{
  "abstract": "FINDING: Search results are a mixed bag of Numberphile/Veritasium videos on open problems (Hadwiger-Nelson, odd perfect numbers, Catalan's conjecture, Josephus problem, zero division) plus one unrelated arXiv paper on omnidirectional video quality assessment. No single unified mathematical discovery emerges.\n\nMATH: - Hadwiger-Nelson: chromatic number of the plane χ(ℝ²) — known bounds 5 ≤ χ ≤ 7 (recent lower bound 5 via de Grey's unit-distance graph, 2018). No exact value. - Odd perfect numbers: N odd, σ(N) = 2N. No existence proof; known constraints (e.g., N > 10^1500, at least 101 prime factors). - Catalan's conjecture (proved 2002, Mihăilescu): only consecutive perfect powers are 8 and 9 → x^a − y^b = 1 has unique solution 3² − 2³ = 1. - Josephus problem: recurrence J(n,k) = (J(n−1,k)+k) mod n, J(1,k)=0; closed form for k=2: J(n) = 2(n − 2^⌊log₂ n⌋) + 1. - Zero division: undefined; 0⁰ is indeterminate in limits, convention 1 in combinatorics.\n\nCONNECTION: - Hadwiger-Nelson relates\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/4g4z40ckc58tg.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490896",
  "fulltext_url": null,
  "id": "4g4z40ckc58tg",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23490896",
  "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": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g4z40ckc58tg.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:23Z",
      "native_id": "23490896",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23490896"
    }
  ],
  "subjects": [],
  "title": "Mixed Search Results: No Unified Mathematical Discovery Emerges — E8 Intelligence Research",
  "title_text": "Mixed Search Results: No Unified Mathematical Discovery Emerges — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:23Z",
  "url": "https://research.draconitic.com/paper/4g4z40ckc58tg",
  "venue": "Zenodo",
  "versions": []
}