{
  "abstract": "We study a real-valued max-plus particle system on a finite periodic lattice. Its three-dimensional fundamental diagram relates the mean flow to two densities: the conserved particle density and a second density defined by a local state function. We prove that the deviation from the diagram tends to zero for arbitrary initial data with all state values in [0,1]. The proof uses two nonnegative local quantities and their evolution relations. For rational initial data with all state values in $[0,1]$, the orbit is eventually periodic, and the fundamental-diagram relation holds exactly on the periodic orbit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00957",
  "author_total": 3,
  "authors": [
    {
      "name": "Daisuke Takahashi"
    },
    {
      "name": "Junta Matsukidaira"
    },
    {
      "name": "Kazuya Okamoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0n9jq9smehxej.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00957",
  "fulltext_url": null,
  "id": "0n9jq9smehxej",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00957",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.CG"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "1703|Cellular Automata and Applications"
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  ],
  "openalex": "W7216257169",
  "pdf_url": "https://arxiv.org/pdf/2610.00957",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0n9jq9smehxej.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00957",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00957"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CG",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Analytical derivation of a three-dimensional fundamental diagram for a real-valued max-plus particle system",
  "title_text": "Analytical derivation of a three-dimensional fundamental diagram for a real-valued max-plus particle system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/0n9jq9smehxej",
  "venue": "arXiv",
  "versions": []
}