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 →
Where Galaxies Point: First Measurement of the Large-Scale Axial Intrinsic Alignment
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
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.
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
- 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.
Referee Report
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)
- [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
- [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.
- [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.
- [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)
- [App. A; Sec. III] The text switches between DS/BS and DD/BD for the same samples; please unify the notation.
- [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.
- [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.
- [References] Reference [2] is malformed: it reads "10.21105/astro.2309.08605" in place of a journal/citation format.
- [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
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
free parameters (6)
- Lensing-leakage amplitude =
1′ ± 0.2′ (BUZZARD-calibrated), applied as a random 1′ axial rotation per mock realization
- PSF de-leakage coefficient η_R =
≈ 0.05
- 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
- θ_IA saturation model =
App. D Eq. D5: φ'=0 for φ<θ_IA, else φ−θ_IA; K(φ)=2/π
- Misclassification fractions κ =
κ_l = 0.27% (DD), κ_e = 26.55% (BD)
- Spatial and redshift split boundaries =
z=0.4; α=30°; δ=−35°
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
- domain assumption Thin-disk approximation: for late-type galaxies the projected minor axis traces the 3D spin axis
- domain assumption DES Y3 metacalibration shapes faithfully deconvolve PSF anisotropy for position angles on large angular scales
- ad hoc to paper Misclassified galaxies contribute ⟨(d̂·â)²⟩ ≈ 1/2 (on average perpendicular to the dominant population's alignment)
- 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)
- standard math An ideal full-sky weak-lensing shear (spin-2) cannot produce a genuine orientation dipole
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
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
Reference graph
Works this paper leans on
-
[1]
N. E. Chisari, Astron. Astrophys. Rev.33, 5 (2025), arXiv:2510.15738 [astro-ph.CO]
arXiv 2025
-
[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]
C. M. Hirata and U. Seljak, Phys. Rev. D70, 063526 (2004), [Erratum: Phys.Rev.D 82, 049901 (2010)], arXiv:astro-ph/0406275
Pith/arXiv arXiv 2004
-
[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]
Pith/arXiv arXiv 2023
-
[6]
B. Joachimiet al., Space Sci. Rev.193, 1 (2015), arXiv:1504.05456 [astro-ph.GA]
Pith/arXiv arXiv 2015
-
[7]
J. Blazek, Z. Vlah, and U. Seljak, JCAP08, 015, arXiv:1504.02510 [astro-ph.CO]
-
[8]
R. G. Crittenden, P. Natarajan, U.-L. Pen, and T. Theuns, Astrophys. J.559, 552 (2001), arXiv:astro- ph/0009052
arXiv 2001
-
[9]
S. Codis, C. Pichon, and D. Pogosyan, Mon. Not. Roy. Astron. Soc.452, 3369 (2015), arXiv:1504.06073 [astro- ph.CO]
Pith/arXiv arXiv 2015
-
[10]
N. E. Chisariet al., Mon. Not. Roy. Astron. Soc.454, 2736 (2015), arXiv:1507.07843 [astro-ph.CO]
Pith/arXiv arXiv 2015
-
[11]
D. Kirket al., Space Sci. Rev.193, 139 (2015), arXiv:1504.05465 [astro-ph.GA]
Pith/arXiv arXiv 2015
-
[12]
A. Kiesslinget al., Space Sci. Rev.193, 67 (2015), [Erra- tum: Space Sci.Rev. 193, 137 (2015)], arXiv:1504.05546 [astro-ph.GA]
Pith/arXiv arXiv 2015
-
[13]
S. Samuroff, R. Mandelbaum, and J. Blazek, Mon. Not. Roy. Astron. Soc.508, 637 (2021), arXiv:2009.10735 [astro-ph.CO]
Pith/arXiv arXiv 2021
-
[14]
K. Kraljic, R. Dave, and C. Pichon, Mon. Not. Roy. Astron. Soc.493, 362 (2020), arXiv:1906.01623 [astro- ph.GA]
Pith/arXiv arXiv 2020
-
[15]
F. Schmidt, N. E. Chisari, and C. Dvorkin, JCAP10, arXiv:1506.02671 [astro-ph.CO]
-
[16]
J. Blazek, R. Mandelbaum, U. Seljak, and R. Nakajima, JCAP2012(5), 041, arXiv:1204.2264 [astro-ph.CO]
-
[17]
Zhan, Chinese Science Bulletin66, 1290 (2021)
H. Zhan, Chinese Science Bulletin66, 1290 (2021)
2021
-
[18]
Kogaiet al., Journal of Cosmology and Astroparticle Physics2018(08), 014
K. Kogaiet al., Journal of Cosmology and Astroparticle Physics2018(08), 014
-
[19]
Scaramellaet al., Astronomy & Astrophysics662, A112 (2022)
R. Scaramellaet al., Astronomy & Astrophysics662, A112 (2022)
2022
-
[20]
LSST Collaboration, Large synoptic survey tele- scope: Dark energy science collaboration (2012), arXiv:1211.0310 [astro-ph.CO]
Pith/arXiv arXiv 2012
-
[21]
M. L. Brownet al., Mon. Not. Roy. Astron. Soc.333, 501 (2002), arXiv:astro-ph/0009499
Pith/arXiv arXiv 2002
-
[22]
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...
Pith/arXiv arXiv 2025
-
[23]
S. Hilbertet al., Mon. Not. Roy. Astron. Soc.468, 790 (2017), arXiv:1606.03216 [astro-ph.CO]
Pith/arXiv arXiv 2017
-
[24]
A. Smargonet al., Mon. Not. Roy. Astron. Soc.423, 856 (2012), arXiv:1109.6020 [astro-ph.CO]
Pith/arXiv arXiv 2012
-
[25]
C. Lammanet al., Mon. Not. Roy. Astron. Soc.534, 3540 (2024), arXiv:2408.11056 [astro-ph.CO]
Pith/arXiv arXiv 2024
-
[26]
E.Abdallaet al.,JHEAp34,49(2022),arXiv:2203.06142 [astro-ph.CO]
Pith/arXiv arXiv 2022
-
[27]
Di Valentinoet al.(CosmoVerse), Phys
E. Di Valentinoet al.(CosmoVerse), Phys. Dark Univ. 49, 101965 (2025), arXiv:2504.01669 [astro-ph.CO]
Pith/arXiv arXiv 2025
-
[28]
K. Minato, A. Taruya, T. Okumura, and M. Shiraishi, arXiv e-prints (2025), arXiv:2505.19941 [astro-ph.CO]
Pith/arXiv arXiv 2025
-
[29]
M. O. Calvao, G. I. Gomero, B. Mota, and M. J. Rebou- cas, Class. Quant. Grav.22, 1991 (2005), arXiv:astro- ph/0404536
arXiv 1991
-
[30]
M. Bartelmann and P. Schneider, Phys. Rept.340, 291 (2001), arXiv:astro-ph/9912508
Pith/arXiv arXiv 2001
-
[31]
M. A. Troxel and M. Ishak, Physics Reports558, 1 (2015), 1407.6990
Pith/arXiv arXiv 2015
-
[32]
J. Blazek, M. McQuinn, and U. Seljak, JCAP2011(5), 010, arXiv:1101.4017 [astro-ph.CO]
-
[33]
P. Catelan, M. Kamionkowski, and R. D. Blandford, Mon. Not. Roy. Astron. Soc.320, L7 (2001), arXiv:astro- ph/0005470
arXiv 2001
-
[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]
Pith/arXiv arXiv 1927
-
[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]
Pith/arXiv arXiv 2021
-
[36]
Bridle and L
S. Bridle and L. King, New Journal of Physics9, 444 (2007)
2007
-
[37]
J. A. Blazeket al., Physical Review D100, 103506 (2019)
2019
-
[38]
F. H. Peterset al., Astron. Astrophys.699, A201 (2025), arXiv:2412.01790 [astro-ph.CO]
Pith/arXiv arXiv 2025
-
[39]
B. Ghosh, R. Durrer, and B. M. Schaefer, Mon. Not. Roy. Astron. Soc.505, 2594 (2021), arXiv:2005.04604 [astro- ph.CO]
Pith/arXiv arXiv 2021
-
[40]
M. C. Fortunaet al., Astronomy & Astrophysics654, A76 (2021)
2021
-
[41]
C. Georgiouet al., Astron. Astrophys.699, A252 (2025), arXiv:2502.09452 [astro-ph.CO]
Pith/arXiv arXiv 2025
-
[42]
Tempel, R
E. Tempel, R. S. Stoica, and E. Saar, Monthly Notices of the Royal Astronomical Society428, 1827 (2013)
2013
-
[43]
Lee and P
J. Lee and P. Erdogdu, The Astrophysical Journal671, 1248 (2007)
2007
-
[44]
A. M. Delgadoet al., Monthly Notices of the Royal As- tronomical Society523, 5899 (2023), 2304.12346
Pith/arXiv arXiv 2023
-
[45]
N. D. Padilla and M. A. Strauss, Monthly Notices of the Royal Astronomical Society388, 1321 (2008), 0802.0877
Pith/arXiv arXiv 2008
-
[46]
M. Gattiet al.(DES), Mon. Not. Roy. Astron. Soc.504, 4312 (2021), arXiv:2011.03408 [astro-ph.CO]
Pith/arXiv arXiv 2021
-
[47]
Sevilla-Noarbeet al.(DES), Astrophys
I. Sevilla-Noarbeet al.(DES), Astrophys. J. Suppl.254, 24 (2021), arXiv:2011.03407 [astro-ph.CO]
arXiv 2021
-
[48]
F. Ferrari, R. R. de Carvalho, and M. Trevisan, Astro- phys. J.814, 55 (2015), arXiv:1509.05430 [astro-ph.GA]
Pith/arXiv arXiv 2015
-
[49]
K. M. Górskiet al., Astrophys. J.622, 759 (2005), arXiv:astro-ph/0409513
Pith/arXiv arXiv 2005
-
[50]
C.-H. Toet al., Astrophys. J.961, 59 (2024), arXiv:2303.12104 [astro-ph.CO]
Pith/arXiv arXiv 2024
-
[51]
N. Aghanimet al.(Planck), Astron. Astrophys.641, A1 (2020), arXiv:1807.06205 [astro-ph.CO]
Pith/arXiv arXiv 2020
-
[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]
Pith/arXiv arXiv 2016
-
[53]
R. Tullyet al., Astrophys. J.880, 24 (2019), arXiv:1905.08329 [astro-ph.CO]
Pith/arXiv arXiv 2019
-
[54]
Pedregosaet al., Journal of Machine Learning Re- search12, 2825 (2011)
F. Pedregosaet al., Journal of Machine Learning Re- search12, 2825 (2011)
2011
-
[55]
C. J. Lintottet al., Mon. Not. Roy. Astron. Soc.389, 1179 (2008), arXiv:0804.4483 [astro-ph]
Pith/arXiv arXiv 2008
-
[56]
C. R. Bomet al., MNRAS528, 4188 (2024), arXiv:2306.08684 [astro-ph.GA]
Pith/arXiv arXiv 2024
-
[57]
Rodrigues, Journal de Mathématiques Pures et Ap- pliquées , 380 (1840)
O. Rodrigues, Journal de Mathématiques Pures et Ap- pliquées , 380 (1840)
-
[58]
C. Lammanet al., Mon. Not. Roy. Astron. Soc.522, 117 (2023), arXiv:2209.03949 [astro-ph.CO]
Pith/arXiv arXiv 2023
- [59]
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.