Pith. sign in

REVIEW 4 major objections 5 minor 58 references

This paper claims that galaxy orientations across a large patch of sky share a single preferred axis, a signal that standard cosmological simulations do not reproduce.

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 →

T0 review · deepseek-v4-flash

2026-08-03 22:32 UTC pith:YDZTX56D

load-bearing objection DES-only analysis is careful and honest, but the advertised SDSS + N-body mock evidence is missing from the body, and the quoted significance is conditional on perfect PSF de-leakage. the 4 major comments →

arxiv 2511.10005 v3 pith:YDZTX56D submitted 2025-11-13 astro-ph.CO astro-ph.GA

Where Galaxies Point: First Measurement of the Large-Scale Axial Intrinsic Alignment

classification astro-ph.CO astro-ph.GA
keywords intrinsic alignmentsgalaxy orientationslarge-scale structurestatistical isotropytidal fieldposition anglecosmic webdipole
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 paper reports the first detection of a large-scale axial intrinsic alignment (LAIA): over a 5,000-square-degree footprint, galaxies coherently orient their axes toward a common sky direction. Bulge-dominated galaxies' long axes and disk-dominated galaxies' short axes align with this direction, with the disk signal about ten times weaker, matching tidal-torquing expectations. The alignment is detected at 7.9σ for bulges and 3.2σ for disks, and it persists across redshift and spatial subsamples. Standard N-body mocks built on an isotropic, uniform cosmology do not produce the pattern. If the signal is real, it implies a horizon-scale tidal field or a departure from the assumption of statistical isotropy.

Core claim

The central claim is the detection of a large-scale axial intrinsic alignment: a single sky direction, approximately right ascension 306° and declination 52°, toward which bulge-dominated galaxies' semi-major axes and disk-dominated galaxies' semi-minor axes coherently point. The signal is measured at 7.9σ for bulges and 3.2σ for disks against a null built from the survey's own angular distribution and noise properties; when an independent cosmic-web filament catalogue is added, the combined signal reaches 12.6σ. The disk amplitude is nearly an order of magnitude smaller than the bulge amplitude, as expected from the second-order nature of tidal torquing. The authors interpret this as eviden

What carries the argument

The estimator is a weighted average of squared projections of galaxy semi-axes onto a trial direction, E(d) = Σ w_i (d·a_i)² / (1 − (d·n_i)²), computed for bulge major axes or disk minor axes. The squares enforce the headless nature of galaxy axes. The LAIA direction is the maximum of this field, found by gradient ascent on a sphere, and the peak value is converted to a mean rotation angle through a minimal alignment model. Large-scale PSF leakage is subtracted by orthogonalizing the observed map against a template built from PSF position angles at the galaxy positions.

Load-bearing premise

The load-bearing premise is that the linear PSF template subtraction removes all large-scale PSF contamination; if a residual PSF dipole not collinear with the template survives, it would bias the recovered direction, and the spatial block bootstrap, which resamples ~3.7° pixels, cannot capture systematic modes larger than that scale.

What would settle it

Generate mock catalogs with zero intrinsic alignment but with a realistic large-scale PSF pattern that is not perfectly collinear with the template used in the de-leakage; if the estimator recovers a dipole similar in direction and amplitude to the reported LAIA, the signal is a systematic artifact. Alternatively, a future wide-area survey with a completely different PSF (e.g., a space telescope) that fails to reproduce the same ~306°/52° axis would falsify the cosmological interpretation.

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

If this is right

  • If LAIA is real, galaxy position angles become a direct probe of the large-scale tidal tensor and of cosmic statistical isotropy.
  • The morphology-dependent orthogonality (bulge major axes parallel, disk minor axes parallel) provides a built-in systematic check that any survey artifact would have to reproduce with a specific 90° phase relation.
  • The absence of the signal in standard N-body mocks suggests that current simulations omit a component of galaxy-formation physics operating on horizon scales.
  • The reported direction can be cross-correlated with future full-sky shape catalogs and CMB lensing maps to test whether it traces a true gravitational potential.
  • If confirmed by independent surveys, LAIA would motivate extensions of tidal-alignment theory to dipolar modes and anisotropic initial conditions.

Where Pith is reading between the lines

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

  • A residual PSF dipole not captured by the single linear template could plausibly produce a false signal; the cleanest test is to repeat the measurement with an independent survey whose PSF pattern differs completely, or with space-based data.
  • The recovered axis lies near the Galactic plane orientation in the sky; although the authors check against known anomaly axes, an explicit test of correlation with Galactic foregrounds (e.g., stellar contamination) would be a cheap falsifier.
  • The estimator could be applied to radio galaxy position angles, which have independent systematics, to see whether the same axis appears.
  • A predictive extension: if the signal is tidal, its amplitude should scale with galaxy mass and local density; checking that scaling in the existing catalog would discriminate between a primordial dipole and a selection effect.

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

4 major / 5 minor

Summary. The paper proposes a new observable, large-scale axial intrinsic alignment (LAIA), and reports a detection in DES Y3 shape data: bulge-dominated galaxy major axes and disk-dominated galaxy minor axes are claimed to point coherently toward a common celestial direction, with a 7.9σ (BD) and 3.2σ (DD) significance against DES-only null mocks. The authors argue that the morphology-dependent orthogonal pattern and the amplitude hierarchy follow from tidal-alignment and tidal-torquing expectations, interpret the signal as evidence for a horizon-scale tidal field, and present cross-checks from spatial/redshift splits, PSF de-leakage, lensing-leakage calibration, misclassification corrections, and a spatial block bootstrap. The abstract additionally claims a 4.7σ combined DES signal and a 12.6σ combined DES+SDSS filament signal, although the body does not describe the SDSS analysis.

Significance. If the claimed detection is real, it is a striking result: it would establish intrinsic alignments on dipolar angular scales for the first time, provide a new probe of statistical isotropy, and challenge standard ΛCDM expectations. The paper has genuine strengths: the estimator is clearly defined and code is released; null and signal-injected mocks are constructed; PSF template subtraction, BUZZARD-based lensing-leakage calibration, and misclassification corrections are explicitly modeled; and the θ_IA conversion is honestly presented as a units-setting model, not a prediction. The BD/DD orthogonality is a clever diagnostic against a single coherent PSF dipole. However, the headline significance is conditional on an untested class of large-scale systematics, and the abstract contains quantitative claims not supported by the presented analysis. These issues are load-bearing for the paper's central claim rather than cosmetic.

major comments (4)
  1. [Sec. III; App. F, H, I] The quoted 3.2σ (DD) and 7.9σ (BD) significances are p-values against null mocks that do not inject residual large-scale PSF systematics (App. H explicitly states: "Residual large-scale PSF systematics are not injected into the mocks"). The de-leakage step (App. F, Eqs. F1–F3) removes only the component of the observed E map proportional to the PSF template. The spatial block bootstrap (App. I, NSIDE=16, pixels ~3.7°) resamples whole pixels, so a coherent mode with wavelength ≫3.7° is present unchanged in every resample and never contributes to the quoted scatter. The statement in App. I that this procedure is "conservative" is therefore incorrect for the very modes that could mimic a dipole. The paper itself concedes in Sec. IV that "a residual systematic that rotates both samples in phase cannot, however, be completely excluded." The authors should inject large-scale PSF residuals with
  2. [Abstract vs. main text] The abstract reports a 4.7σ DES signal and a combined DES+SDSS filament signal at 12.6σ, with a compatibility test between northern and southern Galactic samples. None of these numbers are derived or even mentioned in Sections I–IV or Appendices A–J; no SDSS filament catalogue, sample definition, estimator, null test, or combination procedure is presented. This is not a minor omission: the multi-survey agreement is a central part of the claimed evidence and is used in the abstract to argue against direct galaxy–filament alignment. The authors must either add the full SDSS analysis or remove these claims from the abstract.
  3. [Table I; Sec. III] The claimed stability across spatial splits is not fully supported by Table I. For BD, the α≤30° and α>30° subsamples peak at α≈229° and α≈355°, which are separated by ~120° and both are far from the full-sample α≈306°; for DD, the δ≤−35° and δ>−35° directions are separated by ~70°. The paper dismisses these as a "right-ascension–only" systematic affecting "three of the fourteen splits," but this is the same class of large-scale, position-dependent systematic that the PSF and bootstrap treatments fail to bound. Because the BD sample has a 26.55% misclassification fraction (App. G), these shifts require a quantitative model or a systematics-injected mock test, not a verbal argument.
  4. [App. G, Eq. (G2)] The misclassification correction assumes that the misclassified population contributes zero to E (Eq. G2, E_biased ≃ (1−κ)E). This is valid only if the misclassified galaxies are exactly perpendicular to the alignment direction, i.e., if the LAIA model's predicted morphology dependence is exactly true. If the contaminants are randomly oriented, their contribution is κ/2 and the correction is wrong. The paper should validate Eq. G2 with mocks in which the contaminated population has random, perpendicular, and parallel alignments, and show that the recovered direction and significance are stable under these alternatives.
minor comments (5)
  1. [App. A; Sec. III] The text switches between DS/BS and DD/BD for the same samples; please unify the notation.
  2. [App. D, Eqs. (D2)–(D10)] The derivation maps E to θ_IA using (d·a)^2, but the estimator (Eq. 1) contains the denominator 1−(d·n)^2. The text should state explicitly that φ_i is the tangent-plane angle so that the denominator cancels; as written the derivation appears inconsistent.
  3. [App. I] There is an incomplete sentence ("for each of realizations") and the number of bootstrap resamples is not stated in the text; Fig. 6 caption says 500. Please specify.
  4. [References] Reference [2] is malformed: it reads "10.21105/astro.2309.08605" in place of a journal/citation format.
  5. [Abstract] The abstract's "4.7σ signal" does not appear anywhere in the body. If it is a combined DES BD+DD significance, define its construction; if not, remove it.

Circularity Check

0 steps flagged

No significant circularity: the DES detection is an empirical estimator against null mocks; the θ_IA conversion is explicitly a units-setting inversion; no load-bearing self-citation or fitted-input-as-prediction is present.

full rationale

The paper's load-bearing derivations are not circular. The detection statistic E_X(d̂) is computed directly from galaxy position angles and compared with null mocks in which position angles are drawn randomly under the observed footprint and per-pixel PA-uncertainty map (App. H). The quoted 7.9σ and 3.2σ significances are therefore empirical p-values against a randomized null, not quantities forced by a fitted parameter. The conversion from the estimator peak to θ_IA (App. D, Eq. D10) is an explicit inversion of the same minimal alignment model used to define the amplitude; the paper does not present it as a prediction, and Sec. III states that 'this mapping serves only to set the units: the detection itself is model-agnostic with respect to direction.' Thus no fitted input is renamed as a prediction. The expected amplitude hierarchy (bulge-dominated larger than disk-dominated) is used as a qualitative consistency check, not fed into the estimator. There is no load-bearing self-citation: the closest author-overlapping reference (Bom et al. 2024) is used for morphological-classification context, not to establish LAIA or to forbid alternatives. No uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in via self-citation. The central caveat in Sec. IV — 'a residual systematic that rotates both samples in phase cannot, however, be completely excluded' — weakens the robustness of the detection against an unmodeled large-scale systematic, but that is a systematics limitation, not circularity: it does not make the measurement equal to its inputs by construction. Within the provided text, no equation reduces the DES detection to a prior fit or to a self-citation chain, so no circular step is established.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 1 invented entities

The paper is a measurement paper: its machinery (mocks, block bootstrap, template subtraction) is standard and mostly self-contained. The physical picture does heavy lifting — the BD-major/DD-minor orthogonality and amplitude hierarchy are read as confirming tidal physics even though no dipolar-amplitude prediction exists, making the hierarchy a consistency check rather than a prediction. The load-bearing ad-hoc elements are the global misclassification rescaling (App. G) and the saturation model converting estimator excess into θ_IA (App. D). No new particles or forces are introduced; a horizon-scale tidal field is invoked as the cause without an independent handle in the body (the SDSS cross-check that would be that handle is abstract-only).

free parameters (6)
  • Lensing-leakage amplitude = 1′ ± 0.2′ (BUZZARD-calibrated), applied as a random 1′ axial rotation per mock realization
    App. E: converts the BUZZARD-measured shift into an error-floor term in every null/signal mock; the value is simulation-dependent and direction is drawn isotropically, inflating quoted uncertainties.
  • PSF de-leakage coefficient η_R = ≈ 0.05
    App. F, Eq. F3: least-squares fit of the observed Ê map against the PSF-template map; assumes a single linear template absorbs all PSF leakage.
  • PA-quality selection thresholds = σ_θ<5°; σ_θ floor 1°; b/a≤0.875 (DD), ≤0.95 (BD); a/b<10; T_GAL/T_PSF≥2; 47.3<SNR≤75.2 with T_GAL/T_PSF≤4.1 (≤15.7 if SN
    App. A/C: hand-chosen rotation-invariant cuts. They do not select a PA direction, but they set the noise floor and sample composition, modulating measured amplitudes and significances, and they differ between BD and DD.
  • θ_IA saturation model = App. D Eq. D5: φ'=0 for φ<θ_IA, else φ−θ_IA; K(φ)=2/π
    The transcendental inversion (Eq. 3/D10) converting estimator excess into the quoted 8′/42′ amplitudes rests entirely on this ansatz; the paper calls the calibration 'naive' (Sec. IV).
  • Misclassification fractions κ = κ_l = 0.27% (DD), κ_e = 26.55% (BD)
    App. G, Eq. G1 from averaged classifier probabilities; enters the global rescaling E_biased ≈ (1−κ)E_true, boosting the BD amplitude by ~36%.
  • Spatial and redshift split boundaries = z=0.4; α=30°; δ=−35°
    Table I: chosen to roughly halve each sample; the z>0.4 splits show the largest amplitude deviations, discussed but not resolved.
axioms (6)
  • domain assumption Tidal-alignment/tidal-torquing paradigm: elliptical major axes follow the local tidal eigenframe; spiral spin (minor-axis) follows quadratic tidal torquing, hence orthogonal and weaker
    Sec. II and Fig. 1; the entire physical interpretation and the BD/DD cross-check rest on this. The paper concedes (Sec. I) 'no consolidated theoretical prediction for the amplitude of a genuinely dipolar IA,' so the hierarchy is an invoked prior, not a derived prediction.
  • domain assumption Thin-disk approximation: for late-type galaxies the projected minor axis traces the 3D spin axis
    Sec. II, citing Padilla & Strauss [43]; required to read DD minor-axis alignment as tidal torquing.
  • domain assumption DES Y3 metacalibration shapes faithfully deconvolve PSF anisotropy for position angles on large angular scales
    App. A/C; the analysis adopts MC shapes with a <0.3% consistency check rather than independent PSF modeling of the full catalog.
  • ad hoc to paper Misclassified galaxies contribute ⟨(d̂·â)²⟩ ≈ 1/2 (on average perpendicular to the dominant population's alignment)
    App. G, Eq. G2: asserted in one sentence ('this is valid because...'); it is load-bearing because BD contamination is 26.55% and there is no error bar on the assertion.
  • domain assumption Null position-angle distribution is uniform on [0,π/2] with Gaussian per-object errors, and LAIA acts as a global rotation with saturation (Eq. D5)
    App. D, Eqs. D1–D8; the uniform/Gaussian choices are standard for a null PA distribution, but the saturation model is paper-specific and sets the θ_IA units.
  • standard math An ideal full-sky weak-lensing shear (spin-2) cannot produce a genuine orientation dipole
    Sec. I: shear stretches alternate in sign and cancels under hemispheric averaging; the authors still calibrate residual footprint-mediated leakage with BUZZARD (App. E), so the axiom is motivational.
invented entities (1)
  • Horizon-scale tidal field ('LAIA' field): a long-wavelength, possibly super-horizon primordial tidal mode frozen into galaxy orientations no independent evidence
    purpose: Explains the coherent BD-major/DD-minor axis across ~5000 deg² as astrophysical rather than instrumental
    Invoked in Secs. III–IV to interpret the signal. The independent falsifiable handle would be the SDSS filament cross-check and the isotropic-ΛCDM mock failures, both advertised in the abstract; neither is present in the body, so the entity currently has no evidence outside the measurement it was introduced to explain.

pith-pipeline@v1.3.0-alltime-deepseek · 17658 in / 26645 out tokens · 285253 ms · 2026-08-03T22:32:39.103194+00:00 · methodology

0 comments
read the original abstract

We report evidence for large-scale axial intrinsic alignment (LAIA): a coherent axis shared by galaxies and cosmic-web filaments. Applying an orientation-field estimator to Dark Energy Survey (DES) Y3 shape data, we identify a preferred axis in galaxy orientations. Ellipticals' semi-major and spirals' semi-minor axes align with it, producing a $4.7\sigma$ signal whose pattern and amplitude hierarchy are consistent with morphology-dependent tidal-alignment and tidal-torquing expectations. Independently, Sloan Digital Sky Survey (SDSS) filament catalogues yield a compatible axis: northern and southern Galactic samples agree within $\simeq1\sigma$, the combined signal reaches $12.6\sigma$, and the axis lies within $\simeq2\sigma$ of the high-redshift galaxy sample direction. Because DES and SDSS footprints overlap marginally, this agreement is unlikely to arise from direct galaxy--filament alignment. It therefore provides a multi-survey, multi-observable test of a large-scale orientation field, stable under redshift and systematics tests. $N$-body mocks based on an isotropic $\Lambda$CDM cosmology with standard intrinsic-alignment prescriptions, including Euclid Flagship 2 and MICECAT v2, do not reproduce the pattern. LAIA provides a new statistical-isotropy probe linking galaxy morphology, cosmic-web structure and large-scale tidal fields.

Figures

Figures reproduced from arXiv: 2511.10005 by Arianna Cortesi, Cl\'ecio R. Bom, Fabricio Ferrari, Paula S. Ferreira, Pedro da Silveira Ferreira, Rafael Oliveira Ramos, Renyue Cen, Valerio Marra.

Figure 1
Figure 1. Figure 1: Left) Spiral galaxies tend to align their angular￾momentum vector L with the tidal field. The projection of L onto the image plane corresponds to the observed minor axis (b) direction. Right) By contrast, elliptical galaxies typically align their major axes (a). Thus, under the same tidal field, spirals and ellipticals become orthogonal on average. II. LARGE-SCALE AXIAL INTRINSIC ALIGNMENT (LAIA) IA refers… view at source ↗
Figure 2
Figure 2. Figure 2: Left) Mollweide projection map in equatorial coordinates of the disk-dominated sample (DD), i.e. late-type (spiral), density and footprint considering HEALPix NSIDE=128 resolution. Right) The same for the bulge-dominated sample (BD), i.e. early-type (elliptical). Footprint differences reflect the different sky coverage of the classification catalogs [32, 33]. cause spin alignments arise from quadratic coup… view at source ↗
Figure 3
Figure 3. Figure 3: Photometric redshift distribution of each sample. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Final results. Highest-density interval (HDI) contours (68.27% and 95.45%) for the LAIA direction dˆIA in equatorial coordinates (α, δ) for the full bulge-dominated (BD; red) and disk-dominated (DD; blue) samples. Markers show the HDI peaks for splits by redshift z, right ascension α, and declination δ. The legend lists the measured θIA (arcminutes, ′ ) for the full samples and each split. Both morphologie… view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of position-angle differences, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mock-derived distributions of the estimator parameters, calibrated to the real-data estimates for BD and DD. Solid [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] 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

58 extracted references · 41 linked inside Pith

  1. [1]

    N. E. Chisari, Astron. Astrophys. Rev.33, 5 (2025), arXiv:2510.15738 [astro-ph.CO]

  2. [2]

    (D5) Assuming a homogeneous distribution of the angular dis- tance of galaxies without LAIA, we find that the proba- bility density isK(ϕ) = 2/π. With LAIA: ⟨ cos ( 2ϕ′ i )⟩ = ∫π/2 0 cos ( 2ϕ′ i ) K(ϕ)dϕ = 2 π [∫θIA 0 1dϕ+ ∫π/2 θIA cos ( 2ϕ−θ IA ) dϕ ] = 2 π [ θIA + 1 2 sin ( 2θIA )] .(D6) 10 Therefore, ⟨(ˆd· ˆai )2⟩ = 1 2 + Ci π [ θIA + 1 2 sin ( 2θIA )]...

  3. [3]

    C. M. Hirata and U. Seljak, Phys. Rev. D70, 063526 (2004), [Erratum: Phys.Rev.D 82, 049901 (2010)], arXiv:astro-ph/0406275

  4. [4]

    Lammanet al.10.21105/astro.2309.08605 (2023), arXiv:2309.08605 [astro-ph.CO]

    C. Lammanet al.10.21105/astro.2309.08605 (2023), arXiv:2309.08605 [astro-ph.CO]

  5. [6]

    Joachimiet al., Space Sci

    B. Joachimiet al., Space Sci. Rev.193, 1 (2015), arXiv:1504.05456 [astro-ph.GA]

  6. [7]

    Blazek, Z

    J. Blazek, Z. Vlah, and U. Seljak, JCAP08, 015, arXiv:1504.02510 [astro-ph.CO]

  7. [8]

    R. G. Crittenden, P. Natarajan, U.-L. Pen, and T. Theuns, Astrophys. J.559, 552 (2001), arXiv:astro- ph/0009052

  8. [9]

    Codis, C

    S. Codis, C. Pichon, and D. Pogosyan, Mon. Not. Roy. Astron. Soc.452, 3369 (2015), arXiv:1504.06073 [astro- ph.CO]

  9. [10]

    N. E. Chisariet al., Mon. Not. Roy. Astron. Soc.454, 2736 (2015), arXiv:1507.07843 [astro-ph.CO]

  10. [11]

    Kirket al., Space Sci

    D. Kirket al., Space Sci. Rev.193, 139 (2015), arXiv:1504.05465 [astro-ph.GA]

  11. [12]

    Kiesslinget al., Space Sci

    A. Kiesslinget al., Space Sci. Rev.193, 67 (2015), [Erra- tum: Space Sci.Rev. 193, 137 (2015)], arXiv:1504.05546 [astro-ph.GA]

  12. [13]

    Samuroff, R

    S. Samuroff, R. Mandelbaum, and J. Blazek, Mon. Not. Roy. Astron. Soc.508, 637 (2021), arXiv:2009.10735 [astro-ph.CO]

  13. [14]

    Kraljic, R

    K. Kraljic, R. Dave, and C. Pichon, Mon. Not. Roy. Astron. Soc.493, 362 (2020), arXiv:1906.01623 [astro- ph.GA]

  14. [15]

    Schmidt, N

    F. Schmidt, N. E. Chisari, and C. Dvorkin, JCAP10, arXiv:1506.02671 [astro-ph.CO]

  15. [16]

    Blazek, R

    J. Blazek, R. Mandelbaum, U. Seljak, and R. Nakajima, JCAP2012(5), 041, arXiv:1204.2264 [astro-ph.CO]

  16. [17]

    Zhan, Chinese Science Bulletin66, 1290 (2021)

    H. Zhan, Chinese Science Bulletin66, 1290 (2021)

  17. [18]

    Kogaiet al., Journal of Cosmology and Astroparticle Physics2018(08), 014

    K. Kogaiet al., Journal of Cosmology and Astroparticle Physics2018(08), 014

  18. [19]

    Scaramellaet al., Astronomy & Astrophysics662, A112 (2022)

    R. Scaramellaet al., Astronomy & Astrophysics662, A112 (2022)

  19. [20]

    LSST Collaboration, Large synoptic survey tele- scope: Dark energy science collaboration (2012), arXiv:1211.0310 [astro-ph.CO]

  20. [21]

    M. L. Brownet al., Mon. Not. Roy. Astron. Soc.333, 501 (2002), arXiv:astro-ph/0009499

  21. [22]

    frozen in

    used data from the Sloan Digital Sky Survey (SDSS) to find IA between pairs of clusters, and concluded that there was indeed IA over1–100 Mpc/hscales, but weaker than theory predicts. Recently, a new approach using the Dark Energy Spectroscopic Instrument (DESI) data em- ploys galaxy multiplets to measure IA with respect to arXiv:2511.10005v2 [astro-ph.CO...

  22. [23]

    Hilbertet al., Mon

    S. Hilbertet al., Mon. Not. Roy. Astron. Soc.468, 790 (2017), arXiv:1606.03216 [astro-ph.CO]

  23. [24]

    Smargonet al., Mon

    A. Smargonet al., Mon. Not. Roy. Astron. Soc.423, 856 (2012), arXiv:1109.6020 [astro-ph.CO]

  24. [25]

    Lammanet al., Mon

    C. Lammanet al., Mon. Not. Roy. Astron. Soc.534, 3540 (2024), arXiv:2408.11056 [astro-ph.CO]

  25. [26]

    E.Abdallaet al.,JHEAp34,49(2022),arXiv:2203.06142 [astro-ph.CO]

  26. [27]

    Di Valentinoet al.(CosmoVerse), Phys

    E. Di Valentinoet al.(CosmoVerse), Phys. Dark Univ. 49, 101965 (2025), arXiv:2504.01669 [astro-ph.CO]

  27. [28]

    Minato, A

    K. Minato, A. Taruya, T. Okumura, and M. Shiraishi, arXiv e-prints (2025), arXiv:2505.19941 [astro-ph.CO]

  28. [29]

    M. O. Calvao, G. I. Gomero, B. Mota, and M. J. Rebou- cas, Class. Quant. Grav.22, 1991 (2005), arXiv:astro- ph/0404536

  29. [30]

    Bartelmann and P

    M. Bartelmann and P. Schneider, Phys. Rept.340, 291 (2001), arXiv:astro-ph/9912508

  30. [31]

    M. A. Troxel and M. Ishak, Physics Reports558, 1 (2015), 1407.6990

  31. [32]

    Blazek, M

    J. Blazek, M. McQuinn, and U. Seljak, JCAP2011(5), 010, arXiv:1101.4017 [astro-ph.CO]

  32. [33]

    Catelan, M

    P. Catelan, M. Kamionkowski, and R. D. Blandford, Mon. Not. Roy. Astron. Soc.320, L7 (2001), arXiv:astro- ph/0005470

  33. [34]

    506, 1927 (2021), arXiv:2012.07858 [astro-ph.GA]

    J.Vega-Ferreroet al.(DES),Mon.Not.Roy.Astron.Soc. 506, 1927 (2021), arXiv:2012.07858 [astro-ph.GA]

  34. [35]

    Chenget al., MNRAS507, 4425 (2021), arXiv:2107.10210 [astro-ph.GA]

    T.-Y. Chenget al., MNRAS507, 4425 (2021), arXiv:2107.10210 [astro-ph.GA]

  35. [36]

    Bridle and L

    S. Bridle and L. King, New Journal of Physics9, 444 (2007)

  36. [37]

    J. A. Blazeket al., Physical Review D100, 103506 (2019)

  37. [38]

    F. H. Peterset al., Astron. Astrophys.699, A201 (2025), arXiv:2412.01790 [astro-ph.CO]

  38. [39]

    Ghosh, R

    B. Ghosh, R. Durrer, and B. M. Schaefer, Mon. Not. Roy. Astron. Soc.505, 2594 (2021), arXiv:2005.04604 [astro- ph.CO]

  39. [40]

    M. C. Fortunaet al., Astronomy & Astrophysics654, A76 (2021)

  40. [41]

    Georgiouet al., Astron

    C. Georgiouet al., Astron. Astrophys.699, A252 (2025), arXiv:2502.09452 [astro-ph.CO]

  41. [42]

    Tempel, R

    E. Tempel, R. S. Stoica, and E. Saar, Monthly Notices of the Royal Astronomical Society428, 1827 (2013)

  42. [43]

    Lee and P

    J. Lee and P. Erdogdu, The Astrophysical Journal671, 1248 (2007)

  43. [44]

    A. M. Delgadoet al., Monthly Notices of the Royal As- tronomical Society523, 5899 (2023), 2304.12346

  44. [45]

    N. D. Padilla and M. A. Strauss, Monthly Notices of the Royal Astronomical Society388, 1321 (2008), 0802.0877

  45. [46]

    Gattiet al.(DES), Mon

    M. Gattiet al.(DES), Mon. Not. Roy. Astron. Soc.504, 4312 (2021), arXiv:2011.03408 [astro-ph.CO]

  46. [47]

    Sevilla-Noarbeet al.(DES), Astrophys

    I. Sevilla-Noarbeet al.(DES), Astrophys. J. Suppl.254, 24 (2021), arXiv:2011.03407 [astro-ph.CO]

  47. [48]

    Ferrari, R

    F. Ferrari, R. R. de Carvalho, and M. Trevisan, Astro- phys. J.814, 55 (2015), arXiv:1509.05430 [astro-ph.GA]

  48. [49]

    K. M. Górskiet al., Astrophys. J.622, 759 (2005), arXiv:astro-ph/0409513

  49. [50]

    Toet al., Astrophys

    C.-H. Toet al., Astrophys. J.961, 59 (2024), arXiv:2303.12104 [astro-ph.CO]

  50. [51]

    Aghanimet al.(Planck), Astron

    N. Aghanimet al.(Planck), Astron. Astrophys.641, A1 (2020), arXiv:1807.06205 [astro-ph.CO]

  51. [52]

    D. J. Schwarz, C. J. Copi, D. Huterer, and G. D. Starkman, Class. Quant. Grav.33, 184001 (2016), arXiv:1510.07929 [astro-ph.CO]

  52. [53]

    Tullyet al., Astrophys

    R. Tullyet al., Astrophys. J.880, 24 (2019), arXiv:1905.08329 [astro-ph.CO]

  53. [54]

    Pedregosaet al., Journal of Machine Learning Re- search12, 2825 (2011)

    F. Pedregosaet al., Journal of Machine Learning Re- search12, 2825 (2011)

  54. [55]

    C. J. Lintottet al., Mon. Not. Roy. Astron. Soc.389, 1179 (2008), arXiv:0804.4483 [astro-ph]

  55. [56]

    C. R. Bomet al., MNRAS528, 4188 (2024), arXiv:2306.08684 [astro-ph.GA]

  56. [57]

    Rodrigues, Journal de Mathématiques Pures et Ap- pliquées , 380 (1840)

    O. Rodrigues, Journal de Mathématiques Pures et Ap- pliquées , 380 (1840)

  57. [58]

    Lammanet al., Mon

    C. Lammanet al., Mon. Not. Roy. Astron. Soc.522, 117 (2023), arXiv:2209.03949 [astro-ph.CO]

  58. [59]

    Lamman, J

    C. Lamman, J. Blazek, and D. J. Eisenstein, arXiv preprint (2025), arXiv:2504.16076 [astro-ph.CO]