{
  "abstract": "We prove that a random 3-SAT formula with $n$ variables and $\\lfloor 4.268n\\rfloor$ clauses is unsatisfiable with high probability. The satisfiability threshold has attracted considerable attention: successive upper bounds reached 4.4898 in the work of Díaz, Kirousis, Mitsche, and Pérez-Giménez, while the cavity method predicts a value near 4.267. Our bound brings the rigorous upper estimate close to this prediction. The proof builds on earlier interpolation methods, including the energetic approach of Achlioptas and Menchaca-Méndez. We study the smallest number of clauses that any assignment must violate, comparing the random formula with a simpler system of constraints on individual variables. This comparison reduces the bound to a finite calculation, which we verify using exact rational arithmetic. The proof is formalized in Lean 4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10599",
  "author_total": 1,
  "authors": [
    {
      "name": "Fedor Vorobyev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2p2pfp0qpjs34.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10599",
  "fulltext_url": null,
  "id": "2p2pfp0qpjs34",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10599",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1705|Constraint Satisfaction and Optimization"
    ]
  ],
  "openalex": "W7221102324",
  "pdf_url": "https://arxiv.org/pdf/2610.10599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2p2pfp0qpjs34.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "An upper bound of 4.268 for the random 3-SAT satisfiability threshold",
  "title_text": "An upper bound of 4.268 for the random 3-SAT satisfiability threshold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/2p2pfp0qpjs34",
  "venue": "arXiv",
  "versions": []
}