{"id":"b3861085-6c77-4196-896c-ff9d9f4efb92","arxiv_id":"2411.14947","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A full window-convolution pipeline for the galaxy bispectrum in the TripoSH basis, implemented as a single window matrix and validated against DESI DR1 mocks.","lead":"Galaxy survey measurements are distorted by the survey window, and this paper builds a fast, matrix-based method to apply that window correction to the three-point clustering signal. It validates the pipeline on DESI DR1 mock galaxies and shows the correction changes the bispectrum by many sigma, making it usable for current cosmological surveys.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Validation chi2 uses the cut-sky covariance while the proxy model and the reference are measured from the same 25 AbacusSummit realizations, so the residual is not compared against its correct noise; the 'no noticeable deviation' claim is statistically under-supported.","rationale":"The reader's weakest_assumption is the integral-constraint approximation (eq. 3.1), which is a real limitation but is explicitly acknowledged, deferred to future work, and shown to be numerically negligible in the validated sample (Sec. 4.2, weight-function tests). Even if the true integral constraint is scale-dependent, the central validation for the DESI DR1 LRG SGC sample is not directly broken by that assumption. The more load-bearing concern is the statistical design of the validation itself: using the same 25 simulations for both the unwindowed model and the windowed reference means the residual is not independent of the model, and the covariance used in eq. (4.2) is not the covariance of that residual. The small chi2 values and the dismissal of the complete-mock beta offsets as 'within the fractional error of the measurements' therefore do not establish the claimed 'no noticeable deviation' at the precision implied. The paper's formalism (linearity, window matrix, FFTLog implementation) appears sound, and the visual agreement is encouraging, but the quantitative validation needs a different noise model or out-of-sample input. This does not change the overall verdict from CONDITIONAL, so the reader's verdict is left unchanged.","tokens_in":25125,"tokens_out":11705,"duration_ms":118983,"concrete_test":"Recompute the validation using a paired-difference or split-sample statistic. Concretely: (i) for each of the 25 realizations form the paired residual D_i = B_cut^i - W B_box^i (or run the window matrix on each realization's unwindowed measurement), estimate C_D from the 25 D_i, and evaluate chi2 = <D>^T C_D^{-1} <D>; if chi2/dof >> 1, the claimed agreement fails. (ii) Alternatively, replace the cubic-box mean with an analytic bispectrum model independent of the mocks as input B; then the cut-sky covariance is the correct noise and the agreement can be assessed without common-mode cancellation. Either test should also be applied to the complete LRG mocks to decide whether beta = 3-4% is a real bias.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central validation (Sec. 4.2) does not use a noise model appropriate for the comparison being made. The unwindowed proxy model is the mean of 25 cubic-box measurements and the windowed reference is the mean of 25 cut-sky mocks drawn from the same AbacusSummit realizations; the cut-sky catalogues are explicitly 'replicated from the snapshots' (Sec. 4). Thus B_box and B_cut share the same cosmic variance, and the residual R = <B_cut> - W<B_box> has a covariance set by shot noise, fibre assignment and window-convolution error, not by Cov(B_cut). Eq. (4.2) nevertheless inverts C_{l1l2L} estimated from the 25 cut-sky measurements, which includes the common large-scale signal variance and therefore inflates the noise entering the chi2. The quoted chi2 per bin (0.08 for the monopole, 0.03 for the quadrupole) and the statement 'no noticeable deviation' are not statistically supported. The same issue affects the interpretation of the complete-LRG amplitude offsets beta ~ 3-4% (App. A): saying these are 'within the fractional error of the measurements' compares the offset to the box-model error, whereas the relevant error is the error on the paired difference B_cut - W B_box, which is much smaller because the signal cancels. Consequently the validation does not exclude a small but systematic amplitude bias in the window-convolved bispectrum.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a practical forward-modelling pipeline for the survey window convolution of galaxy bispectrum multipoles in the tripolar spherical harmonic (TripoSH) basis. The windowed 3PCF multipoles are written as a series over window-function and unwindowed 3PCF multipoles, following Sugiyama et al. (2019); the paper adds a double spherical Bessel transform implementation, a linear algebra formulation in which the full convolution is encapsulated as a window matrix W multiplying an unwindowed bispectrum model vector, and an extensive validation against DESI DR1 LRG SGC mocks built from 25 AbacusSummit realizations. The validation includes convergence tests for the window-function measurement and for the truncated series, identifies a reduced convolution formula, and compares the window-convolved proxy model with cut-sky mocks, quoting chi-square per bin of 0.08 and 0.03 for the monopole and quadrupole. The authors also apply the pipeline to QSO and complete-mock samples in an appendix and report small amplitude offsets beta of a few percent.","tokens_in":25435,"tokens_out":7047,"duration_ms":57246,"significance":"If the validation is accepted, this is a valuable methods contribution: it gives the community a reusable, public-code pipeline for a step that has so far been either approximated or deferred in bispectrum analyses of DESI and Euclid. The TripoSH basis reduces the dimensionality of the problem, and the window-matrix formulation makes the convolution fast enough for repeated likelihood evaluations. The paper is careful about convergence in several independent directions, and the claim that the window matrix reproduces the step-by-step convolution to floating-point precision is checked directly. The main weakness is that the statistical validation of the final model against the mocks uses a covariance that is not appropriate for the comparison being made, so the headline 'no noticeable deviation' and the quoted chi-square values are not yet supported. The integral-constraint approximation is also explicitly left as future work, and its impact on the validated scales is not quantified.","major_comments":[{"comment":"The validation compares the mean of 25 cut-sky measurements with the window matrix applied to the mean of 25 cubic-box measurements from the same AbacusSummit realizations. As the cut-sky catalogues are 'replicated from the snapshots' (Sec. 4), the residual R = <B_cut> - W<B_box> does not contain the common cosmic variance of the two means, but the covariance C in Eq. (4.2) is estimated from the 25 cut-sky measurements and therefore includes that common variance. Inverting this covariance inflates the noise entering the chi-square, so the quoted values of 0.08 per bin (monopole) and 0.03 per bin (quadrupole), and the statement that the model has 'no noticeable deviation', are not statistically supported. The same issue affects Appendix A, where the beta ~ 3-4% offsets are said to be within the fractional error of the measurements; the relevant error is on the paired difference B_cut - W B_box, which is much smaller because the signal cancels. Please recompute the residual chi-square using a covariance estimated from the 25 paired realizations, or an analytic shot-noise plus window-convolution error model, and reassess whether the amplitude offsets are consistent with zero.","section":"Sec. 4.2, Eq. (4.2); App. A"},{"comment":"The integral-constraint correction is assumed to be a constant determined by the isotropic condition of Eq. (3.1), and radial integral constraints are explicitly ignored; the authors defer a more consistent treatment to future work. This is an acknowledged limitation, but because the validation in Sec. 4.2 currently uses the incorrect residual covariance (see previous comment), the approximation is not actually tested at the precision claimed. Since the pipeline is intended for cosmological analyses of DESI DR1 and Euclid, I ask for at least a sensitivity test: adopt a simple scale-dependent or radial integral-constraint ansatz and check that the window-convolved bispectrum changes by less than the paired residual error over the reported scale range. Without such a test, the approximation remains a correctness risk for the final application, even though it does not invalidate the algebraic structure of the window convolution.","section":"Sec. 3.1, Eq. (3.1); Sec. 4.2"},{"comment":"The reduced window convolution formula (4.4) is obtained by ranking term contributions with the weight function (4.3), which is evaluated against the same cut-sky measurements later used to quote the performance of the reduced formula ('the loss function (4.2) remains the same as for the full reference formula'). This is a selection on the validation data, so the reported chi-square for the reduced model is not an independent test of the truncation. To make the truncation robust, either demonstrate from the intrinsic amplitudes of the measured window multipoles and the model multipoles that the omitted terms are negligible, or validate the reduced formula on a subset of realizations not used for ranking the terms.","section":"Sec. 4.2, Eqs. (4.3)-(4.4)"}],"minor_comments":[{"comment":"The phrase 'truncated at a finite of number of terms' should read 'truncated at a finite number of terms'.","section":"Abstract"},{"comment":"The sentence 'The truncation of the window convolution series eq. (2.8b) to achieve convergence' appears to refer to the convolution series of Eq. (3.3), not to the double spherical Bessel transform of Eq. (2.8b). Please correct the equation reference.","section":"Sec. 3.3"},{"comment":"The caption states 'Inverse absolute value of the window matrix elements, (W)^{-1}_{IJ}'. If the plotted quantity is 1/|W_IJ|, this should be written explicitly; if it is the inverse matrix, the caption is misleading because the text describes the inverse absolute value of the elements.","section":"Fig. 8 caption"},{"comment":"The text uses 'ATMLs' where the acronym is introduced elsewhere as 'AMTL' (alternate merged target ledgers). Please make the acronym usage consistent.","section":"App. A"},{"comment":"In the sentence 'the number density of the random catalogue appears to have an effect on the largest scales, but there is no discernible trend with alpha^{-1}', the attribution to sample variance would be more convincing if the different-density random catalogues were compared against the same underlying window rather than independent realisations; this is a minor presentation point.","section":"Sec. 4.1.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is well within the scope of JCAP and represents a useful step toward practical bispectrum window convolution. The algebraic development is sound, and the code availability is a genuine strength. My main concern is the validation statistics: the residual between the windowed proxy model and the cut-sky mocks is compared against the wrong covariance, so the headline chi-square values and 'no noticeable deviation' statement are not yet supported. This is fixable by a paired-realization or analytic residual covariance. The integral-constraint approximation is a known limitation, but given the statistical issue it is currently not tested at the precision required; a sensitivity test would strengthen the revision. The truncation of the reduced formula also involves selection on the same data used for the final chi-square, which should be acknowledged and addressed. With these points addressed, I would support publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is the paper that makes bispectrum window convolution practical for DESI DR1 and Euclid, and the linear-algebra window matrix is a genuinely useful contribution. The formal core holds up. But the validation section has a real statistical problem, and the authors' 'no noticeable deviation' claim is weaker than the quoted chi2 values suggest.\n\nWhat's actually new: relative to Sugiyama et al. 2019, which kept only the leading term, and the configuration-space follow-up, they implement the Fourier-space version including non-leading-order terms and show those terms matter. The window-matrix formulation—precompute a matrix from unit vectors, then any model vector gets convolved by a matrix multiply—is clean and obviously useful for likelihood analyses. The convergence checks on mesh sampling, random-catalogue density, and series truncation are thorough. Code and data are public, and the authors clearly flag the integral-constraint approximation as future work, which is honest.\n\nSoft spots, in order of importance. First, the stress-test note is correct. The cube-box proxy and cut-sky reference are built from the same 25 AbacusSummit realizations, so the cosmic signal cancels in the residual. The covariance in eq. (4.2) is estimated from the cut-sky realizations and includes that common large-scale variance, so it is the wrong noise for the comparison. The quoted chi2 per bin of 0.03–0.08 is therefore not evidence of 'no noticeable deviation' at the claimed precision. Second, the reduced window formula is selected on the same 25 cut-sky mocks used to compute the final chi2, so part of the agreement is in-sample. Split-sample or out-of-sample truncation choice would address this. Third, the complete-LRG 3–4% amplitude offset is not clearly excluded by the 'within fractional error of the box model' argument, because the relevant error is on the paired difference, which is much smaller. The authors' own discussion of possible causes is fair, but the offset remains an open loose end.\n\nNone of this sinks the method. The window matrix reproducing the direct convolution to floating-point precision is a formal result that stands on its own, and the pipeline is a real advance. But the validation as written does not establish the precision it claims.\n\nWho this is for: anyone doing three-point clustering in DESI/Euclid analyses. It deserves a serious referee. In review I would ask for a corrected validation: use a paired-difference covariance or split-sample approach, and reinterpret or re-quantify the amplitude offset. That is major revision, not rejection.","headline":"A genuinely useful Fourier-space bispectrum window-convolution pipeline whose formal window-matrix result holds up, but whose headline validation chi2s are computed against the wrong noise and overstate the precision of the 'no noticeable deviation' claim.","tokens_in":26146,"tokens_out":3599,"would_cite":true,"duration_ms":38100,"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":"This paper shows that the full survey-window convolution of the galaxy bispectrum reduces to one linear-algebra operation, $\\tilde{B} = W B$, and validates that the window-convolved model reproduces DESI DR1 cut-sky measurements where the…","keywords":["galaxy clustering","bispectrum","survey window function","tripolar spherical harmonics","three-point correlation function","window convolution","redshift-space distortions"],"falsifier":"Re-run the DESI DR1 LRG SGC validation replacing the constant integral-constraint correction with a scale-dependent correction generalised from two-point analyses, and compare the largest-scale diagonal monopole bins of the window-convolved model with the 25-mock cut-sky mean; if the shift exceeds the mock error in those bins, the constant-correction assumption is falsified on the scales used here.","tokens_in":24875,"feed_emoji":"🔭","tokens_out":11955,"duration_ms":103834,"temperature":0.7,"pith_summary":"Galaxy surveys observe clustering after it has been filtered by the survey geometry—the sky footprint, the radial selection function, and systematic weights—so theoretical bispectra must be convolved with a window function before comparison. This paper establishes that for the tripolar-spherical-harmonic (TripoSH) decomposition of the bispectrum, that convolution is a linear operation: the whole four-step pipeline (window-function measurement, double spherical Bessel transform, convolution series, transform back) can be precomputed into a single window matrix $W$ such that $\\tilde{B} = W B$. Using the Dark Energy Spectroscopic Instrument (DESI) DR1 luminous red galaxy sample in the South Galactic Cap at $0.4 \\le z \\le 0.6$, the authors validate the procedure against cut-sky mock catalogues, finding that the window-convolved model matches the windowed measurements while the unwindowed model is off by up to $14\\sigma$ in the monopole and $5\\sigma$ in the quadrupole. A reader should care because correct window convolution is a prerequisite for cosmological parameter inference from non-Gaussian clustering in current and next-generation redshift surveys.","feed_headline":"Bispectrum survey-window effect now fits in one matrix multiply","feed_subtitle":"Matches DESI cut-sky measurements while ignoring the window deviates by up to 14 sigma.","key_machinery":"The load-bearing object is the tripolar spherical harmonic (TripoSH) decomposition, which expands the bispectrum into multipoles $B_{\\ell_1\\ell_2L}(k_1,k_2)$ using three coupled spherical harmonics and a Wigner 3-j symbol, reducing a triangle configuration to two wavenumbers. The same basis decomposes the three-point correlation function and the survey window function $Q_{\\ell_1\\ell_2L}(r_1,r_2)$, so the window can be measured from random catalogues with the same FFT-based estimators used for the clustering statistics themselves. The argument is carried by the window-convolution series, a linear combination of window and model multipoles with geometric coefficients, together with the double spherical Bessel transform implemented by FFTLog that moves between configuration and Fourier space. Because each step is linear, the paper constructs the window matrix $W$ by pushing unit vectors through the pipeline and uses it for fast repeated evaluation of models in a likelihood analysis.","core_discovery":"This paper establishes that the survey-window effect on the galaxy bispectrum can be fully forward-modelled in the TripoSH basis at a cost comparable to power-spectrum window convolution. In this basis the bispectrum multipoles $B_{\\ell_1\\ell_2L}(k_1,k_2)$ depend on two wavenumbers and three angular degrees, and the window function is decomposed into the same type of multipoles $Q_{\\ell_1\\ell_2L}(r_1,r_2)$, measurable from random catalogues with fast Fourier transforms. Window convolution is then a series expansion in configuration space, and because every step is linear, the entire procedure can be compressed into a window matrix $W$; the windowed model vector is $\\tilde{B} = W B$. Validation on DESI DR1 LRG SGC mocks in the wavenumber range $k \\le 0.12\\,h\\,\\mathrm{Mpc}^{-1}$ shows that the window-convolved proxy model has no noticeable deviation from the cut-sky measurements, whereas omitting the window produces deviations up to $14\\sigma$ (monopole) and $5\\sigma$ (quadrupole). The same procedure is applied to the QSO sample at higher redshift with a larger volume, where the window effect is milder but still correctly captured.","pith_inferences":["An implication the authors leave implicit is that the linear-algebra formulation should extend to the trispectrum, since the constituent steps are all linear; the practical obstacle is the rapid growth of the window matrix with the number of multipoles and sample points.","The constant integral-constraint assumption is the most direct target for a stress test: if a scale-dependent generalisation of the two-point integral constraint changes the largest-scale $\\tilde{B}_{000}$ bins by more than the cut-sky errors, the window matrix would need to be recomputed with modified series coefficients.","The small but nonzero amplitude offsets seen for the complete LRG mocks suggest that residual systematics beyond the window—possibly shot-noise subtraction—can be absorbed by the offset parameter $\\beta$; a clean test would be to apply the pipeline to mocks with a known shot-noise contribution and check whether $\\beta$ returns to zero.","End-to-end validation could be strengthened by a blind cosmological test: generate cut-sky mocks with several underlying cosmologies, run the windowed model through a likelihood, and check whether the recovered parameters are unbiased on the scales the series was truncated at."],"forward_implications":["A bispectrum likelihood analysis can precompute the window matrix once per survey geometry and then evaluate any unwindowed model at a cost of order $10^{-2}$ seconds per call instead of $10^{-1}$ seconds for the full pipeline.","The diagonal bispectrum monopole and quadrupole of a DESI-scale survey are contaminated by several unwindowed multipoles through mode mixing, so modelling the window is not an optional refinement: neglecting it produces $14\\sigma$ and $5\\sigma$ residuals.","Window convolution in the TripoSH basis differs from the power-spectrum case in that a bispectrum analysis, even restricted to the diagonal $B_{\\ell_1\\ell_2L}(k,k)$, requires the full two-dimensional window function multipoles $Q_{\\ell_1\\ell_2L}(r_1,r_2)$.","The truncation of the window-convolution series must be re-derived for each survey sample, since the reduced formula that works for the LRG SGC sample differs from those for the QSO NGC sample and for complete (non-fibre-assigned) mocks.","The same pipeline, with its public implementation, can be applied to the Euclid survey geometry once the corresponding random catalogue window multipoles are measured."],"supporting_citations":[{"why":"This reference supplies the TripoSH basis, the FFT-based estimators for bispectrum, 3PCF and window function multipoles, the shot-noise subtraction, and the leading-order window-convolution series on which the method builds.","marker":"[33]"},{"why":"This reference extends the TripoSH formalism to configuration-space 3PCF analysis and provides the framework whose truncation the paper tests here in Fourier space.","marker":"[34]"},{"why":"This reference establishes the standard power-spectrum window convolution as configuration-space multiplication, the two-point analogue that the paper generalises to the bispectrum.","marker":"[13]"},{"why":"This reference demonstrates forward-modelling of the survey window for Fourier-space clustering multipoles and motivates the same strategy for three-point statistics.","marker":"[14]"},{"why":"This reference defines the power-spectrum window-matrix linear algebra formulation that the paper extends to the bispectrum.","marker":"[16]"},{"why":"This reference gives the alternative Scoccimarro-basis bispectrum window convolution via Hankel transforms, the computationally heavier approach that motivates the TripoSH formulation.","marker":"[32]"},{"why":"This reference defines the DESI DR1 sample selection, effective volumes, and mock catalogues used for the validation tests.","marker":"[55]"},{"why":"This reference supplies the mock simulation suite whose cubic-box realisations serve as unwindowed proxy models and whose cut-sky catalogues provide the windowed reference measurements.","marker":"[65]"},{"why":"This reference describes the alternate-target-ledger mock catalogues that realistically simulate fibre assignment and are used as the fiducial cut-sky validation samples.","marker":"[69]"}],"fun_headline_variants":["Bispectrum window: now a matrix, not a series","Survey window for bispectrum boils down to one multiply","Bispectrum convolution: linear algebra replaces series","Cut-sky bispectrum: window matrix ends the pain","Bispectrum window effect: one matrix does it all"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the integral-constraint correction—the adjustment required because the survey's mean density is estimated from the same data—is a single constant fixed by the isotropic condition $\\int dr_1 r_1^2 dr_2 r_2^2 \\,\\zeta_{000}(r_1,r_2)=0$, with radial and scale-dependent integral constraints ignored; if the true correction varies with scale over the validated range, the window-convolved bispectrum model would be biased.","fun_headline_variants_meta":{"raw":{"variants":["Bispectrum window: now a matrix, not a series","Survey window for bispectrum boils down to one multiply","Bispectrum convolution: linear algebra replaces series","Cut-sky bispectrum: window matrix ends the pain","Bispectrum window effect: one matrix does it all"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000511,"raw_usage":{"total_tokens":2565,"prompt_tokens":1106,"completion_tokens":1459,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":722,"completion_tokens_details":{"reasoning_tokens":1375}},"tokens_in":722,"tokens_out":1459,"duration_ms":19352,"temperature":1.0,"reasoning_tokens":1375,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:40:42.347738+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the DESI DR1 LRG SGC validation replacing the constant integral-constraint correction with a scale-dependent correction generalised from two-point analyses, and compare the largest-scale diagonal monopole bins of the window-convolved model with the 25-mock cut-sky mean; if the shift exceeds the mock error in those bins, the constant-correction assumption is falsified on the scales used here.","supporting_citations":[],"review_version":1}