pith. sign in

arxiv: 2407.03397 · v1 · submitted 2024-07-03 · 🌌 astro-ph.CO

No evidence for parity violation in BOSS

Alex Krolewski , Simon May , Kendrick Smith , Hans Hopkins This is my paper

Pith reviewed 2026-05-23 22:52 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords parity violationBOSS surveyfour-point correlation functioneight-point correlation functiongalaxy clusteringchi-squared statisticcosmological mocks
0
0 comments X

The pith

Reanalysis shows the apparent parity violation signal in BOSS is explained by bias in the eight-point correlation function.

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

Earlier work reported up to 7 sigma evidence for parity violation in the BOSS galaxy survey by measuring the parity-odd four-point correlation function with a chi-squared statistic. That statistic mixes any true parity-odd signal with a bias that arises when the parity-even eight-point correlation function differs between the data and the mock catalogs used for comparison. The paper builds two new statistics that treat the parity violation amplitude and the eight-point bias as separate parameters and fit them together. When these statistics are applied to BOSS, the parity violation amplitude is consistent with zero to 2.5 sigma while the bias term reaches about 6 sigma. This separation matters because it removes a known source of false positives before using the same approach on larger future surveys.

Core claim

The chi-squared statistic used in prior BOSS analyses is biased whenever the parity-even eight-point correlation function of the data differs from that of the mocks; the new statistics chi-squared-cross and chi-squared-null separate the parity-violation amplitude from this bias term, and their joint fit to BOSS data yields a parity-violation signal between zero and 2.5 sigma while the bias term is detected at roughly 6 sigma.

What carries the argument

The statistics chi-squared-cross and chi-squared-null, which jointly fit the parity-violation amplitude and the eight-point bias term by isolating their distinct contributions to the observed four-point signal.

If this is right

  • The parity-violation amplitude measured in BOSS is consistent with zero once the eight-point bias is removed.
  • The eight-point correlation function of the BOSS data differs from the mocks at approximately 6 sigma.
  • The same pair of statistics can be applied directly to DESI and other forthcoming surveys to test for parity violation without the previous bias.
  • Claims of 7 sigma parity violation are accounted for by the eight-point bias term rather than by a true parity-odd signal.

Where Pith is reading between the lines

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

  • Survey teams preparing mock catalogs for future data releases should match higher-order even correlation functions more closely to reduce this class of bias.
  • If a genuine parity-violation signal appears in a later survey after the bias is removed, it would require an extension of standard cosmological models.
  • The method offers a template for testing other higher-order correlation-function signals that are similarly vulnerable to even-order mismatches between data and mocks.

Load-bearing premise

The only source of bias in the original statistic is the mismatch in the parity-even eight-point correlation function, and the new statistics fully isolate the parity-violation signal from that mismatch.

What would settle it

Running the new statistics on mock catalogs that have been deliberately altered to contain a known parity-violation amplitude plus a controlled eight-point mismatch should recover the injected amplitude without residual bias.

read the original abstract

Recent studies have found evidence for parity violation in the BOSS spectroscopic galaxy survey, with statistical significance as high as $7\sigma$. These analyses assess the significance of the parity-odd four-point correlation function (4PCF) with a statistic called $\chi^2$. This statistic is biased if the parity-even eight-point correlation function (8PCF) of the data differs from the mock catalogs. We construct new statistics $\chi^2_\times$, $\chi^2_{\mathrm{null}}$ that separate the parity violation signal from the 8PCF bias term, allowing them to be jointly constrained. Applying these statistics to BOSS, we find that the parity violation signal ranges from $0$ to $2.5\sigma$ depending on analysis choices, whereas the 8PCF bias term is $\sim 6\sigma$. We conclude that there is no compelling evidence for parity violation in BOSS. Our new statistics can be used to search for parity violation in future surveys, such as DESI, without 8PCF biases.

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.

Referee Report

1 major / 2 minor

Summary. The paper argues that previous claims of parity violation in BOSS (up to 7σ) based on a χ² statistic applied to the parity-odd 4PCF are biased by mismatches in the parity-even 8PCF between data and mocks. It introduces new statistics χ²_× and χ²_null designed to jointly constrain the parity-odd signal and the 8PCF bias term. Application to BOSS data yields a parity signal of 0–2.5σ (depending on choices) while the bias reaches ~6σ, leading to the conclusion of no compelling evidence for parity violation. The new statistics are proposed for use in future surveys like DESI.

Significance. If the separation holds, the result is significant for large-scale structure cosmology: it removes a potential systematic from parity-violation searches that could otherwise be misinterpreted as new physics. The ~6σ detection of the 8PCF bias term itself is a notable finding about mock-data mismatch. The method supplies a practical, jointly-constrained estimator that future analyses can adopt without the original bias, strengthening the robustness of parity tests in DESI and similar surveys.

major comments (1)
  1. [Methods (new statistics construction)] The central claim that χ²_× and χ²_null fully isolate the parity-odd 4PCF signal while absorbing the entire 8PCF mismatch rests on the assumptions that (i) the original χ² is exactly linear in the 8PCF difference, (ii) the parity-odd 4PCF does not couple to any other even N-point functions that differ between data and mocks, and (iii) the covariance is identical. These are load-bearing for the reported 0–2.5σ signal bound; explicit mock tests demonstrating orthogonality to other even-sector contaminants are needed in the section deriving the new statistics.
minor comments (2)
  1. [Abstract / Results] The abstract states the bias reaches ~6σ and the signal ≤2.5σ, but the precise dependence on analysis choices should be quantified with a table or figure in the results section for reproducibility.
  2. [Introduction / Methods] Notation for χ²_× and χ²_null should be defined with an equation immediately upon first use rather than described only in prose.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which help strengthen the robustness of our analysis. We address the major comment point by point below.

read point-by-point responses

  1. Referee: The central claim that χ²_× and χ²_null fully isolate the parity-odd 4PCF signal while absorbing the entire 8PCF mismatch rests on the assumptions that (i) the original χ² is exactly linear in the 8PCF difference, (ii) the parity-odd 4PCF does not couple to any other even N-point functions that differ between data and mocks, and (iii) the covariance is identical. These are load-bearing for the reported 0–2.5σ signal bound; explicit mock tests demonstrating orthogonality to other even-sector contaminants are needed in the section deriving the new statistics.

    Authors: We appreciate the referee's identification of the key assumptions. In the derivation (Section 3), the original χ² is expanded explicitly, showing that the 8PCF mismatch enters linearly as an additive bias term that χ²_× and χ²_null are constructed to isolate and fit jointly; this directly supports (i). The covariance is estimated once from the mocks and applied uniformly, consistent with (iii). For (ii), the 8PCF mismatch is the leading even-sector discrepancy identified in prior work, and the new statistics absorb this term by design. While couplings to other even N-point functions are possible in principle, they are subdominant at the orders considered. To address the referee's request for explicit validation, we will add mock-based tests (injecting controlled mismatches in additional even N-point functions and verifying orthogonality of the recovered parity signal) to the revised manuscript, with results presented in the section deriving the statistics. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained with no reduction to inputs by construction

full rationale

The paper defines new statistics χ²_× and χ²_null explicitly to jointly constrain the parity-odd 4PCF signal and the 8PCF bias term, then applies them to BOSS data and mocks. The reported outcome (bias ~6σ, signal 0-2.5σ) is a direct measurement from the data rather than a fitted parameter or self-citation that forces the result. No equations reduce the central claim to a tautology, and no load-bearing step relies on prior self-citations or ansatzes that smuggle in the conclusion. The derivation is therefore independent of its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard assumptions in cosmological statistics about correlation functions and mock catalogs, with the main domain assumption being the source of the bias in the original statistic.

axioms (1)
  • domain assumption The χ² statistic for the parity-odd 4PCF is biased if the parity-even 8PCF of the data differs from that of the mocks.
    This is the key premise stated in the abstract that motivates the new statistics.

pith-pipeline@v0.9.0 · 5710 in / 1464 out tokens · 38161 ms · 2026-05-23T22:52:52.256821+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

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

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.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Testing parity with composite-field spectra of BOSS and DESI luminous red galaxies

    astro-ph.CO 2026-04 accept novelty 7.0

    No evidence for cosmological parity violation is found in the first kurto-spectrum analysis of BOSS DR12 and DESI DR1 luminous red galaxies.

  2. Parity Violation in Galaxy Shapes: Primordial Non-Gaussianity

    astro-ph.CO 2025-09 conditional novelty 6.0

    The parity-odd intrinsic alignment power spectrum probes the collapsed limit of the parity-odd primordial trispectrum and can tighten constraints on parity-violating PNG when bias parameters are calibrated from N-body...

  3. Theoretical and Observational Bounds on Dynamical Chern-Simons Gravity as an Effective Field Theory

    hep-th 2026-04 unverdicted novelty 5.0

    Dynamical Chern-Simons gravity is bounded by causality and perturbativity to produce only tiny corrections on macroscopic gravitational systems.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages · cited by 3 Pith papers · 15 internal anchors

  1. [1]

    J. Hou, Z. Slepian and R.N. Cahn,Measurement of Parity-Odd Modes in the Large-Scale 4-Point Correlation Function of SDSS BOSS DR12 CMASS and LOWZ Galaxies, arXiv:2206.03625

    work page arXiv

  2. [2]

    Philcox,Probing parity violation with the four-point correlation function of BOSS galaxies, Phys

    O.H.E. Philcox,Probing parity violation with the four-point correlation function of BOSS galaxies, Phys. Rev. D106 (2022) 063501 [arXiv:2206.04227]

    work page arXiv 2022

  3. [3]

    R.N. Cahn, Z. Slepian and J. Hou,Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies, Phys. Rev. Lett.130 (2023) 201002 [2110.12004]

    work page arXiv 2023

  4. [4]

    Hou, R.N

    J. Hou, R.N. Cahn, O.H.E. Philcox and Z. Slepian,Analytic Gaussian covariance matrices for galaxy N-point correlation functions, Phys. Rev. D106 (2022) 043515 [arXiv:2108.01714]

    work page arXiv 2022

  5. [5]

    Cabass, S

    G. Cabass, S. Jazayeri, E. Pajer and D. Stefanyszyn,Parity violation in the scalar trispectrum: no-go theorems and yes-go examples, JHEP 02 (2023) 021 [2210.02907]

    work page arXiv 2023

  6. [6]

    Creque-Sarbinowski, S

    C. Creque-Sarbinowski, S. Alexander, M. Kamionkowski and O. Philcox,Parity-violating trispectrum from Chern-Simons gravity, JCAP 11 (2023) 029 [2303.04815]

    work page arXiv 2023

  7. [7]

    Jazayeri, S

    S. Jazayeri, S. Renaux-Petel, X. Tong, D. Werth and Y. Zhu,Parity violation from emergent nonlocality during inflation, Phys. Rev. D108 (2023) 123523 [2308.11315]

    work page arXiv 2023

  8. [8]

    Fujita, T

    T. Fujita, T. Murata, I. Obata and M. Shiraishi,Parity-violating scalar trispectrum from a rolling axion during inflation, 2310.03551

    work page arXiv

  9. [9]

    Vanzan, M

    E. Vanzan, M. Kamionkowski and S.C. Hotinli,Phenomenology of a vector-field-induced (and possibly parity breaking) compensated isocurvature perturbation, 2311.18121

    work page arXiv

  10. [10]

    Callister, L

    T. Callister, L. Jenks, D. Holz and N. Yunes,A New Probe of Gravitational Parity Violation Through (Non-)Observation of the Stochastic Gravitational-Wave Background, 2312.12532

    work page arXiv

  11. [11]

    Cabass, M.M

    G. Cabass, M.M. Ivanov and O.H.E. Philcox,Colliders and ghosts: Constraining inflation with the parity-odd galaxy four-point function, Phys. Rev. D107 (2023) 023523 [2210.16320]

    work page arXiv 2023

  12. [12]

    Philcox and J

    O.H.E. Philcox and J. Ereza,Could Sample Variance be Responsible for the Parity-Violating Signal Seen in the BOSS Galaxy Survey?, 2401.09523

    work page arXiv

  13. [13]

    Minami and E

    Y. Minami and E. Komatsu,New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data, Phys. Rev. Lett.125 (2020) 221301 [2011.11254]

    work page arXiv 2018

  14. [14]

    Diego-Palazuelos et al.,Cosmic Birefringence from the Planck Data Release 4, Phys

    P. Diego-Palazuelos et al.,Cosmic Birefringence from the Planck Data Release 4, Phys. Rev. Lett. 128 (2022) 091302 [2201.07682]

    work page arXiv 2022

  15. [15]

    Eskilt and E

    J.R. Eskilt and E. Komatsu,Improved constraints on cosmic birefringence from the WMAP and Planck cosmic microwave background polarization data, Phys. Rev. D106 (2022) 063503 [2205.13962]

    work page arXiv 2022

  16. [16]

    Philcox,Do the CMB Temperature Fluctuations Conserve Parity?, Phys

    O.H.E. Philcox,Do the CMB Temperature Fluctuations Conserve Parity?, Phys. Rev. Lett. 131 (2023) 181001 [2303.12106]

    work page arXiv 2023

  17. [17]

    DESI collaboration collaboration, DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, 2404.03002

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  18. [18]

    X. Xu, N. Padmanabhan, D.J. Eisenstein, K.T. Mehta and A.J. Cuesta,A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillations - II. Fitting techniques, MNRAS 427 (2012) 2146 [1202.0091]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  19. [19]

    Computing the Three-Point Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time

    Z. Slepian and D.J. Eisenstein,Computing the three-point correlation function of galaxies in O(N2) time, Mon. Not. Roy. Astron. Soc.454 (2015) 4142 [1506.02040]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  20. [20]

    The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release

    F.-S. Kitaura et al.,The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release, Mon. Not. Roy. Astron. Soc.456 (2016) 4156 [1509.06400]. – 28 –

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  21. [21]

    S.A. Rodríguez-Torres et al.,The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: modelling the clustering and halo occupation distribution of BOSS CMASS galaxies in the Final Data Release, Mon. Not. Roy. Astron. Soc.460 (2016) 1173 [1509.06404]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  22. [22]

    Villaescusa-Navarro, C

    F. Villaescusa-Navarro, C. Hahn, E. Massara, A. Banerjee, A.M. Delgado, D.K. Ramanah et al.,The Quijote Simulations, ApJS 250 (2020) 2 [1909.05273]

    work page arXiv 2020

  23. [23]

    Detection of Baryon Acoustic Oscillation Features in the Large-Scale 3-Point Correlation Function of SDSS BOSS DR12 CMASS Galaxies

    Z. Slepian et al.,Detection of baryon acoustic oscillation features in the large-scale three-point correlation function of SDSS BOSS DR12 CMASS galaxies, Mon. Not. Roy. Astron. Soc.469 (2017) 1738 [1607.06097]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  24. [24]

    S. Alam, M. Ata, S. Bailey, F. Beutler, D. Bizyaev, J.A. Blazek et al.,The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample, MNRAS 470 (2017) 2617 [1607.03155]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  25. [25]

    SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way Galaxy, and Extra-Solar Planetary Systems

    D.J. Eisenstein, D.H. Weinberg, E. Agol, H. Aihara, C. Allende Prieto, S.F. Anderson et al., SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way, and Extra-Solar Planetary Systems, AJ 142 (2011) 72 [1101.1529]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  26. [26]

    The Baryon Oscillation Spectroscopic Survey of SDSS-III

    K.S. Dawson, D.J. Schlegel, C.P. Ahn, S.F. Anderson, É. Aubourg, S. Bailey et al.,The Baryon Oscillation Spectroscopic Survey of SDSS-III, AJ 145 (2013) 10 [1208.0022]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  27. [27]

    The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space

    F. Beutler, H.-J. Seo, S. Saito, C.-H. Chuang, A.J. Cuesta, D.J. Eisenstein et al.,The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: anisotropic galaxy clustering in Fourier space, MNRAS 466 (2017) 2242 [1607.03150]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  28. [28]

    Modelling Baryon Acoustic Oscillations with Perturbation Theory and Stochastic Halo Biasing

    F.S. Kitaura, G. Yepes and F. Prada,Modelling baryon acoustic oscillations with perturbation theory and stochastic halo biasing., MNRAS 439 (2014) L21 [1307.3285]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  29. [29]

    SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 12: galaxy target selection and large scale structure catalogues

    B. Reid et al.,SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 12: galaxy target selection and large scale structure catalogues, Mon. Not. Roy. Astron. Soc.455 (2016) 1553 [arXiv:1509.06529]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  30. [30]

    Power Spectrum Analysis of Three-Dimensional Redshift Surveys

    H.A. Feldman, N. Kaiser and J.A. Peacock,Power-Spectrum Analysis of Three-dimensional Redshift Surveys, ApJ 426 (1994) 23 [astro-ph/9304022]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  31. [31]

    H. Guo, I. Zehavi and Z. Zheng,A New Method to Correct for Fiber Collisions in Galaxy Two-point Statistics, ApJ 756 (2012) 127 [1111.6598]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  32. [32]

    A.J. Ross, F. Beutler, C.-H. Chuang, M. Pellejero-Ibanez, H.-J. Seo, M. Vargas-Magaña et al., The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: observational systematics and baryon acoustic oscillations in the correlation function, MNRAS 464 (2017) 1168 [1607.03145]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  33. [33]

    Philcox, J

    O.H.E. Philcox, J. Hou and Z. Slepian,A First Detection of the Connected 4-Point Correlation Function of Galaxies Using the BOSS CMASS Sample, arXiv e-prints (2021) arXiv:2108.01670 [2108.01670]

    work page arXiv 2021

  34. [34]

    Cahn and Z

    R.N. Cahn and Z. Slepian,Isotropic N-point basis functions and their properties, J. Phys. A56 (2023) 325204 [2010.14418]

    work page arXiv 2023

  35. [35]

    Philcox, Z

    O.H.E. Philcox, Z. Slepian, J. Hou, C. Warner, R.N. Cahn and D.J. Eisenstein,encore: an O(N2 g ) estimator for galaxyN-point correlation functions, Mon. Not. Roy. Astron. Soc.509 (2021) 2457 [2105.08722]

    work page arXiv 2021

  36. [36]

    Landy and A.S

    S.D. Landy and A.S. Szalay,Bias and Variance of Angular Correlation Functions, ApJ 412 (1993) 64

    work page 1993

  37. [37]

    Szapudi and A.S

    I. Szapudi and A.S. Szalay,A New Class of Estimators for the N-Point Correlations, ApJ 494 (1998) L41. – 29 –

    work page 1998

  38. [38]

    Chudaykin, M.M

    A. Chudaykin, M.M. Ivanov, O.H.E. Philcox and M. Simonović,Nonlinear perturbation theory extension of the Boltzmann code CLASS, Phys. Rev. D102 (2020) 063533 [2004.10607]

    work page arXiv 2020

  39. [39]

    analytic

    P. Adari and A. Slosar,Searching for Parity Violation in SDSS DR16 Lyman-α Forest Data, 2405.04660. A Deriving the analytic covariance Recall from section 3.2 that the “analytic” covariance matrix(Cana)ab = Cov(bEa,bEb) is the estimator covariance under the approximations thatδg(x) is a Gaussian field, and the survey geometry is a 3D periodic box with fid...

    work page arXiv

  40. [40]

    Gaussian

    = J(C1, C2). • Statistical interpretation: J(C1, C2) is the symmetrized KL-divergence(KL(ρ1, ρ2) + KL(ρ2, ρ1))/2, where ρi(x) ≡ Det(2πCi)−1/2 exp(−xT C−1 i x/2) is a multivariate Gaus- sian probability density function (PDF) with covarianceCi. Thus, J(C1, C2) quantifies statistical distinguishability of the PDFsρ1, ρ2: they can be distinguished withN sam-...

    work page 1972