, OneCovariance, Nautilus), and the Appendix A approximation is explicitly validated at the few-percent level. Because the identified concern is a missing robustness test rather than a demonstrated internal contradiction, the appropriate verdict remains conditional on that test.","tokens_in":33892,"tokens_out":7445,"duration_ms":72328,"concrete_test":"Re-run the BNT construction and the Table III Halofit/BCM forecasts with a deliberately wrong distance-redshift relation for the transform and cut calibration only: for example, use Π0_wrong = (Ωm=0.35, h=0.75) to compute p_i^a, n0_i, n1_i, and R(kcut, Π0), while still generating mock Cℓ at the true fiducial cosmology. Compare the bias in S8 and σS8 at (kcut, TFD) = (0.33, 0.02) and (0.1, 0.02) with the fiducial-BNT entries in Table III. If the bias remains within 1σ and σS8 changes by less than about 20%, the asserted insensitivity is supported; if the bias grows or the constraints degrade substantially, the central claim is conditional on knowing Π0.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is in Section III A, in the unnumbered paragraph after Eq. 19: the paper states that the choice of cosmology used for the BNT transform 'does not affect the results' and that 'our approach remains unbiased even with imperfect nulling.' This matters because the BNT coefficients p_i^a are fixed by n0_i and n1_i (Eqs. 3-7), which depend on the distance-redshift relation, and the ℓ-cut is chosen from R(kcut, Π0) (Eq. 19), also evaluated at the fiducial cosmology. If the true distance-redshift relation differs from Π0, the BNT kernels Ŵ^a are not fully nulled and can overlap for bins with |a-b|≥2, so the ℓ-to-k mapping broadens. The cut-defining ratio R then no longer equals the true fraction of k<kcut power at a given ℓ, and high-k contamination can persist in retained ℓ modes. The paper provides no derivation or wrong-cosmology test for this invariance; the assertion is qualitative. This is exactly the feature that carries the advertised advantage that 'a cut in ℓ-space is much closer to a cut in k-space', so a failure here would directly weaken the central claim. The forecasts in Tables II and III do not exercise this failure mode, because the same fiducial cosmology is used to build the transform, set the cuts, and generate the mock data.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that applying scale cuts in harmonic space to BNT-transformed weak lensing data behaves much more like a k-space cut than conventional tomographic scale cuts, so that theoretical uncertainties in the nonlinear matter power spectrum can be controlled with less information loss. The authors define a leakage estimator R, construct ℓ-cuts from the ratio R(kcut, Π0) with a tolerance TFD, and run MCMC forecasts for Euclid-like surveys, comparing analyses based on HMcode against mock data generated with Halofit, the Baryon Correction Model, and AxionHMcode. Their central claims are that BNT-transformed data retain cosmological constraining power for small kcut and TFD, while conventional noBNT analyses either lose constraining power or remain biased after marginalizing over nuisance parameters.","tokens_in":34132,"tokens_out":4632,"duration_ms":45497,"significance":"If the central claim holds, the paper provides a practical and timely method for Stage-IV weak lensing surveys to mitigate nonlinear and baryonic systematics without discarding as much information as standard scale cuts. The manuscript has clear strengths: the theoretical framework is laid out explicitly, the calculations use public tools (CCL, OneCovariance, Nautilus, Getdist), and the code is made available on GitHub, which strengthens reproducibility. The introduction of a quantitative scale-leakage diagnostic is a useful contribution in itself. The main limitation is that the advertised robustness of the method to the fiducial cosmology used for the BNT transform and for setting the cuts is asserted rather than demonstrated, and the forecast setup does not exercise that failure mode. This is fixable and does not undermine the overall framework, but it is load-bearing for the paper's main advantage claim.","major_comments":[{"comment":"This is load-bearing because the central advertised advantage is that an ℓ-space cut is much closer to a k-space cut; if the cut calibration is sensitive to the assumed cosmology, the advantage may degrade in real analyses.","section":"Section III A, unnumbered paragraph after Eq. (19)"},{"comment":"This is load-bearing for the numerical claims of bias significance and information retention, even though the qualitative BNT/noBNT hierarchy may survive.","section":"Section IV A, covariance paragraph"},{"comment":"This is a diagnostic, not a fit, so it is not circular, but its model dependence needs to be quantified for the estimator to be a reliable tool.","section":"Section III B, Eq. (29)"}],"minor_comments":[{"comment":"The caption contains a typo: 'dashed ines' should be 'dashed lines'.","section":"Figure 2 caption"},{"comment":"The legend uses 'FD' instead of 'TFD' in multiple places, which is confusing because TFD is the threshold parameter defined in Section III A.","section":"Figure 5"},{"comment":"The caption reads 'Sam as Figure 7' and should read 'Same as Figure 7'.","section":"Figure 8 caption"},{"comment":"There is a typo in 'the haracteristic scale' near the BCM setup description; it should be 'the characteristic scale'.","section":"Section IV C"},{"comment":"The symbol R is used both for the cut-ratio in Eq. (19) and for the leakage ratio in Eq. (25). These are different quantities, and this can be confusing; consider using a distinct symbol such as L for the leakage ratio.","section":"Notation, Eqs. (19) and (25)"},{"comment":"The sentence 'we have verified that the results do not change significantly' when fixing multiplicative biases and redshift errors is not accompanied by any details of the verification; please state what was checked and the size of the change.","section":"Section IV A, parameter sampling"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and is a methodologically useful contribution. I do not see grounds for rejection: the BNT framework is standard, the forecast tools are public, and the missing wrong-Π0 test and covariance details are concretely addressable. The main risk is that the paper's headline claim of robustness to the fiducial cosmology is currently an assertion; once that is tested, I would be happy to reconsider for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: this is a useful, well-executed proof-of-concept for applying BNT-transformed scale cuts in Stage-IV cosmic shear. The paper shows convincingly that, within its own fiducial setup, an ℓ-cut on BNT data behaves far more like a k-cut than standard tomographic cuts, and that this preserves constraining power while suppressing nonlinear model bias. The main thing I'd want before signing off is a wrong-cosmology test: the claim that the transform's results are insensitive to the fiducial cosmology is asserted, not demonstrated.\n\nWhat's actually new: the TFD-threshold ℓ-cut recipe, the scale-leakage estimator R, and the systematic forecast across four nonlinear P(k) models (HMcode, Halofit, BCM, AxionHMcode). The comparison with noBNT is fair—same parameters, same nuisance treatment—and the results are striking: for aggressive cuts like kcut=0.1 Mpc^-1 or TFD=0.004, BNT retains tight S8 constraints while noBNT blows up. The mock-vs-sampling model mismatch in Figs 9-11 is a good stress test of bias, and BNT comes out clean while noBNT stays biased even after marginalizing over AB. The code is public and the tools are standard, so the results are reproducible.\n\nNow the soft spots, in order of size. First, the robustness to the fiducial cosmology is a genuine gap. The BNT coefficients and the ℓ-cut definition both depend on the distance-redshift relation. If the true cosmology (or photo-z calibration) is off, the kernels don't null as well, and the ℓ-to-k mapping broadens. The paper's statement that the choice 'does not affect the results' and 'remains unbiased even with imperfect nulling' is made in passing, with no derivation and no numerical test. This isn't fatal—the effect is likely small given current parameter uncertainties—but the central claim is about ℓ-k equivalence, and that claim is exactly what would degrade. A simple wrong-Π0 test (shifting Ωm or h by a few sigma in the transform, then re-running the forecasts) would settle it.\n\nSecond, the introduction's 'free of any assumptions' is an overstatement. The cut recipe uses a fiducial P(k) to define R, and the leakage estimator uses a specific (Amod, S8) pair. That's not a flaw in the method, but it should be phrased more carefully. Third, there's no quantitative comparison with the x-cut method of Taylor et al. (2021), which is the closest prior art. The paper cites it but doesn't compare performance. Fourth, the forecast omits intrinsic alignments; the authors acknowledge this and argue it won't change the conclusions, but it remains untested.\n\nWho should read this: anyone planning the cosmic shear analysis pipeline for Euclid, Rubin, or Roman. It's a serious methodological contribution with a clear, fixable gap. I'd send it to peer review, and I'd ask for the wrong-Π0 test (and ideally an x-cut comparison) before acceptance.","headline":"BNT scale cuts are a genuinely promising recipe for Stage-IV cosmic shear, but the claimed robustness to the fiducial cosmology is asserted, not tested.","tokens_in":34736,"tokens_out":3389,"would_cite":true,"duration_ms":31362,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Weak lensing scale cuts that use the BNT transform preserve cosmological constraints while removing small-scale theoretical bias.","keywords":["weak lensing","cosmic shear","BNT transform","scale cuts","scale leakage","nonlinear matter power spectrum","S8 tension","tomography"],"falsifier":"Run the same forecast pipeline on a mock survey produced with a nonlinear power spectrum that is deliberately far from the fiducial cosmology (for example, $S_8$ below 0.7 or strong baryonic suppression), then evaluate the leakage ratio of Eq. (25) for each tomographic pair below its $\\ell_{\\mathrm{cut}}$; if the ratio rises substantially above the value predicted near the fiducial cosmology, the claimed equivalence between $\\ell$-cut and $k$-cut is broken.","tokens_in":33657,"feed_emoji":"🔭","tokens_out":10027,"duration_ms":76644,"temperature":0.7,"pith_summary":"Weak lensing measures mass in projection, so small-scale uncertainties in the matter power spectrum bleed into every angular scale. This paper argues that the standard remedy—cutting small angular scales—is both inefficient and insufficient, because an angular cut is not the same as a physical-scale cut. It proposes instead to apply the Bernardeau-Nishimichi-Taruya (BNT) transform, a linear rearrangement of tomographic lensing kernels, before cutting in angular frequency. In BNT space the connection between angular scale and three-dimensional wavenumber is much tighter, so a cut in $\\ell$ behaves nearly like a cut in $k$ and the problematic small-scale modes can be discarded while the cosmological signal is kept. Forecasts using several competing nonlinear power-spectrum models show the BNT approach recovering unbiased cosmological parameters where the standard approach fails.","feed_headline":"Weak-lensing transform makes angular cuts behave like physical cuts","feed_subtitle":"Rearranging galaxy-shear spectra lets surveys cut unreliable small scales without sacrificing cosmological precision.","key_machinery":"The BNT transform, a linear invertible matrix applied to tomographic cosmic-shear spectra, constructed by requiring each new lensing kernel to have vanishing zeroth and first redshift moments (Eqs. 6 and 7), so that kernels from bins more than one apart no longer overlap. This is what localizes lenses in redshift and makes an $\\ell$-cut approximate a $k$-cut. The accompanying machinery is the ratio $R(k_{\\mathrm{cut}}, \\Pi_0)$ defining a tolerance band $1 \\pm T_{\\mathrm{FD}}$, and the leakage statistic $R = \\chi^2[k > k_{\\mathrm{cut}}, \\ell < \\ell_{\\mathrm{cut}}] / \\chi^2[\\ell < \\ell_{\\mathrm{cut}}]$ (Eq. 25) that measures how much small-scale model-dependent power remains in the kept data.","core_discovery":"The central claim is that an angular-scale cut applied to BNT-transformed weak lensing spectra is a close proxy for a physical wavenumber cut in the three-dimensional density field, whereas in standard tomographic spectra the same cut still admits substantial leakage from high-$k$ modes. The BNT transform linearly combines lensing kernels from consecutive redshift bins so that each new kernel is localized in redshift, which in turn aligns $\\ell$ with $k$. The paper quantifies the alignment with the ratio $R^{(a,b)}(\\ell; k_{\\mathrm{cut}}, \\Pi_0)$, the fraction of a given spectrum contributed by modes with $k < k_{\\mathrm{cut}}$, and defines per-bin $\\ell$-cuts by requiring this ratio to stay within $1 \\pm T_{\\mathrm{FD}}$ of unity. For BNT spectra the transition between sensitive and insensitive $\\ell$ is sharp; for standard spectra, even very low $\\ell$ are affected by a cut at $k_{\\mathrm{cut}} = 0.3\\,\\mathrm{Mpc}^{-1}$. A new leakage statistic, the fraction of $\\chi^2$ coming from $k > k_{\\mathrm{cut}}$ below the cut, shows that BNT reduces leakage by a large factor across the whole $(k_{\\mathrm{cut}}, T_{\\mathrm{FD}})$ plane. In forecast analyses where the true nonlinear power spectrum is described by Halofit, the Baryon Correction Model, or an axion dark-matter model while the likelihood assumes a different model, ordinary scale cuts either leave a significant bias in $S_8$ and $\\Omega_m$ or destroy the constraints; the BNT analysis recovers the fiducial values within one $\\sigma$ with only modest degradation.","pith_inferences":["The leakage statistic $R$ could be used on real data as an operational diagnostic: compute it bin-by-bin and down-weight any tomographic pair whose measured leakage exceeds the fiducial prediction, rather than relying on a fixed global $k_{\\mathrm{cut}}$.","Because the BNT transform is linear and invertible, the same $\\ell$-to-$k$ alignment should carry over to convergence maps and higher-order statistics, so the method's reach likely extends beyond the power-spectrum forecasts made here.","A practical implementation will need an iterative scheme: estimate cosmological parameters, rebuild the BNT matrix, and check that the derived cuts do not move; the paper argues residual shifts are negligible, but quantifying this drift on real data would settle the point."],"forward_implications":["With BNT, a survey can keep data out to $\\ell \\simeq 5000$ while enforcing a strict cut at $k_{\\mathrm{cut}} \\simeq 1.5\\,\\mathrm{Mpc}^{-1}$, whereas the standard approach with the same strictness reaches only $\\ell \\simeq 300$.","Marginalizing over a baryon-feedback nuisance parameter does not by itself remove nonlinear-model bias in Stage-IV analyses; scale cuts on BNT data do.","BNT constraints degrade gently as $k_{\\mathrm{cut}}$ or the tolerance $T_{\\mathrm{FD}}$ is tightened, while noBNT constraints inflate rapidly and can vanish entirely, e.g. no constraints at $k_{\\mathrm{cut}} = 0.1\\,\\mathrm{Mpc}^{-1}$, $T_{\\mathrm{FD}} = 0.02$.","If the true nonlinear power spectrum differs from the assumed one, through baryons or ultralight axion dark matter, the BNT analysis recovers the fiducial $S_8$ and $\\Omega_m$ within $1\\sigma$, while the standard analysis is biased by several sigma or loses all constraining power."],"supporting_citations":[{"why":"Introduces the BNT transform, the linear rearrangement of lensing kernels that the paper's cut strategy is built on.","marker":"[17]"},{"why":"Shows how to tune cosmic-shear sensitivity in k-space with BNT-style cuts, the direct precursor of this method.","marker":"[18]"},{"why":"Applies x-cut cosmic shear to remove baryonic and nonlinear sensitivity, motivating the leakage-controlled analysis here.","marker":"[19]"},{"why":"Provides the HMcode nonlinear power spectrum used as the baseline model in the likelihood sampling.","marker":"[25]"},{"why":"Provides the Halofit version used as one of the alternative true nonlinear power spectra for the bias forecasts.","marker":"[33]"},{"why":"Provides the Baryon Correction Model used to generate mock observations with baryonic feedback.","marker":"[35]"},{"why":"Provides AxionHMcode, used to generate the fuzzy dark matter scenario.","marker":"[36]"},{"why":"Source of the S8-tension experiment design where a nonlinear amplitude parameter is varied.","marker":"[31]"},{"why":"Shows baryonic and nonlinear contributions can bias S8, motivating the need to quantify scale leakage.","marker":"[29]"}],"fun_headline_variants":["BNT transform turns angular cuts into physical cuts","Angular cuts that behave like physical ones in lensing","BNT method stops nonlinear leakage in weak lensing","Scale leakage tamed by BNT transform in lensing surveys","BNT cuts mimic physical scales without losing precision"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the cosmology used to build the BNT transform is close enough to the true cosmology that imperfect nulling still leaves angular cuts behaving like physical cuts; if the true cosmology were far from that fiducial, the new kernels could overlap and small-scale modes could leak back into the kept data.","fun_headline_variants_meta":{"raw":{"variants":["BNT transform turns angular cuts into physical cuts","Angular cuts that behave like physical ones in lensing","BNT method stops nonlinear leakage in weak lensing","Scale leakage tamed by BNT transform in lensing surveys","BNT cuts mimic physical scales without losing precision"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000228,"raw_usage":{"total_tokens":1571,"prompt_tokens":1138,"completion_tokens":433,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":754,"completion_tokens_details":{"reasoning_tokens":356}},"tokens_in":754,"tokens_out":433,"duration_ms":3802,"temperature":1.0,"reasoning_tokens":356,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:59:25.717580+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same forecast pipeline on a mock survey produced with a nonlinear power spectrum that is deliberately far from the fiducial cosmology (for example, $S_8$ below 0.7 or strong baryonic suppression), then evaluate the leakage ratio of Eq. (25) for each tomographic pair below its $\\ell_{\\mathrm{cut}}$; if the ratio rises substantially above the value predicted near the fiducial cosmology, the claimed equivalence between $\\ell$-cut and $k$-cut is broken.","supporting_citations":[{"cited_title":"The removal of shear-ellipticity correlations from the cosmic shear signal via nulling techniques","cited_arxiv_id":"0804.2292","evidence_quote":"Provides the HMcode nonlinear power spectrum used as the baseline model in the likelihood sampling."},{"cited_title":"On constraining Cosmology and the Halo Mass Function with Weak Gravitational Lensing","cited_arxiv_id":"2302.00780","evidence_quote":"Provides the Halofit version used as one of the alternative true nonlinear power spectra for the bias forecasts."},{"cited_title":"Novel geometrical test of cosmological expansion from photometric data","cited_arxiv_id":"2502.02243","evidence_quote":"Source of the S8-tension experiment design where a nonlinear amplitude parameter is varied."},{"cited_title":"Figure 3 shows that the parameter AB [24] can specifically bias the power spectrum for k >1 Mpc−1, potentially resulting in a bi- ased S8 if left uncorrected","cited_arxiv_id":null,"evidence_quote":"Shows baryonic and nonlinear contributions can bias S8, motivating the need to quantify scale leakage."}],"review_version":1}