{
  "abstract": "For a balanced Boolean function $f$ on the discrete hypercube, we study the $α$-stability $\\mathbb{E}[(T_ρf)^α]$, where $T_ρ$ is the Boolean noise operator and $0<α<1$. Using the asymmetric Hellinger kernel estimates recently established by OpenAI, we prove that dictators minimize the $7/8$-stability in every dimension and at every correlation $0\\leρ\\le1$. At interior correlations they are the only minimizers. As a consequence, dictators minimize the $α$-stability for every $7/8\\leα<1$, maximize the $α$-stability for every $1<α<2$, and maximize the one-sided Shannon entropy stability $\\mathbb{E}[T_ρf\\log T_ρf]$. This resolves a conjecture of Li and Médard and strengthens the Courtade--Kumar conjecture in the balanced setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00868",
  "author_total": 1,
  "authors": [
    {
      "name": "Lei Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnsay7my0g0bf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00868",
  "fulltext_url": null,
  "id": "bnsay7my0g0bf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00868",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00868",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnsay7my0g0bf.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00868",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00868"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Noise Stability on the Hypercube: Order $7/8$",
  "title_text": "Noise Stability on the Hypercube: Order 7/8",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/bnsay7my0g0bf",
  "venue": "arXiv",
  "versions": []
}