{
  "abstract": "A weak form of the Hellinger conjecture of Anantharam, Bogdanov, Chakrabarti, Jayram, and Nair for the binary symmetric channel is proved: dictator functions maximize Hellinger $Φ$-entropy among all Boolean functions of the input and all one-bit statistics of the output of a noisy channel. The technical heart of the matter is an explicit inequality in three real parameters, which is proved using explicit polynomial approximations and computer-assisted positivity checks. The results are also formally verified in Lean 4.",
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  "article_type": null,
  "arxiv": "2609.28534",
  "author_total": 3,
  "authors": [
    {
      "name": "Polona Durcik"
    },
    {
      "name": "Marco Fraccaroli"
    },
    {
      "name": "Joris Roos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/02b2rpb16fkcn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28534",
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  "id": "02b2rpb16fkcn",
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  "landing_url": "https://arxiv.org/abs/2609.28534",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "cs.IT"
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      "arxiv",
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  "pdf_url": "https://arxiv.org/pdf/2609.28534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/02b2rpb16fkcn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.28534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28534"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A weak Hellinger inequality for noisy Boolean channels",
  "title_text": "A weak Hellinger inequality for noisy Boolean channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/02b2rpb16fkcn",
  "venue": "arXiv",
  "versions": []
}