{
  "abstract": "We quantify the information content of the configuration-space two-, three-, and connected four-point correlation functions of Quijote dark-matter haloes at $z=0$ and fixed number density. We build Fisher forecasts for $\\{Ω_m, Ω_b, h, n_s, σ_8, M_ν\\}$ in real and redshift space from ${\\sim}38{,}000$ GPU-accelerated $N$-point measurements. Treating the statistics as a ladder, $\\mathrm{2PCF} \\rightarrow +\\mathrm{3PCF} \\rightarrow +ζ^{(4)}_{\\mathrm{conn}}$, we report the information gained at each rung. The 3PCF supplies most of the accessible higher-order information: it tightens every parameter, most strongly $σ_8$ and $M_ν$, whose degeneracy it partially breaks, by factors of $1.6$--$6.3$ over the redshift-space $\\{ξ_0,ξ_2\\}$ baseline with per-parameter gains consistent with those of the Fourier-space halo bispectrum on the same simulations. The 3PCF gains persist under conservative, modelling-motivated scale cuts: restricted to the tree-level-validated regime with minimum triangle side $\\ge40\\,h^{-1}{\\rm Mpc}$, it still improves $M_ν$ by $3.9\\times$. The connected 4PCF adds a further $\\sim1.2$--$1.5\\times$, an increment insensitive to whether the quadrupole is included in the baseline but traceable to small-scale configurations with sides $\\lesssim30\\,h^{-1}{\\rm Mpc}$. This rung-to-rung increment is stable against derivative-sample noise and compression regularization, whereas the absolute constraints remain limited by the finite simulation ensembles and are reported as preliminary. The configuration-space ladder thus offers an independent and complementary route to the higher-order information probed by the Fourier-space poly-spectra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.09116",
  "author_total": 3,
  "authors": [
    {
      "name": "Sumi Kim"
    },
    {
      "name": "Cristiano G. Sabiu"
    },
    {
      "name": "Inkyu Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3sxqh0tdet1kr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09116",
  "fulltext_url": null,
  "id": "3sxqh0tdet1kr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09116",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.09116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3sxqh0tdet1kr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2607.09116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09116"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "Climbing the $N$-point Ladder Part I: Information in the Higher-Order Configuration-Space Clustering of Dark Matter Halos",
  "title_text": "Climbing the N-point Ladder Part I: Information in the Higher-Order Configuration-Space Clustering of Dark Matter Halos",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/3sxqh0tdet1kr",
  "venue": "arXiv",
  "versions": []
}