{
  "abstract": "Let the graph algebraic immunity of a Boolean map f:F_2^n -> F_2^m be the least degree of a nonzero reduced Boolean polynomial vanishing on its graph. We prove that the dimension bound, the least d with sum_{j=0}^d binomial(n+m,j)>2^n, is attained for every n,m>=1. Translation invariance gives a rank-density inequality for every subset of the Boolean cube. Rado's classical independent-representative theorem, applied after adjoining dummy vectors, yields a basis using distinct input fibres. Completing those points to a graph proves the result. The proof is self-contained and answers the unrestricted existence question in Oberwolfach Report 31/2007. No balancing, permutation, or additional cryptographic property is imposed. Exact finite certificates accompany the argument. This is an unrefereed preprint using classical matroid tools, with no absolute priority claim.",
  "abstract_shown": true,
  "affiliations": [
    "Mercury Software GmbH"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Alper Ferudun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bagrwqyngcmxv.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587039",
  "fulltext_url": null,
  "id": "bagrwqyngcmxv",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23587039",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23587039/files/OWR-1587-003.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bagrwqyngcmxv.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:51Z",
      "native_id": "23587039",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587039"
    }
  ],
  "subjects": [],
  "title": "The Dimension Bound for Graph Algebraic Immunity Is Attainable",
  "title_text": "The Dimension Bound for Graph Algebraic Immunity Is Attainable",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:51Z",
  "url": "https://research.draconitic.com/paper/bagrwqyngcmxv",
  "venue": "Zenodo",
  "versions": []
}