{"id":"48595c8e-31c6-43a9-87de-ee5ecc1e5085","arxiv_id":"2506.17217","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The authors derive and validate lensing-hardened estimators for stacked patchy screening measurements, show the unmitigated lensing bias dominates the ACT x unWISE signal, and place an upper bound on the screening amplitude.","lead":"This paper develops methods to remove the large CMB lensing contamination in stacked measurements of the patchy screening effect, the blurring of the CMB by gas around galaxies. The methods are validated on simulations and applied to ACT and unWISE data, yielding an upper bound on the screening signal.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"ACT×unWISE result rests on an unvalidated small-scale Cκg model; the quoted screening upper bound is only as strong as that extrapolation.","rationale":"The paper's central derivation is coherent: the lens-hardened weights satisfy the stated response constraints, the stacked-hardening formula (Eq. 11) follows from the linear response, and the simulation comparison supports the subtraction logic. I cannot identify a fatal flaw in the method itself. The most load-bearing uncertainty is in the headline application: §V's conclusion that the ACT×unWISE profile is consistent with pure lensing, and the resulting τ0<1.1×10^-4 bound, is computed from Eq. (12) with an analytic Cκg model at multipoles beyond where CMB lensing data validate it. This is a model-dependence issue, not an internal inconsistency, and it is precisely what a CONDITIONAL verdict should require the authors to quantify. The placeholder companion citation [13] is a secondary reproducibility issue: the quantitative agreement in Fig. 3 is delegated to an unavailable paper. Neither issue impugns the derivations, so I keep the reader's CONDITIONAL verdict rather than escalating to REJECT.","tokens_in":15236,"tokens_out":12436,"duration_ms":136672,"concrete_test":"Recompute the §V mean lensing bias using Eq. (12) with Cκg_L treated two ways: (a) the fiducial Aemulus/linear-bias model, and (b) Cκg_L matched to the measured ACT DR6×unWISE cross-spectrum on the overlapping L≤3000 range and extended to L>3000 with a halo-model or hydro-simulation calibration. If the predicted lensing bias and the resulting τ0 bound change by more than the quoted 68% statistical uncertainty, the upper bound is model-dominated. Also report the ratio of modeled to measured Cκg bandpowers over the overlapping range; a systematic departure toward L~3000 would show that the small-scale extrapolation is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"At the level of the formalism, I find no internal inconsistency: Eqs. (8), (11), and (12) follow from the stated linear-response assumptions, and Fig. 3 shows that the subtraction prescription reproduces a lensing-only simulation profile. The load-bearing weak point is §V. There, the ACT×unWISE profile is debiased via Eq. (12) with Cκg_L obtained from the Kaiser-Limber approximation, a linear bias model, and the Aemulus ν nonlinear matter power spectrum. The lensing response RTκ_L(r) is non-negligible out to L≃8000 for the ξ=0 case used for unWISE (Fig. 2), while the paper itself notes that ACT DR6 lensing is reliable only to L≃3000 (§III C). The model is not compared with any measured unWISE×lensing cross-spectrum, and no uncertainty is propagated from the L>3000 extrapolation. The no-detection conclusion and the τ0<1.1×10^-4 bound therefore stand or fall with an unvalidated nonlinear/bias model: if Cκg_L is wrong by tens of percent on these scales, the residual lensing bias can mimic or hide a screening signal at the level of the quoted bound. This does not invalidate the hardening formalism, but it is exactly the kind of model-dependence a CONDITIONAL verdict should require quantifying. Secondary reproducibility gap: the §IV simulation validation is delegated to companion [13], cited only as arXiv:2411.XXXX, so Fig. 3 cannot currently be audited.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper addresses the problem of CMB lensing contamination in stacked estimators of patchy screening (the 'blurring' Sunyaev-Zel'dovich effect). The authors derive the linear response of a general class of stacked estimators to lensing and present three mitigation strategies: field-level bias hardening via a constrained minimum-variance quadratic estimator; stacked hardening, in which an external convergence estimate is filtered by the stacked estimator's lensing response and subtracted; and mean hardening, in which the average lensing bias is computed from a model for the lensing-galaxy cross-spectrum Ckg_L. The field-level and stacked methods are validated against lensed CMB simulations built from AbacusSummit, showing that both reproduce the simulated lensing bias profile. The mean-hardening method is then applied to ACT DR6 temperature maps stacked on unWISE galaxies; the predicted lensing bias dominates the raw profile, and after subtraction the authors obtain no detection of patchy screening, quoting a 68% upper bound of tau0 < 1.1e-4 for a Gaussian electron profile with 2 arcmin FWHM.","tokens_in":15524,"tokens_out":6963,"duration_ms":64924,"significance":"If the results hold, the paper provides a practical route to unbiased stacked screening measurements for any large-scale structure tracer, removing what would otherwise be a dominant systematic. The analytic derivations in Sec. III and Appendices A-C are careful and self-contained, and the hardening methods themselves introduce no free parameters. The simulation comparison in Sec. IV, although partly delegated to the companion paper, provides a non-trivial validation of the subtraction prescription against lensed maps with no screening signal. The ACT x unWISE application is a useful demonstration that the expected lensing bias indeed dominates the raw stacked profile, and the resulting upper bound is consistent with expectations from recent kSZ measurements. The main weakness is that the unWISE bound rests on a small-scale model of Ckg_L that is not currently validated against data.","major_comments":[{"comment":"The ACT x unWISE no-detection conclusion and the tau0 < 1.1e-4 bound in §V rest on the mean-hardening estimate of Eq. (12), which uses Ckg_L obtained from the Kaiser-Limber approximation, a linear bias model, and the Aemulus nu matter power spectrum. As shown in Fig. 2, the lensing response RTkappa_L(r) for the xi=0 configuration used for unWISE is non-negligible up to L ~ 8000, while §III C notes that ACT DR6 lensing is reliable only to L ~ 3000. The paper does not compare this model with a measured unWISE x lensing cross-spectrum, and it does not propagate any uncertainty from the L > 3000 extrapolation. If the true Ckg_L differs from the model by tens of percent on these scales, the residual lensing bias could mimic or hide a screening signal at the level of the quoted bound. The authors should quantify this sensitivity, for example by varying the linear bias, magnification bias, and nonlinear matter power within plausible ranges and recomputing the profile and upper bound, or by validating Ckg_L against an external cross-correlation measurement.","section":"§V, Eq. (12), Fig. 4"},{"comment":"The central simulation validation of stacked and mean hardening is presented in Fig. 3, but the measurement of the lensed-CMB stacked profile (the 'lensing only sims.' curve) is delegated to the companion paper [13], cited as arXiv:2411.XXXX with no further details. The description in §IV specifies the filters and beam, but the construction of the lensed CMB maps, the galaxy catalog, the bandpower window used for binning, and the 0.5 arcmin smoothing applied in stacked hardening are not described here. Since the agreement between the predicted and simulated lensing biases is the empirical basis for the central claim, the authors should either include these details in the present paper or provide the actual arXiv number of the companion paper so that the validation can be audited.","section":"§IV, Fig. 3, companion paper [13]"},{"comment":"Higher-order lensing contributions and extragalactic foregrounds are acknowledged as unquantified (Eq. A13 and §VI). For the stacked and mean-hardening validation this is a reasonable leading-order treatment, but for the ACT x unWISE upper bound the same statement applies: the bound assumes that the quadratic-order lensing term and foreground contamination are subdominant relative to the quoted 68% limit. The authors should state, even approximately, the expected size of these terms for the unWISE analysis (for example, the post-Born or foreground bias to the stacked profile compared with the tau0 < 1.1e-4 bound), or explicitly rescope the claim to be conditional on these terms being negligible.","section":"Appendix A, Eq. (A13), §VI"}],"minor_comments":[{"comment":"Reference [13] is cited as arXiv:2411.XXXX throughout; the final arXiv number should be inserted before publication.","section":"References, [13]"},{"comment":"The sentence 'the long map Tl appearing the numerator of Eq. (5)' should read 'appearing in the numerator'.","section":"§V, text near Eq. (5)"},{"comment":"The units of the y-axis label '10^4 x (avg. lensing bias) to T-hat(r)' are not defined; please state that the profile T-hat is dimensionless and that the vertical axis is the lensing bias scaled by 10^4.","section":"Fig. 3"},{"comment":"In Appendix B, the contour deformation for the Fourier transform of the signed and thresholded weight is described verbally and illustrated in Fig. 5; a one-line statement of the convergence condition (e.g., the sign of Im(T) required for omega > 0) would improve readability.","section":"Appendix B, Fig. 5"},{"comment":"The practical details of the mean-hardening implementation, specifically how the bandpower window is applied to the smooth prediction in Eq. (12) before comparing with the binned profile, are mentioned only in the figure caption; a brief description in the text would make the comparison reproducible.","section":"§IV, mean-hardening implementation"}],"recommendation":"major_revision","confidential_remarks":"This is a solid methodology paper with a sound central derivation and a credible simulation test, but the ACT x unWISE upper bound is conditioned on an unvalidated small-scale Ckg_L model. I recommend major revision rather than rejection because the issue is quantifiable: adding sensitivity tests or an external validation of Ckg_L would resolve the concern. The companion-paper dependency is also unusual; the placeholder arXiv ID should be replaced with a real identifier before the claims in Fig. 3 can be independently checked."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Best to read this as a methods paper. The new and durable part is the linear lensing response of general stacked estimators (Appendix A, Eq. A12), the W[T]-independence for disjoint filters, and the stacked and mean hardening schemes built on it. Those derivations are clean, the simulation agreement in Fig. 3 is good (modulo the companion-paper delegation), and the application to ACT×unWISE makes the stakes concrete: without mitigation the lensing bias dominates, and the hardening removes it. Credit where due: the paper states the assumptions, flags the higher-order lensing and foreground terms it leaves out, and does not oversell the upper bound.\n\nThe soft spot is the unWISE analysis. Equation (12) needs Cκg_L out to L~8000 for the ξ=0 filter, while ACT DR6 lensing is trustworthy to ~3000. The model uses Kaiser-Limber + linear bias + Aemulus ν; the linear and magnification biases are inherited from unWISE cross-correlation analyses, so the model is not fully external. The paper shows an excellent match between the predicted lensing profile and the measured unfiltered ACT×unWISE profile, which is a useful consistency check, but it is not a sharp validation of the high-L extrapolation, because the profile integral weights Cκg_L with RTκ_L. If that model is off by tens of percent above L=3000, the quoted τ0<1.1×10^-4 bound could shift by order unity. That should be quantified with a conservative model envelope or by restricting the analysis to L≲3000 where the lensing map is reliable. This is a fixable weakness, not a reason to reject.\n\nOne reproducibility gripe: the simulation validation in §IV is deferred to a companion paper cited as arXiv:2411.XXXX. Figure 3 cannot be audited until that ID is replaced. Minor, but should be fixed before publication.\n\nOverall: the central formalism is sound and useful. The paper belongs in the literature and deserves a serious referee. The referee should push on the Cκg robustness and the placeholder citation, but this is not a desk reject.","headline":"The hardening formalism is the real contribution and it holds up; the ACT×unWISE upper bound is the soft part because it leans on an unvalidated high-L Cκg model.","tokens_in":16085,"tokens_out":2799,"would_cite":true,"duration_ms":28045,"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":"Lensing bias in stacked patchy-screening profiles can be nulled or accurately modeled, making robust gas-profile measurements possible.","keywords":["patchy screening","CMB lensing","bias hardening","stacked estimators","Sunyaev-Zel'dovich effect","optical depth profiles","unWISE galaxies","CMB secondary anisotropies"],"falsifier":"Run the hardened stacked estimator on simulated lensed CMB maps that contain a known injected screening signal and also on maps with no screening; if the screening-free hardened profile deviates from zero beyond the noise, or if the residual matches the quadratic lensing response function, then linear-order hardening is insufficient.","tokens_in":14991,"feed_emoji":"🌌","tokens_out":9841,"duration_ms":99558,"temperature":0.7,"pith_summary":"Patchy screening, the suppression of CMB temperature fluctuations by Thomson scattering off free electrons, is a direct probe of ionized gas around galaxies, but the quadratic estimators used to isolate it are contaminated by CMB lensing. The paper shows that when stacking on unWISE galaxies, this lensing bias dominates the screening signal if left untreated. It extends lens-hardening, previously available for standard quadratic estimators, to the stacked estimators used for gas profiles, giving three options: field-level hardening, stacked hardening against a convergence map, and mean hardening from the lensing-galaxy cross-spectrum. Simulations with LRG-like galaxies show that stacked and mean hardening reproduce the simulated lensing bias, and applying mean hardening to current CMB temperature maps stacked on unWISE galaxies leaves an upper bound on the screening signal.","feed_headline":"Lensing bias in stacked screening profiles can be nulled","feed_subtitle":"Field-level and stacked hardening remove the CMB-lensing contamination that otherwise dominates gas-profile measurements.","key_machinery":"The load-bearing object is the pair of linear response functions of the CMB temperature covariance: $f^\\tau_{\\ell,L-\\ell}=-(C^{TT}_\\ell+C^{TT}_{|L-\\ell|})$ for patchy screening and $f^\\kappa_{\\ell,L-\\ell}=2\\frac{L}{L^2}\\cdot[\\ell C^{TT}_\\ell+(L-\\ell)C^{TT}_{|L-\\ell|}]$ for lensing. These kernels specify how a fixed optical-depth or convergence mode creates off-diagonal covariance, so the estimator design problem is to choose weights $F_{\\ell,L-\\ell}$ that respond to $\\tau$ and are blind to $\\kappa$. The paper transfers that logic to the real-space stacked estimator through a stacked response $R^{T\\kappa}_L(r)$, which turns a convergence estimate into a radial lensing bias, and to mean hardening through the integral $\\langle\\mathrm{lensing\\ bias}\\rangle(r)=\\int\\frac{L\\,dL}{2\\pi}R^{T\\kappa}_L(r)C^{\\kappa g}_L$. The response formalism also shows that the signed-and-thresholded estimator has the same leading-order lensing response as the standard stacked estimator, so hardening applies unchanged to that variant.","core_discovery":"The central claim is that the lensing contamination of stacked patchy-screening estimators can be nulled or accurately modeled. Lensing changes the CMB covariance through a known linear response kernel $f^\\kappa_{\\ell,L-\\ell}$, and by choosing quadratic weights that are normalized to the screening response $f^\\tau_{\\ell,L-\\ell}$ but orthogonal to $f^\\kappa$, the paper constructs a lens-hardened estimator whose stacked profile is unbiased. For the real-space long-short split estimator, the same logic runs through an effective response $R^{T\\kappa}_L(r)$ that converts any unbiased convergence estimate into a predicted radial lensing bias, and in the mean-hardening variant the convergence map is replaced by the lensing-galaxy cross-spectrum $C^{\\kappa g}_L$. The paper validates both approaches against lensed CMB simulations with mock LRG-like galaxies, finding that both track the lensing-only simulated profile. Applying mean hardening to the published unWISE stacked measurement yields a screened profile consistent with zero, with an upper bound $\\tau_0<1.1\\times10^{-4}$ at 68% confidence.","pith_inferences":["Editorial inference: because the linear-response argument is independent of the weighting function, the same hardening logic should transfer to other quadratic stacked estimators, such as kinematic Sunyaev-Zel'dovich or cluster-lensing profiles, provided the relevant response kernels are re-derived.","Editorial inference: the recommendation to evaluate the long and short maps at identical positions shrinks the lensing response on scales $L\\gtrsim3000$, so this choice may reduce the need for hardening even before any subtraction is applied.","Editorial inference: a direct small-scale measurement of the galaxy-CMB-lensing correlation would replace the extrapolated cross-spectrum in mean hardening and make the unWISE upper bound model-independent.","Editorial inference: future high-resolution lensing maps could turn mean hardening into stacked or field-level hardening on the same data, which would test the parametric extrapolation by comparing the two debiased profiles."],"forward_implications":["Stacked patchy-screening profiles can be measured without the lensing bias for any galaxy tracer, using either field-level or stacked hardening.","Mean hardening lets surveys with only large-scale lensing maps predict and subtract the dominant small-scale lensing bias from a stacked profile.","The signed-and-thresholded estimator used in earlier work has the same leading-order lensing response, so its measurements can be interpreted and corrected with the same formalism.","The published unfiltered ACT times unWISE profile is consistent with lensing bias alone; after subtraction, the screening signal is bounded by $\\tau_0<1.1\\times10^{-4}$ at 68% confidence.","Lower-mass galaxy samples, having weaker clustering, will show a larger relative lensing bias, so bias hardening becomes more necessary for future surveys."],"supporting_citations":[{"why":"Defines the quadratic-estimator formalism and the linear response of the CMB covariance to patchy screening; this is the starting point for all estimators considered.","marker":"[5]"},{"why":"Derives the lensing bias to patchy screening reconstruction and the lens-hardening idea that the paper extends to stacked estimators.","marker":"[6]"},{"why":"Proposes the long-short split stacked estimator for patchy screening that forms the basis of the real-space estimator.","marker":"[11]"},{"why":"Provides the observed stacked profile on unWISE galaxies and the signed-and-thresholded estimator variant; it is the measurement that mean hardening is tested against.","marker":"[12]"},{"why":"Companion paper supplying the simulated lensed CMB maps, mock LRG-like galaxies, and measured lensing-only stacked profiles used for validation.","marker":"[13]"},{"why":"Gives the minimum-variance quadratic-estimator weights and lensing response function on which the hardened weights are built.","marker":"[14]"},{"why":"Public CMB lensing map whose reliable scale range motivates the mean-hardening fallback that avoids high-resolution lensing reconstruction.","marker":"[33]"},{"why":"Simulation catalogues used to build the mock galaxies whose lensing-only stacked profile is the validation baseline.","marker":"[35]"},{"why":"Non-linear matter power spectrum used to compute the lensing-galaxy cross-correlation for the unWISE mean-hardening prediction.","marker":"[42]"}],"fun_headline_variants":["Hardened estimators null CMB lensing bias in screening profiles","Lensing contamination eliminated in stacked screening estimators","Optimal lens-hardened estimators for patchy screening profiles","Unbiased gas profiles via lens-hardened CMB screening estimators","CMB lensing bias nulled in stacked screening measurements"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the leading-order (linear) lensing effect is the dominant contamination, with higher-order lensing and extragalactic foregrounds small enough to ignore; for the unWISE upper bound, one must also trust the predicted galaxy-lensing correlation on small angular scales where it has not been directly measured.","fun_headline_variants_meta":{"raw":{"variants":["Hardened estimators null CMB lensing bias in screening profiles","Lensing contamination eliminated in stacked screening estimators","Optimal lens-hardened estimators for patchy screening profiles","Unbiased gas profiles via lens-hardened CMB screening estimators","CMB lensing bias nulled in stacked screening measurements"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000211,"raw_usage":{"total_tokens":1404,"prompt_tokens":927,"completion_tokens":477,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":543,"completion_tokens_details":{"reasoning_tokens":397}},"tokens_in":543,"tokens_out":477,"duration_ms":4936,"temperature":1.0,"reasoning_tokens":397,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:09:20.300604+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the hardened stacked estimator on simulated lensed CMB maps that contain a known injected screening signal and also on maps with no screening; if the screening-free hardened profile deviates from zero beyond the noise, or if the residual matches the quadratic lensing response function, then linear-order hardening is insufficient.","supporting_citations":[{"cited_title":"Gluscevic, M","cited_arxiv_id":null,"evidence_quote":"Proposes the long-short split stacked estimator for patchy screening that forms the basis of the real-space estimator."},{"cited_title":"Hadzhiyska, N","cited_arxiv_id":null,"evidence_quote":"Companion paper supplying the simulated lensed CMB maps, mock LRG-like galaxies, and measured lensing-only stacked profiles used for validation."}],"review_version":2}