{
  "abstract": "Basin entropy measures uncertainty about a network's long-term behavior. For every critical one-input synchronous Boolean network with $m$ relevant nodes, we show that the permutation structure induced by its feedback loops determines basin entropy, up to a universal error. Although the loops oscillate independently, their relative phases can be offset, producing a deviation from additivity that can grow linearly in $m$. Yet at the ensemble level, a previously derived additive prediction is preserved through the first subleading term, with the discrepancy appearing at order $\\ln m\\ln\\ln m$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08532",
  "author_total": 6,
  "authors": [
    {
      "name": "Ruodan Liu"
    },
    {
      "name": "Ahana Ghosh"
    },
    {
      "name": "Sean Campbell"
    },
    {
      "name": "Venkata Sai Narayana Bavisetty"
    },
    {
      "name": "Matthew Wheeler"
    },
    {
      "name": "Claus Kadelka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hn7r6s60sgeg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08532",
  "fulltext_url": null,
  "id": "8hn7r6s60sgeg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08532",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "nlin.AO"
    ],
    [
      "arxiv",
      "q-bio.MN"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hn7r6s60sgeg.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:04Z",
      "native_id": "2611.08532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08532"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.MN",
      "subfield": "systems-synthetic"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Permutation order governs basin entropy in critical one-input Boolean networks",
  "title_text": "Permutation order governs basin entropy in critical one-input Boolean networks",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:10Z",
  "url": "https://research.draconitic.com/paper/8hn7r6s60sgeg",
  "venue": "arXiv",
  "versions": []
}