{
  "abstract": "This paper proves the Mézard-Parisi formula for the free energy of random $K$-sat and diluted $p$-spin models with even $p$, completing an approach developed in earlier work of the author and collaborators. The upper bound was established by Franz and Leone. Here the matching lower bound is proved for a general class of diluted models under symmetry and integrability assumptions. The main new contribution is a proof of an approximate form of the Mézard-Parisi reproducibility hypothesis without assuming that the overlap distribution has finite support.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39545",
  "author_total": 1,
  "authors": [
    {
      "name": "Dmitry Panchenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7edh4xsrm1tfc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39545",
  "fulltext_url": null,
  "id": "7edh4xsrm1tfc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39545",
  "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",
      "math.PR"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7edh4xsrm1tfc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Mézard-Parisi formula",
  "title_text": "The Mézard-Parisi formula",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7edh4xsrm1tfc",
  "venue": "arXiv",
  "versions": []
}