{
  "abstract": "FINDING: The search results are a mixed bag of Numberphile videos on unsolved problems (Hadwiger-Nelson, odd perfect numbers, Josephus problem, hat problems, zero) plus one irrelevant arXiv paper on omnidirectional video quality. No single new mathematical discovery is presented; rather, these are pedagogical expositions of known open problems. The only concrete mathematical content is the *existence* of these problems and their known partial results.\n\nMATH: - **Hadwiger-Nelson problem**: The chromatic number of the plane, χ(ℝ²). Known bounds: 5 ≤ χ ≤ 7 (as of 2018; the lower bound was raised from 4 to 5 by de Grey using a 1581-vertex unit-distance graph). No exact value. - **Odd perfect numbers**: If N is odd and perfect, then N = p^α · m² where p ≡ α ≡ 1 (mod 4) (Euler form). No such N known; lower bound N > 10^1500 (current). - **Josephus problem**: For n people, step k, the survivor J(n,k) satisfies J(1,k)=1; J(n,k) = (J(n-1,k)+k-1) mod n + 1. Closed form for k=2: J(n,2) = 2l\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ytsq7eecz6mx.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465123",
  "fulltext_url": null,
  "id": "1ytsq7eecz6mx",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23465123",
  "language": "eng",
  "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": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ytsq7eecz6mx.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:47Z",
      "native_id": "23465123",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23465123"
    }
  ],
  "subjects": [],
  "title": "Numberphile Videos Survey Unsolved Problems Without New Mathematical Discovery — E8 Intelligence Research",
  "title_text": "Numberphile Videos Survey Unsolved Problems Without New Mathematical Discovery — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:47Z",
  "url": "https://research.draconitic.com/paper/1ytsq7eecz6mx",
  "venue": "Zenodo",
  "versions": []
}