{
  "abstract": "For even k, we derive a reflection identity for the basic count distributions in the problem of maximizing the probability that all n k-wise independent Bernoulli variables equal one. After separating the distinguished node n, the other support nodes reflect by s -> n-1-s while the Bernoulli parameter changes from p to 1-p. Corresponding basic weights differ by an explicit positive factor. Thus interior feasibility sets, and local changes of optimal support with their multiplicities, are reflected. This gives a proof of the exceptional-point reflection in Conjecture 5.11 of Berend, Ernst, Kontorovich and Kumar. The argument uses Lagrange interpolation and an elementary binomial reweighting identity; it does not require a conjectured ordering or connectedness of the feasibility sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25595",
  "author_total": 1,
  "authors": [
    {
      "name": "Roy Hermann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65tae2f6wp13s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25595",
  "fulltext_url": null,
  "id": "65tae2f6wp13s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25595",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65tae2f6wp13s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Reflection of optimal supports for k-wise independent bits",
  "title_text": "Reflection of optimal supports for k-wise independent bits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/65tae2f6wp13s",
  "venue": "arXiv",
  "versions": []
}