{
  "abstract": "We introduce a novel notion of Ollivier-Ricci curvature for causal sets using Lorentzian optimal transport. The construction is motivated by a new Lorentzian asymptotic formula of independent interest, which recovers timelike Ricci curvature, up to higher-order terms, from the transport distance between probability measures on nearby causal diamonds. Passing to the discrete setting, this leads to a mesoscopic notion of Ricci curvature defined along maximal chains and built from probability measures on causal diamonds. We study several variants, including idle and Lin-Lu-Yau type curvatures, prove local-to-global propagation results and timelike Bonnet-Myers theorems, and compute the curvature for a range of explicit causal sets. We design high-density Poisson sprinkling numerical experiments recovering the expected constant-curvature signatures of Minkowski, de Sitter, and anti-de Sitter space. These results provide evidence that the construction captures timelike Ricci curvature from order-theoretic data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.04910",
  "author_total": 3,
  "authors": [
    {
      "name": "Joe Barton"
    },
    {
      "name": "Samuël Borza"
    },
    {
      "name": "Jona Röhrig"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ats8pf1antq0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.04910",
  "fulltext_url": null,
  "id": "ats8pf1antq0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.04910",
  "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",
      "gr-qc"
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.DG"
    ],
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      "math.MG"
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7163545687",
  "pdf_url": "https://arxiv.org/pdf/2606.04910",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ats8pf1antq0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2606.04910",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.04910"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Ollivier-Ricci curvature for causal sets",
  "title_text": "Ollivier-Ricci curvature for causal sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/ats8pf1antq0g",
  "venue": "arXiv",
  "versions": []
}