Pith. sign in

REVIEW 3 major objections 3 minor 13 references

Augur Fisher forecasts reproduce full posterior contours for LSST 3x2pt analyses, the paper shows, once its numerical settings are stabilized.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Augur is a validated DESC Fisher-forecasting pipeline whose Y1/Y10 3x2pt constraints match nested sampling and external forecast codes when derivative step sizes and redshift sampling are chosen in a stable regime.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Worth a serious referee: the validation is real, but the 500-knot claim conflicts with the 1000-knot caption in Fig. 6. the 3 major comments →

arxiv 2608.03876 v1 pith:BELET4L5 submitted 2026-08-04 astro-ph.CO

Fisher Forecasting for the DESC with $\texttt{Augur}$

Paul Rogozenski , Sankarshana Srinivasan , Javier S\'anchez , Nora Elisa Chisari , Arthur Loureiro , Marc Paterno , Rebekah Polen , Heather Prince
show 10 more authors
Biancamaria Sersante An\v{z}e Slosar Sandro Vitenti Carlos Garc\'ia-Garc\'ia Eric Gawiser Christos Georgiou C. Danielle Leonard Ayan Mitra Jeremy Neveu The LSST Dark Energy Science Collaboration
This is my paper
classification astro-ph.CO
keywords Fisher forecast3x2pt analysisLSSTangular power spectranumerical derivativesnested sampling validationdark energy figure of meritcosmological parameter constraints
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.

The reading

Augur is a public Fisher-forecasting library for the LSST Dark Energy Science Collaboration that computes parameter constraints from the curvature of the log-likelihood, using numerical derivatives of 3x2pt angular power spectra (galaxy clustering, galaxy-galaxy lensing, and cosmic shear). The paper's central claim is that, when operated in a stable numerical configuration — 5-point-stencil derivatives with step sizes around 5% of the prior extent and redshift distributions sampled with about 500 knots — Augur's Fisher contours reproduce the shape, orientation, and area of posterior contours obtained by direct nested sampling, with correlation-matrix differences below 0.05. The same configuration reproduces the Dark Energy Figure of Merit of the DESC Science Requirements Document pipeline to 10% (Year 1) and 2% (Year 10), and agrees near-exactly with an independent Fisher implementation sharing the same likelihood. This matters because survey designers can then test modeling choices cheaply, without running full MCMC or nested sampling, while staying inside the software stack that will be used for the actual data analysis. The paper also documents where the approximation breaks down: sub-percent step sizes produce overly optimistic figures of merit and incorrect degeneracy directions.

Core claim

The paper establishes a reliable operating point for Augur: normalized derivative step size of 5% of the uniform prior range for every parameter, evaluated with the 5-point stencil or numdifftools, and n(z) represented by roughly 500 spline knots. At this point the Fisher matrix approximates the local likelihood well enough that its full correlation matrix sits within 0.05 of the nested-sampling correlation matrix for both Y1 and Y10 setups, its w0-wa degeneracy direction matches sampling, and its Dark Energy Figure of Merit agrees with the DESC SRD pipeline to 10% (Y1) and 2% (Y10). The paper also characterizes unstable regimes: at smaller step sizes, oscillatory features in non-linear matt

What carries the argument

The engine is the Fisher information matrix evaluated from numerical derivatives of the harmonic-space angular power spectrum data vector, F_alpha_beta = (df/dtheta_alpha)^T C^{-1} (df/dtheta_beta), evaluated at the fiducial cosmology under a Gaussian likelihood with parameter-independent covariance. The practical workhorse is the 5-point stencil derivative; the step size is normalized to 5% of each parameter's uniform prior extent, and the redshift distribution is supplied as a spline over roughly 500 knots. These two choices control the trade-off between truncation error and numerical noise that dominates Fisher computations for cosmological two-point functions, and the paper's stability t

Load-bearing premise

The whole validation rests on the log-posterior being locally quadratic at the fiducial cosmology and on the data covariance being independent of the cosmological parameters; if either fails, the Fisher contours will misstate the posterior even in the numerically stable regime.

What would settle it

Re-run the Augur-versus-PolyChord comparison at a shifted fiducial cosmology, say w0 = -1.3 with the other parameters rescaled consistently, and check whether the correlation-matrix difference stays below 0.1 and the DEFOM within 20%. If those criteria fail, the claimed stable configuration is specific to the fiducial used here rather than a general property of the pipeline.

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

If this is right

  • Users can replace expensive MCMC or nested-sampling scans with Augur Fisher forecasts for LSST Y1/Y10 3x2pt setups, provided they adopt the documented stable step sizes and n(z) sampling.
  • Forecasts, likelihoods, and covariances now share one ecosystem, so Fisher studies can be compared directly with the actual analysis pipeline rather than a separate forecasting code.
  • Fisher bias estimates can be trusted for small model mis-specifications, up to about 1 sigma in w0 and 0.5 sigma in wa, providing a fast first-pass diagnostic for systematics.
  • Forecasts produced with sub-percent derivative step sizes or sparse n(z) sampling should be treated as unreliable; the paper's thresholds give a concrete way to check stability before interpreting results.
  • Bin-averaging bandpowers stabilizes derivative behavior and changes the DEFOM through scale-cut effects, so binning choices must be reported and tested alongside any Fisher forecast.

Where Pith is reading between the lines

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

  • The validation is fiducial-specific: nothing in the paper demonstrates that the 5%-step / 500-knot recipe transfers to other fiducial cosmologies or to likelihoods with parameter-dependent covariance, so users of Augur should re-run the stability tests for each new model.
  • A natural next test would be repeating the nested-sampling comparison at a shifted fiducial, such as w0 = -1.3, to map how far the linearity region extends; the paper's own procedures provide the tool for that test.
  • The breakdown of Fisher bias beyond roughly 1 sigma suggests a hybrid workflow: use Augur for fast screening, then invoke nested sampling or MCMC only in parameter regions where the bias checks fail the 10% criterion.
  • The sensitivity of Halofit's oscillatory derivatives to step size points toward automatic differentiation or analytic derivative models as a way to push stable Fisher forecasts to smaller scales than finite differencing allows.
Share X Bluesky LinkedIn Reddit HN

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 / 3 minor

Summary. The paper presents Augur, a Fisher forecasting package for the LSST DESC software ecosystem, built on CCL, TJPCov, and firecrown. The authors perform a validation exercise for 3x2pt harmonic-space analyses with LSST Y1/Y10-like setups, testing the stability of Fisher matrices against derivative step size, n(z) knot sampling, matter power spectrum prescription, and bandpower binning. They compare Augur's Fisher contours, correlation matrices, and figures of merit against a CosmoSIS+firecrown Fisher implementation, the DESC SRD pipeline, and direct PolyChord nested sampling, reporting good agreement within the thresholds defined in Section 4. They also test the Fisher bias formalism with one-dimensional parameter shifts. The central claim is that, when operated in a numerically stable configuration, Augur reliably reproduces both external Fisher pipelines and full posterior sampling.

Significance. If the validation holds, Augur provides a useful, publicly available forecasting component for DESC cosmological analyses. The paper's strongest contributions are its external check against nested sampling (Figures 4 and 5), the systematic mapping of numerical hyperparameter sensitivity (Figures 1-3 and 6-7), and the explicit documentation of stability criteria for Fisher-matrix users. The work is methodologically valuable for the DESC software stack and for future Fisher analyses of LSST data. The code is publicly available, which aids reproducibility. The comparison with CosmoSIS is limited by the shared firecrown likelihood, but the paper is appropriately cautious in describing it as a validation of the Fisher implementation rather than of the physical model.

major comments (3)
  1. [Section 5.2 / Figure 6] There is an internal contradiction in the recommended n(z) knot configuration. Section 5.2 states that 'convergence is achieved when the n(z) distribution is sampled with several hundred knots' and adopts 500 knots, while the caption of Figure 6 states that 'stable solutions are generally found when increasing the number of knots in the n(z) distribution to nearly 1000 evaluations, regardless of the analysis year considered.' Since the headline validations in Figures 4, 5, and 8 use 500 knots, this is load-bearing. Please report the DEFOM and Fisher-matrix differences between 500 and 1000+ knots against the Section 4 thresholds; if 500 is not in the converged regime, rerun the comparisons at a converged knot number and update the recommended configuration.
  2. [Section 5.4 / Figure 8] The claimed Y1 DEFOM agreement with the SRD pipeline is not supported by the numbers in Figure 8. The caption lists DEFOM = 36.95 for the DESC SRD Pipeline and 41.36 for Augur (and CosmoSIS), a relative difference of about 12%, which exceeds the 10% agreement threshold stated in Section 4 and the 'within 10%' claim in Section 5.4 and the Conclusion. Please correct either the numbers or the text, and ensure the reported Y1 agreement is consistent with the stated threshold.
  3. [Section 4, stability criterion] The stability criterion is written as (F^{Δs}_{αβ} - F^{Δs'}_{αβ})/F^{Δs'}_{αβ} ≤ 0.1 without an absolute value. As written, any negative relative difference satisfies the inequality, so it does not enforce 'does not change by more than 10%' in the sense intended. If the implementation uses an absolute value, this should be stated explicitly. This matters because the stable configuration chosen in Section 5.1 is selected using this criterion.
minor comments (3)
  1. [Figure 4] The legend text in the figure says 'CosmoSIS+ firecrown Y1 Nested Sampling', but the caption and text attribute the nested sampling to PolyChord. Since the nested sampling run uses the firecrown likelihood but is not a CosmoSIS Fisher run, the legend label should be changed to 'PolyChord nested sampling' for clarity.
  2. [Figure 6] The caption for Figure 6b contains a stray 'the' at the end: 'for the number of knots evaluated in the n(z) distribution. the'.
  3. [Section 2.1] The paper correctly notes that Eq. (4) assumes a parameter-independent covariance. This is an important limitation, particularly for future analyses using model covariances; it would be helpful to state explicitly in the conclusions that this assumption was not varied in the validation.

Circularity Check

0 steps flagged

No significant circularity: Augur's Fisher forecasts are validated against independent nested sampling and external pipelines; the n(z)-knot caption discrepancy is a stability concern, not circularity.

full rationale

Augur's validation chain is not circular. The Fisher matrix (Sec. 2.1, Eq. 4) is computed by finite-differencing the firecrown/CCL model prediction at the fiducial point; the target comparisons are (i) PolyChord nested sampling of the same likelihood (Figs. 4-5), (ii) CosmoSIS+firecrown using a different derivative implementation, and (iii) the DESC SRD pipeline built on CosmoLike, an independent code. None of these targets is used to define the Fisher matrix or to select the stability criteria: the step size Δs=0.05 and the 500-knot n(z) sampling are chosen by the paper's own local-stability tests (relative Fisher-matrix differences ≤10% between adjacent step sizes; DEFOM plateau in Sec. 5.2), not by fitting to the nested-sampling or SRD contours. The paper explicitly restricts the claim: 'This comparison therefore serves not as a validation of the Fisher methodology itself, but as confirmation that Augur's implementation reproduces full-likelihood results when evaluated within its expected domain of stability.' The Fisher-bias recovery test (Sec. 5.5) is an internal code self-check and is presented as such, not as an independent prediction. Self-citations to DESC tools (CCL, firecrown, TJPCov, SRD) are code dependencies; their outputs are externally checked by the CosmoLike-based SRD pipeline. The only substantive concern is an internal inconsistency: Sec. 5.2 concludes convergence at 'several hundred knots' and adopts 500, while the Fig. 6 caption states 'Stable solutions are generally found when increasing the number of knots in the n(z) distribution to nearly 1000 evaluations.' This is a hyperparameter-convergence issue that could affect numerical reliability of the headline comparisons, but it is not a circular derivation of the results from their inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 7 axioms · 0 invented entities

The paper's headline forecasts rest on standard cosmological modeling inputs taken from the DESC SRD and Planck 2015, plus several numerical and statistical assumptions about Fisher validity. The main hand-tuned quantities are the derivative step size and n(z) knot density, both selected through the paper's stability tests. No new physical entities are introduced; Augur is a software artifact.

free parameters (2)
  • Normalized derivative step size Delta s = 0.05 (5% of the extent of the uniform prior range)
    Chosen by scanning step sizes and requiring that adjacent step sizes differ by <10% in Fisher matrix entries and produce stable FOMs; the headline comparisons use this value.
  • n(z) sampling density = 500 knots
    Selected after checking DEFOM convergence; the headline Fisher forecasts and nested sampling comparisons use this resolution. The paper notes the precise threshold is not universal.
axioms (7)
  • domain assumption The log-posterior is locally quadratic around the fiducial model, so the Fisher matrix encodes the covariance (Cramer-Rao bound saturated).
    The paper explicitly limits claims to the regime where the posterior is close to Gaussian and validates this with PolyChord comparisons. Entered in Section 2.1.
  • domain assumption The data likelihood is Gaussian with a parameter-independent covariance matrix.
    Eq. (3)-(4) in Section 2.1 drop covariance derivatives; the paper notes this is often handled iteratively or by assuming the derivatives are small.
  • domain assumption The Limber approximation is valid for the chosen ell bins (ell >= 20).
    Eq. (12) uses the Limber approximation; the paper cites Lemos et al. 2017 for validity but does not quantify residual errors for this setup.
  • domain assumption Linear galaxy bias per tomographic bin and the NLA intrinsic alignment model are sufficient at the chosen scale cuts.
    The paper states this is a simplification and may not be sufficient at LSST small scales; it matches the DESC SRD for comparison.
  • domain assumption The chosen non-linear matter power spectrum prescriptions (EH+Halofit fiducial, plus CAMB+HMCode2020 and CAMB+Halofit) are accurate.
    These are external fitting functions or halo-model prescriptions; their accuracy is assumed from prior literature.
  • domain assumption The DESC SRD covariance matrix is an adequate fixed covariance for Y1/Y10 3x2pt forecasts.
    The Fisher forecast inherits any inaccuracies in this covariance; the paper does not recompute it with Augur/TJPCov for the headline comparisons.
  • ad hoc to paper The stability thresholds (relative Fisher difference <= 10%, correlation matrix difference <= 0.1, FOM difference <= 20%) are adequate measures of good agreement.
    These are practical choices defined in Section 4, not derived from a formal error budget.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Fisher Forecasting for the DESC with $\texttt{Augur}$." pith.science (2026). https://pith.science/paper/BELET4L5

@misc{pith2026260803876,
  author       = {Pith},
  title        = {Pith review of: Fisher Forecasting for the DESC with $\textttAugur$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BELET4L5}},
  note         = {Machine review of arXiv:2608.03876}
}
Share X Bluesky LinkedIn Reddit HN
abstract

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) has begun its ten-year survey of the entire visible southern hemisphere. To ensure robust cosmological measurements, computationally inexpensive investigations of modeling choices must be made to gauge the performance of proposed cosmological analyses. In this paper, we introduce the $\texttt{Augur}$ tool of the Dark Energy Science Collaboration (DESC), which provides Fisher forecasts for cosmological inference for the LSST using software frameworks designed for DESC science. We test the pipeline by comparing it to forecasts produced by external code and direct sampling of the posterior via nested sampling methods, finding good agreement between all methods. We additionally investigate a range of modeling and hyperparameter choices for a 3$\times$2pt investigation in harmonic space, providing users with diagnostics to obtain reliable forecasts. $\texttt{Augur}$ will be continually updated to be compatible with the other tools in the DESC software ecosystem as additional probes and functionality become available.

Figures

Figures reproduced from arXiv: 2608.03876 by An\v{z}e Slosar, Arthur Loureiro, Ayan Mitra, Biancamaria Sersante, Carlos Garc\'ia-Garc\'ia, C. Danielle Leonard, Christos Georgiou, Eric Gawiser, Heather Prince, Javier S\'anchez, Jeremy Neveu, Marc Paterno, Nora Elisa Chisari, Paul Rogozenski, Rebekah Polen, Sandro Vitenti, Sankarshana Srinivasan, The LSST Dark Energy Science Collaboration.

Figure 1
Figure 1. Figure 1: —: Results of the Fisher step-size stability test outlined in Sections 3 and 4, which assesses the relative difference between the Fisher matrix evaluated at a proposed fiducial step size of 5% of the extent of the uniform prior range and adjacent step sizes. The relative difference in the cosmological parameters portion of the Fisher matrices is no more than 3% or 8% for Y1 and Y10, respectively, confirmi… view at source ↗
Figure 2
Figure 2. Figure 2: —: The Y1 DEFOM (top left) LSSFOM (top right), and condition numbers (bottom left) as a function of normalized step size. To ensure robust predictions through Fisher forecasting, we explore this range of derivative step-sizes and alternative non-linear power spectrum modeling choices. Features in the non-linear power spectrum affect the numerical stability of the calculated FOMs, which are present when con… view at source ↗
Figure 3
Figure 3. Figure 3: —: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: —: Augur validation tests comparing Augur Fisher method and contour widths for Y1 (Figure 4a) and Y10 (Figure 4b) to nested sampling of the likelihood through PolyChord. We show the 68% and 95% confidence intervals of the resulting Fisher forecast and PolyChord posterior samples. We transform the Fisher matrix to obtain the derived parameter Ωm and S8 and compare them to the derived parameters obtained by … view at source ↗
Figure 5
Figure 5. Figure 5: —: Augur validation tests comparing PolyChord and Augur correlation matrices for Y1 (Figure 5a) and Y10 (Figure 5b). These tests validate the calculated derivatives of the likelihood by comparing the inferred parameter correlations to direct sampling of the likelihood. We find differences between the correlation matrices for all parameters exceed no more than 0.05, a factor of two below our proposed criter… view at source ↗
Figure 6
Figure 6. Figure 6: —: DEFOM dependencies on the number of n(z) knots for Y1 (Figure 6a) and Y10 (Figure 6b) for different derivative step-sizes, ∆s. Stable solutions are generally found when increasing the number of knots in the n(z) distribution to nearly 1000 evaluations, regardless of the analysis year considered. words, the stability and minimization of the condition number is not sufficient evidence for a stable configu… view at source ↗
Figure 7
Figure 7. Figure 7: —: Variation in the DEFOM when utilizing Top-Hat Bandpower Filters (Finite Bandpowers) when calculating the modeled C(ℓ)’s for Y1 (left) and Y10 (middle). We also plot the fiducial analysis that does not contain bandpowers (No ℓ-Binning). We utilize the same covariance matrix as in the fiducial analysis, isolating potential effects of ℓ bandpower-averaging in the above figures. An overall lower DEFOM is ca… view at source ↗
Figure 8
Figure 8. Figure 8: —: Augur validation tests comparing CosmoSIS Fisher methods and predictions using the DESC SRD Pipeline for Y1 (Figure 8a) and Y10 (Figure 8b). These tests showcase Augur’s ability to reproduce the results of external cosmological forecasting pipelines and Fisher matrix computations. Each of these Fisher analyses utilizes the 5- point stencil method through their own internal mechanisms. While the CosmoSIS… view at source ↗
Figure 9
Figure 9. Figure 9: —: Fisher Bias recovery tests for the Y1 set-up. We generate model predictions biased by a single parameter relative to the fraction of the inferred contour width as input to the Fisher Bias calculation (x-axis) and assess whether the output Fisher Bias implemented in Augur recovers the input value (y-axis). We show these tests when performing a Fisher Bias on w0 (Figure 9a) and wa (Figure 9b) alongside th… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

13 extracted references · 2 canonical work pages · 1 internal anchor

  1. [1]

    A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, and J. Tonry, Astrophysical Journal 116, 1009 (1998), arXiv:astro-ph/9805201 [astro-ph]....

    Pith/arXiv arXiv 1998

  2. [2]

    Report of the dark energy task force,

    Mather, S. Staggs, and N. B. Suntzeff, “Report of the dark energy task force,” (2006), arXiv:astro-ph/0609591 [astro-ph]. B. Abareshiet al., The Astronomical Journal164, 207 (2022). Y. Mellieret al., Astronomy &; Astrophysics697, A1 (2025). H. Ausselet al., “Euclid quick data release (q1) – data release overview,” (2025), arXiv:2503.15302 [astro-ph.GA]. N...

    Pith/arXiv arXiv 2006

  3. [3]

    Slosar, M

    Sanchez, A. Slosar, M. Sullivan, and M. A. Troxel, arXiv e-prints , arXiv:1809.01669 (2018), arXiv:1809.01669 [astro-ph.CO]. N. E. Chisari, D. Alonso, E. Krause, C. D. Leonard, P. Bull, J. Neveu, A. Villarreal, S. Singh, T. McClintock, J. Ellison, Z. Du, J. Zuntz, A. Mead, S. Joudaki, C. S. Lorenz, T. Tr¨ oster, J. Sanchez, F. Lanusse, M. Ishak, R. Hlozek...

    Pith/arXiv arXiv 2018

  4. [4]

    Fisher Matrix Stability

    Campagne, H. Almoubayyed, T. Eifler, M. Kirby, D. Kirkby, S. Plaszczynski, A. Slosar, M. Vrastil, and E. L. Wagoner, The Astrophysical Journal Supplement Series242, 2 (2019a). N. Bhandari, C. D. Leonard, M. M. Rau, and R. Mandelbaum, arXiv e-prints , arXiv:2101.00298 (2021), arXiv:2101.00298 [astro-ph.CO]. D. Huterer and M. Takada, Astroparticle Physics23...

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  5. [5]

    Kneissl, J

    Kisner, R. Kneissl, J. Knoche, L. Knox, M. Kunz, H. Kurki-Suonio, G. Lagache, A. L¨ ahteenm¨ aki, J.-M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, J. P. Leahy, R. Leonardi, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Linden-Vørnle, M. L´ opez-Caniego, P. M. Lubin, J. F. Mac ´ ıas-P´ erez, G. Maggio, D. Maino, N. Mandolesi, A. ...

    Pith/arXiv arXiv 2016

  6. [6]

    Price, P. J. Tait, M. Tanaka, and S.-Y. Wang, Physical Review D108, 123519 (2023), arXiv:2304.00701 [astro-ph.CO]. A. H. Wright, B. St¨ olzner, M. Asgari, M. Bilicki, B. Giblin, C. Heymans, H. Hildebrandt, H. Hoekstra, B. Joachimi, K. Kuijken, S.-S. Li, R. Reischke, M. von

    Pith/arXiv arXiv 2023

  7. [7]

    Porth, M

    Napolitano, L. Porth, M. Radovich, P. Schneider, T. Tr¨ oster, E. Valentijn, A. Wittje, Z. Yan, and Y.-H. Zhang, Astronomy and Astrophysics703, A158 (2025), arXiv:2503.19441 [astro-ph.CO]. 19 DES Collaboration, T. M. C. Abbott, M. Adamow, M. Aguena, A. Alarcon, S. S. Allam, O. Alves, A. Amon, D. Anbajagane, F. Andrade-Oliveira, S. Avila, D. Bacon, E. J. B...

    Pith/arXiv arXiv 2025

  8. [8]

    Yamamoto, B

    Wu, M. Yamamoto, B. Yanny, B. Yin, G. Zacharegkas, Y. Zhang, and J. Zuntz, arXiv e-prints , arXiv:2601.14559 (2026), arXiv:2601.14559 [astro-ph.CO]. A. Nicola, B. Hadzhiyska, N. Findlay, C. Garc ´ ıa-Garc ´ ıa, D. Alonso, A. Slosar, Z. Guo, N. Kokron, R. Angulo, A. Aviles, J. Blazek, J. Dunkley, B. Jain, M. Pellejero, J. Sullivan, C. W

    arXiv 2026

  9. [9]

    Collaboration, Journal of Cosmology and Astroparticle Physics 2024, 015 (2024), arXiv:2307.03226 [astro-ph.CO]. H. Awan, E. Gawiser, J. Sanchez, I. Sevilla-Noarbe, and t. L. D. E. S. collaboration, Journal of Cosmology and Astroparticle Physics2025, 064 (2025). N. E. Chisari, A. J. Mead, S. Joudaki, P. G. Ferreira, A. Schneider, J. Mohr, T. Tr¨ oster, D. ...

    Pith/arXiv arXiv 2024

  10. [10]

    CAMB: Code for Anisotropies in the Microwave Background,

    Daalen, The Open Journal of Astrophysics2(2019b), 10.21105/astro.1905.06082. D. N. Limber, Astrophysical Journal117, 134 (1953). P. Lemos, A. Challinor, and G. Efstathiou, Journal of Cosmology and Astroparticle Physics2017, 014–014 (2017). I. Smail, R. S. Ellis, and M. J. Fitchett, Monthly Notices of the Royal Astronomical Society270, 245 (1994), arXiv:as...

    Pith/arXiv arXiv 1905

  11. [11]

    Cobra: Optimal factorization of cosmological observables,

    Sciences, St. Petersburg, 1853). T. Bakx, N. E. Chisari, and Z. Vlah, “Cobra: Optimal factorization of cosmological observables,” (2025a), arXiv:2407.04660 [astro-ph.CO]. T. Bakx, H. Rubira, N. E. Chisari, and Z. Vlah, (2025b), arXiv:2508.00611 [astro-ph.CO]. G. D’Amico, A. Refregier, L. Senatore, and P. Zhang, “The cosmological analysis of des 3×2pt data...

    Pith/arXiv arXiv 2025

  12. [12]

    Heavens, Monthly Notices of the Royal Astronomical Society 454, 1958 (2015), https://academic.oup.com/mnras/article- pdf/454/2/1958/9381114/stv2036.pdf. D. J. Bartlett, B. D. Wandelt, M. Zennaro, P. G. Ferreira, and H. Desmond, Astronomy and Astrophysics686, A150 (2024), arXiv:2402.17492 [astro-ph.CO]. G. Aric` o, R. E. Angulo, S. Contreras, L. Ondaro-Mal...

    Pith/arXiv arXiv 1958

  13. [13]

    Archibald, A. H. Ribeiro, F. Pedregosa, P. van Mulbregt, and SciPy 1.0 Contributors, Nature Methods17, 261 (2020). J. D. Hunter, Computing in Science & Engineering9, 90 (2007). A. Lewis, Journal of Cosmology and Astroparticle Physics2025, 025 (2025) 20 This paper was built using the Open Journal of As- trophysics LATEX template. The OJA is a journal which...

    work page 2020

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.