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arxiv: 2507.00129 · v1 · submitted 2025-06-30 · 🌌 astro-ph.CO

Lya2pcf: an efficient pipeline to estimate two- and three-point correlation functions of the Lyman-α forest

Josue De-Santiago , Rafael Guti\'errez-Balboa , Gustavo Niz , Alma X. Gonz\'alez-Morales This is my paper

Pith reviewed 2026-05-19 06:52 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Lyman-alpha forestthree-point correlation functiontwo-point correlation functionanisotropic correlationscosmological inferenceSDSS DR16DESI mockGPU acceleration
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The pith

Lya2pcf pipeline extends two-point estimators to measure anisotropic three-point correlations in Lyman-alpha forest data.

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

The paper introduces the Lya2pcf pipeline to compute three-dimensional two-point and three-point correlation functions from Lyman-alpha forest observations in large spectroscopic surveys. It implements standard two-point algorithms including distortion matrices and covariances, then extends the same estimator directly to three-point correlations while using GPU optimization to reduce run times compared to the PICCA code. When applied to SDSS DR16 data and DESI Year-5 mocks, the pipeline produces the first full anisotropic three-point correlation function measurement for all triangle configurations on scales up to 80 Mpc/h. The measured signals reach signal-to-noise ratios above one for many configurations, showing that three-point statistics can be added to cosmological analyses without prohibitive computational cost.

Core claim

Lya2pcf implements the standard algorithms used in current surveys for the two-point correlation function together with its distortion matrix and covariance matrices, and naturally extends the two-point estimator to three-point correlations. GPU optimization yields substantial speed-ups relative to PICCA for both the two-point function and distortion matrix. Application to SDSS DR16 and DESI Y5 mock data demonstrates overall performance gains and delivers the first measurement of the anisotropic three-point correlation function on a large spectroscopic sample for all possible triangles with scales up to 80 Mpc/h, with signal-to-noise above one for many triangle configurations.

What carries the argument

The Lya2pcf pipeline, which directly extends standard two-point correlation estimators to three-point correlations while incorporating GPU acceleration for the distortion matrix and covariance calculations.

If this is right

  • Three-point statistics become computationally viable for inclusion in cosmological inference analyses with existing and upcoming large datasets.
  • The measured signal-to-noise ratios above one for many triangle configurations support adding higher-order correlations to future analyses.
  • Performance gains over PICCA, especially on GPUs, allow processing of the data volumes expected from Stage IV spectroscopic surveys.
  • The first anisotropic three-point measurements on scales up to 80 Mpc/h demonstrate feasibility for constraining small-scale physics at high redshift.

Where Pith is reading between the lines

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

  • Incorporating three-point statistics could provide additional leverage on matter clustering beyond what two-point functions alone supply.
  • The same extension approach might be tested on other high-redshift tracers to broaden the range of available statistics.
  • GPU-based implementations suggest that similar pipelines could scale to even larger volumes from next-generation surveys.

Load-bearing premise

That the standard two-point algorithms can be extended to three-point correlations while preserving accuracy and without introducing unquantified biases from the Lyman-alpha forest properties or survey geometry.

What would settle it

Running Lya2pcf on the same SDSS DR16 dataset and obtaining three-point correlation function values or signal-to-noise ratios that differ substantially from independent calculations performed with another code would indicate that the extension introduces biases.

read the original abstract

Studying the matter distribution in the universe through the Lyman-$\alpha$ forest allows us to constrain small-scale physics in the high-redshift regime. Spectroscopic quasar surveys are generating increasingly large datasets that require efficient algorithms to compute correlation functions. Moreover, cosmological analyses based on Lyman-$\alpha$ forests can significantly benefit from incorporating higher-order statistics alongside traditional two-point correlations. In this work, we present Lya2pcf, a pipeline designed to compute three-dimensional two-point and three-point correlation functions using Lyman-$\alpha$ forest data. The code implements standard algorithms widely used in current spectroscopic surveys for computing the two-point correlation function with its distortion matrix, covariance matrices; and it naturally extends the two-point estimator to three-point correlations. Thanks to GPU optimization, Lya2pcf achieves a substantial reduction in computational time for both the two-point correlation function and its distortion matrix when compared to the widely used PICCA code. We apply Lya2pcf to data from the Sloan Digital Sky Survey (SDSS) sixteenth data release (DR16) and a Dark Energy Spectroscopic Instrument Year-5 (DESI Y5) mock dataset, demonstrating overall performance gains over PICCA, especially on GPUs. We show the first measurement of the anisotropic three-point correlation function on a large spectroscopic sample for all possible triangles with scales up to 80 Mpc/h. The estimator's fast computation and the resulting signal-to-noise ratio -- above one for many triangle configurations -- demonstrate the viability of incorporating three-point statistics into future cosmological inference analyses, particularly with the larger datasets expected from Stage IV spectroscopic surveys.

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

2 major / 2 minor

Summary. The manuscript introduces Lya2pcf, a GPU-optimized pipeline that implements standard algorithms for the three-dimensional two-point correlation function (2PCF) including its distortion matrix and covariance, then extends these to the three-point correlation function (3PCF). The code is applied to SDSS DR16 Lyman-α forest data and DESI Year-5 mocks, with reported speed-ups relative to PICCA; the central result is the first anisotropic 3PCF measurement on a large spectroscopic sample for all triangle configurations with scales up to 80 Mpc/h, where the signal-to-noise ratio exceeds one for many configurations, supporting the viability of three-point statistics for future cosmological analyses.

Significance. If the accuracy of the 3PCF extension is confirmed, the work supplies a practical, scalable tool that could enable inclusion of higher-order statistics in Lyman-α forest analyses. This would be valuable for tightening constraints on small-scale physics at high redshift with Stage-IV datasets, and the reported performance gains plus the demonstration of measurable anisotropic 3PCF signal constitute a concrete step toward that goal.

major comments (2)
  1. [Results section] Results section (3PCF measurement): The manuscript asserts that the direct extension of the 2PCF estimator (with distortion matrix) to 3PCF preserves accuracy, yet provides no quantitative validation—such as recovery tests on mocks with known input 3PCF, comparison of the measured 2PCF against published PICCA results on the same DR16 sample, or an explicit error budget for continuum-fitting and metal-line systematics in the three-point estimator. This is load-bearing for the claim that S/N > 1 for many triangles demonstrates viability.
  2. [Method section] Method section (estimator extension): The text states that the 3PCF extension is 'natural,' but does not specify how the line-of-sight distortion matrix or survey geometry corrections are generalized from the 2PCF pair-counting to the triplet-counting case, nor does it quantify any residual bias introduced by the Lyman-α forest's redshift-space distortions or continuum estimation. A concrete test (e.g., Eq. for the 3PCF estimator or a table of bias values on mocks) is needed to support the central claim.
minor comments (2)
  1. [Abstract] The abstract and introduction would benefit from a brief statement of the precise triangle binning scheme (e.g., side lengths and angles) used for the anisotropic 3PCF measurement.
  2. [Results section] Figure captions for the 3PCF results should explicitly state the number of triangles per configuration and the precise S/N definition employed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comments highlight important areas where additional detail and validation would strengthen the presentation of the 3PCF results. We address each major comment below and have revised the manuscript to incorporate the requested quantitative tests, explicit estimator equations, and systematic error discussion.

read point-by-point responses

  1. Referee: [Results section] Results section (3PCF measurement): The manuscript asserts that the direct extension of the 2PCF estimator (with distortion matrix) to 3PCF preserves accuracy, yet provides no quantitative validation—such as recovery tests on mocks with known input 3PCF, comparison of the measured 2PCF against published PICCA results on the same DR16 sample, or an explicit error budget for continuum-fitting and metal-line systematics in the three-point estimator. This is load-bearing for the claim that S/N > 1 for many triangles demonstrates viability.

    Authors: We agree that explicit validation is necessary to support the accuracy claim. The original manuscript emphasized the pipeline implementation and the first large-sample measurement, but did not include dedicated recovery tests for the 3PCF. In the revised version we have added a new subsection with recovery tests on the DESI Y5 mocks, demonstrating that the input 3PCF is recovered within statistical errors for the triangle configurations considered. We have also included a direct comparison of our 2PCF measurements on the SDSS DR16 sample against published PICCA results on the same data, showing consistency at the percent level. Finally, we have expanded the discussion of systematics to provide an error budget for continuum-fitting and metal-line contamination in the 3PCF estimator, derived from the same mock suite. revision: yes

  2. Referee: [Method section] Method section (estimator extension): The text states that the 3PCF extension is 'natural,' but does not specify how the line-of-sight distortion matrix or survey geometry corrections are generalized from the 2PCF pair-counting to the triplet-counting case, nor does it quantify any residual bias introduced by the Lyman-α forest's redshift-space distortions or continuum estimation. A concrete test (e.g., Eq. for the 3PCF estimator or a table of bias values on mocks) is needed to support the central claim.

    Authors: We acknowledge that the manuscript would benefit from a more explicit description of the generalization. The 3PCF estimator extends the 2PCF by replacing pair counts with triplet counts while applying the distortion matrix to each of the three line-of-sight pairs within a given triangle; survey geometry corrections are implemented via random triplet catalogs generated consistently with the data. We have now inserted the full mathematical expression for the distortion-matrix-corrected 3PCF estimator as a new equation in the Methods section. In addition, we have added a table reporting the residual bias measured on mocks due to redshift-space distortions and continuum estimation; these biases remain subdominant to the statistical uncertainties for the scales up to 80 Mpc/h where S/N > 1 is reported. revision: yes

Circularity Check

0 steps flagged

No significant circularity in pipeline implementation

full rationale

The paper describes a computational pipeline (Lya2pcf) that implements standard 2PCF algorithms with distortion matrix and covariance, then extends them to 3PCF estimation. The central results are performance benchmarks against PICCA on SDSS DR16 and DESI Y5 mocks, plus the first reported anisotropic 3PCF measurement on large samples with S/N >1 for many triangles. No derivations, first-principles predictions, or fitted parameters are presented that reduce by construction to quantities derived from the same dataset. The extension is described as 'natural' without load-bearing self-citations or ansatzes that presuppose the target measurement. The work is self-contained as an implementation and demonstration study against external benchmarks and mocks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a software pipeline paper that implements and optimizes existing standard algorithms for correlation function estimation. No new physical free parameters, axioms, or invented entities are introduced in the abstract description.

pith-pipeline@v0.9.0 · 5855 in / 1277 out tokens · 88811 ms · 2026-05-19T06:52:49.524340+00:00 · methodology

discussion (0)

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Reference graph

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