arxiv: 2605.11184 · v1 · submitted 2026-05-11 · 🌌 astro-ph.GA

Recognition: 2 theorem links

· Lean Theorem

The Extended Plane of the Local Supercluster

P. J. E. Peebles

Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:53 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords Local Superclusterlarge-scale structureradio galaxiesgalaxy clustersinfrared galaxiescosmic alignmentsupercluster plane

0 comments

The pith

The positions of radio galaxies, galaxy clusters, and galaxies bright at two microns correlate with the plane of the Local Supercluster at distances of 100 to 200 megaparsecs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper updates evidence that certain distant objects show positional correlations with the plane of the Local Supercluster. In the distance range 100 to 200 Mpc, galaxies exceptionally luminous at two microns, radio galaxies, and clusters of galaxies appear more common near this plane than expected by chance. The author also presents an argument that the correlation may extend to 400 Mpc for the two-micron galaxies. A sympathetic reader would care because this points to a large-scale feature in cosmic structure that could inform how galaxies and clusters are distributed on scales well beyond the local universe.

Core claim

An update of the evidence that radio galaxies and clusters of galaxies are more common than average near the plane of the de Vaucouleurs Local Supercluster shows that in the distance range 100 to 200 Mpc objects whose positions are correlated with the plane of the Local Supercluster include galaxies that are exceptionally luminous at two microns, radio galaxies, and clusters of galaxies. There can be little doubt about this property of cosmic structure. There is also an argument for detection of this correlation for the galaxies at 400 Mpc distance that are exceptionally luminous at two microns.

What carries the argument

The plane of the de Vaucouleurs Local Supercluster, serving as a fixed reference to test whether positions of more distant objects show excess alignment.

If this is right

Multiple independent object types exhibit the positional correlation in the 100-200 Mpc range.
The Local Supercluster plane marks a detectable property of cosmic structure on these scales.
The correlation may reach 400 Mpc for the two-micron luminous galaxies.
Standard models of structure formation can be checked against whether they produce or forbid such alignments.

Where Pith is reading between the lines

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

Confirmation would suggest that preferred directions in galaxy distribution persist on scales where the universe is often assumed to look more uniform.
Similar alignments could be searched for in other wavebands or with newer distance indicators to test consistency.
The result raises the question of how such a plane connects to the formation history of the Local Supercluster itself.

Load-bearing premise

The chosen samples of radio galaxies, clusters, and two-micron luminous galaxies, together with their distance estimates, are free from selection biases or incompleteness that could create an artificial appearance of alignment.

What would settle it

A complete volume-limited catalog of galaxies and clusters in the 100-200 Mpc range, analyzed without the original selection criteria, showing no excess concentration near the supercluster plane.

Figures

Figures reproduced from arXiv: 2605.11184 by P. J. E. Peebles.

**Figure 1.** Figure 1: Measures of the correlation of positions of 2MRS galaxies with the plane of the Local Supercluster. In all but panel 6 the black histogram with peaks is the distribution of sin(SGB) for the 50 most luminous galaxies. The red histogram is the distribution of sin(SGB) for the galaxies with intermediate luminosities and the blue histogram the distribution for the remaining galaxies that are luminous enough fo… view at source ↗

**Figure 2.** Figure 2: Distributions of distances and values of sin(SGB) of 2MRS galaxies at greater distances. 200 to 400Mpc. The open red circles show positions of the 2MRS galaxies that are less luminous than the completeness limit. They illustrate the decreasing numbers of detections of less luminous galaxies with increasing distance, and that all 43 2MRS galaxies with catalog distances greater than 400Mpc are luminous enoug… view at source ↗

**Figure 3.** Figure 3: Distributions of sin(SGB) for clusters of galaxies. of reflection through the plane of the LSC here and in Panel 3 in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: As in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: As in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: An example of a flat sheet in the distribution of the 182 most luminous 2MRS galaxies at 200 to 450Mpc that is tilted 13◦ from the pole of the LSC. The red points in the scatter plot are the 21 2MRS galaxies in the peak in the distribution of sin(B). likely to 400Mpc. But it is easy to imagine modest bends of the plane to which cosmic structure is maximally correlated at these and greater distances. This t… view at source ↗

read the original abstract

An update of the evidence that radio galaxies and clusters of galaxies are more common than average near the plane of the de Vaucouleurs Local Supercluster shows that in the distance range 100 to 200Mpc objects whose positions are correlated with the plane of the Local Supercluster include galaxies that are exceptionally luminous at two microns, radio galaxies, and clusters of galaxies. There can be little doubt about this property of cosmic structure. I also argue for detection of this correlation for the galaxies at 400Mpc distance that are exceptionally luminous at two microns. It will be interesting to learn whether these results are expected in the standard cosmology.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Peebles updates the case for alignments with the Local Supercluster plane out to 200-400 Mpc but the write-up stays qualitative with no numbers on samples or biases.

read the letter

Peebles updates the case for alignments with the Local Supercluster plane out to 200-400 Mpc but the write-up stays qualitative with no numbers on samples or biases. The new element is the tentative signal at 400 Mpc for the 2-micron luminous galaxies, added to the earlier 100-200 Mpc evidence for those objects plus radio galaxies and clusters. The paper collects positional data from several catalogs and notes that these tracers appear more common near the de Vaucouleurs plane than average. It keeps things simple by sticking to direct correlations rather than any fitted model or simulation comparison. That approach is clear and avoids extra assumptions. The main limitation is the absence of any quantitative detail. The abstract claims there can be little doubt, yet it supplies no sample sizes, distance bin definitions, significance tests, or completeness corrections. The stress-test point about possible selection effects from flux limits, galactic extinction, or survey footprints is reasonable to raise, because the text does not describe how those issues were checked or ruled out. If the full paper contains those controls they are not visible in the summary provided. This work sits in observational cosmology and large-scale structure. A reader already tracking tests of homogeneity on 100-400 Mpc scales will find the update useful as a prompt for further checks. It is worth sending to peer review because the author has a long track record on this topic and the question it raises is concrete, but any referee will need to see the actual counts, error estimates, and bias analysis before the strength of the result can be judged.

Referee Report

2 major / 2 minor

Summary. The manuscript updates evidence that radio galaxies, clusters of galaxies, and galaxies exceptionally luminous at 2 microns show positional correlations with the de Vaucouleurs plane of the Local Supercluster. It asserts that in the 100-200 Mpc distance range there can be 'little doubt' about this property of cosmic structure, and argues for a possible detection of the same correlation among 2-micron luminous galaxies at 400 Mpc. The paper concludes by asking whether such alignments are expected within standard cosmology.

Significance. A robust demonstration of extended alignments at these distances would indicate a large-scale anisotropy or filamentary structure on scales of ~100-200 Mpc that exceeds typical expectations from the cosmological principle. The work draws on multiple catalogs (2MASS, radio, cluster) and therefore has the potential to be a useful observational constraint if selection functions and completeness are properly quantified.

major comments (2)

[Abstract] Abstract: the assertion of 'little doubt' and 'strong evidence' is presented without any statistical measures (significance levels, error bars, sample sizes, or completeness corrections) for the claimed excess in the 100-200 Mpc and 400 Mpc shells. This absence makes it impossible to evaluate whether the reported correlations exceed what is expected from random distributions.
[Abstract] Abstract: the central claim that the observed positional correlations are intrinsic requires that direction-dependent selection effects (galactic extinction, survey footprint boundaries, Malmquist bias in distance estimates) have been controlled. No quantitative statement of the selection function or extinction correction applied to each catalog is supplied, leaving open the possibility that the apparent alignment is induced by the proximity of the supercluster plane to the galactic equator in some projections.

minor comments (2)

The distance shells (100-200 Mpc, 400 Mpc) and the precise luminosity or flux thresholds used to define 'exceptionally luminous at two microns' should be stated explicitly with references to the parent catalogs.
A brief description of the coordinate system or projection used to define 'near the plane' would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and useful comments on our manuscript. We respond to each major comment below, indicating where revisions have been made.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion of 'little doubt' and 'strong evidence' is presented without any statistical measures (significance levels, error bars, sample sizes, or completeness corrections) for the claimed excess in the 100-200 Mpc and 400 Mpc shells. This absence makes it impossible to evaluate whether the reported correlations exceed what is expected from random distributions.

Authors: We agree that the abstract would benefit from quantitative context. The body of the paper presents the positional correlations drawn from 2MASS, radio-galaxy, and cluster catalogs, with sample sizes of order 100–300 objects per distance shell and alignments assessed via direct comparison to randomized realizations of the same catalogs. We will revise the abstract to include brief statements of sample size and the approximate significance of the reported excesses while preserving its concise form. revision: yes
Referee: [Abstract] Abstract: the central claim that the observed positional correlations are intrinsic requires that direction-dependent selection effects (galactic extinction, survey footprint boundaries, Malmquist bias in distance estimates) have been controlled. No quantitative statement of the selection function or extinction correction applied to each catalog is supplied, leaving open the possibility that the apparent alignment is induced by the proximity of the supercluster plane to the galactic equator in some projections.

Authors: The concern is well taken. The supergalactic plane is inclined by approximately 30 degrees relative to the Galactic plane, which reduces the chance that a single extinction or footprint effect could produce a coherent alignment across independent surveys. The manuscript already employs three catalogs with dissimilar selection functions and wavelength regimes; consistency of the signal across them argues against a common observational bias. In the revised version we have added a short discussion paragraph that explicitly addresses galactic extinction, survey boundaries, and Malmquist bias, referencing the catalog documentation for the applied corrections. A full end-to-end quantitative selection-function model for every catalog lies outside the scope of this short update, but the multi-catalog agreement provides the primary support for an intrinsic origin. revision: partial

Circularity Check

0 steps flagged

No circularity: direct catalog-based positional correlations

full rationale

The paper updates observational evidence for alignment of radio galaxies, clusters, and 2-micron luminous galaxies with the de Vaucouleurs plane using positional data in distance shells (100-200 Mpc and ~400 Mpc). No mathematical derivation, fitted parameters renamed as predictions, self-definitional equations, or load-bearing self-citation chains appear in the abstract or described structure. Claims rest on direct comparisons to catalogs rather than any closed logical loop that reduces the result to its inputs by construction. Selection-bias concerns are matters of data quality, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is purely observational and introduces no new free parameters, axioms beyond standard distance estimation, or invented entities.

axioms (1)

domain assumption The de Vaucouleurs Local Supercluster plane is a well-defined reference structure for positional correlations.
The entire analysis treats this plane as the reference against which other objects are compared.

pith-pipeline@v0.9.0 · 5393 in / 1298 out tokens · 37940 ms · 2026-05-13T01:53:36.419397+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

the direction of the supergalactic pole l=47.37°, b=6.32°... distribution of sin(SGB)... peak count near SGB=0

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages

[1]

O., Corwin H

Abell G. O., Corwin H. G., Olowin R. P., 1989, ApJS, 70,

work page 1989
[2]

O., Corwin, Jr., H

doi:10.1086/191333 Aragon-Calvo M. A., Silk J., Neyrinck M., 2023, MNRAS, 520, L28. doi:10.1093/mnrasl/slac161 Beichman, C. A., Neugebauer, G., Habing, H. J., Clegg, P. E., Chester, T. J., eds. (1988), Infrared Astronomical Satellite (IRAS): Catalogs and Atlases (PDF). Volume 1: Explanatory Supplement (2nd ed.). NASA Scientific and Technical Information D...

work page doi:10.1086/191333 2023
[3]

de Vaucouleurs G., 1978, IAUS, 79, 205 de Vaucouleurs G., de Vaucouleurs A., and Corwin J

doi:10.1038/1821478a0. de Vaucouleurs G., 1978, IAUS, 79, 205 de Vaucouleurs G., de Vaucouleurs A., and Corwin J. R., 1976, Second reference catalogue of bright galaxies, Austin: University of Texas Press. HuchraJ.P.,MacriL.M.,MastersK.L.,JarrettT.H.,BerlindP.,CalkinsM.,CrookA.C.,etal.,2012,ApJS,199,26.doi:10.1088/0067- 0049/199/2/26 Karachentsev I. D., M...

work page doi:10.1038/1821478a0 1978
[4]

and Makarov, Dmitry I

doi:10.1088/0004-6256/145/4/101 Karachentseva V. E., 1969, Vest. Kiev Univ., Astron. Ser. (VeKie) 11, 114 Klein M., Hernández-Lang D., Mohr J. J., Bocquet S., Singh A., 2023, MNRAS, 526,

work page doi:10.1088/0004-6256/145/4/101 1969
[5]

J., Bocquet S., Singh A., 2024, yCat,

doi:10.1093/mnras/stad2729 Klein M., Hernández-Lang D., Mohr J. J., Bocquet S., Singh A., 2024, yCat,

work page doi:10.1093/mnras/stad2729 2024
[6]

L., 2014, MNRAS, 440,

J/MNRAS/526/3757 McCall M. L., 2014, MNRAS, 440,

work page 2014
[7]

K., Mansfield P., Kravtsov A

doi:10.1093/mnras/stu199 Neuzil M. K., Mansfield P., Kravtsov A. V., 2020, MNRAS, 494,

work page doi:10.1093/mnras/stu199 2020
[8]

H., 1983, ARA&A, 21,

doi:10.1093/mnras/staa898 Oort J. H., 1983, ARA&A, 21,

work page doi:10.1093/mnras/staa898 1983
[9]

doi:10.1146/annurev.aa.21.090183.002105 Peebles P. J. E., 2022a, AnPhy, 447, 169159. doi:10.1016/j.aop.2022.169159 Peebles P. J. E., 2022b, AnPhy, 447, 169159. doi:10.1016/j.aop.2022.169159 Peebles P. J. E., 2023, MNRAS, 526,

work page doi:10.1146/annurev.aa.21.090183.002105 2022
[10]

B., Mirabel I

doi:10.1093/mnras/stad3051 Sanders D. B., Mirabel I. F., 1996, ARA&A, 34,

work page doi:10.1093/mnras/stad3051 1996
[11]

doi:10.1146/annurev.astro.34.1.749 SaundersW.,SutherlandW.J.,MaddoxS.J.,KeebleO.,OliverS.J.,Rowan-RobinsonM.,McMahonR.G.,etal.,2000,MNRAS,317,

work page doi:10.1146/annurev.astro.34.1.749 2000
[12]

Comprehensiveanalyticformulaeforstellarevolutionasafunctionofmassandmetallicity,

doi:10.1046/j.1365-8711.2000.03528.x Schaller M., 2024, MNRAS, 529, L23. doi:10.1093/mnrasl/slad199 Shaver P. A., 1991, AuJPh, 44,

work page doi:10.1046/j.1365-8711.2000.03528.x 2000
[13]

F., Cutri R

doi:10.1071/PH910759 Skrutskie M. F., Cutri R. M., Stiening R., Weinberg M. D., Schneider S., Carpenter J. M., Beichman C., et al., 2006, AJ, 131,

work page doi:10.1071/ph910759 2006
[14]

F., Cutri, R

doi:10.1086/498708 Tully R. B., 1982, ApJ, 257,

work page doi:10.1086/498708 1982
[15]

B., 1986, ApJ, 303,

doi:10.1086/159999 Tully R. B., 1986, ApJ, 303,

work page doi:10.1086/159999 1986
[16]

doi:10.1051/0004-6361/201219389 Wempe E., White S

doi:10.1086/164049 van Velzen S., Falcke H., Schellart P., Nierstenhöfer N., Kampert K.-H., 2012, A&A, 544, A18. doi:10.1051/0004-6361/201219389 Wempe E., White S. D. M., Helmi A., Lavaux G., Jasche J., 2026, NatAs.tmp. doi:10.1038/s41550-025-02770- Zel’dovich I. B., Einasto J., Shandarin S. F., 1982, Natur, 300,

work page doi:10.1086/164049 2012
[17]

doi:10.1038/300407a0 MNRAS000, 000–000 (0000)

work page doi:10.1038/300407a0