{
  "abstract": "Every monotone Boolean function on the continuous cube admits a coalition of $O(n/(\\varepsilon\\log n))$ coordinates that can force a fixed output (either zero or one) with probability at least $1-\\varepsilon$. This old conjecture of mine was recently proven by Chattopadhyay and Gurumukhani~\\cite{CG}. This writeup contains a simplification of their proof, generated by AI after suggesting the use of the junta theorem of~\\cite{F98} and the discretization procedure of ~\\cite{F04}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03086",
  "author_total": 1,
  "authors": [
    {
      "name": "Ehud Friedgut"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/attwq9w4j9s15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03086",
  "fulltext_url": null,
  "id": "attwq9w4j9s15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03086",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.03086",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/attwq9w4j9s15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03086",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03086"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Small Influential Coalitions in $[0,1]^n$ via the Junta Theorem",
  "title_text": "Small Influential Coalitions in [0,1]^n via the Junta Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/attwq9w4j9s15",
  "venue": "arXiv",
  "versions": []
}