{
  "abstract": "FINDING: Twin prime conjecture remains unproven; recent progress (Maynard, Zhang) establishes bounded gaps, but no proof exists. The arXiv paper claims a sieve-based proof but is not peer-reviewed/validated.\n\nMATH: - Twin primes: \\(p, p+2\\) both prime. - Zhang (2013): \\(\\liminf_{n\\to\\infty} (p_{n+1}-p_n) < 7\\times10^7\\). - Maynard (2013): \\(\\liminf_{n\\to\\infty} (p_{n+1}-p_n) \\le 246\\) (unconditionally, under Elliott–Halberstam: 12). - No exact constant, ratio, or closed form emerges from these results. - The arXiv paper (1708.07884v1) claims: for \\(n\\) increasing by 1, at least 3 new twin prime pairs appear below \\((6n+5)^2\\) — this is a *claim*, not a verified theorem. No rigorous equation given.\n\nCONNECTION: - The modulus \\(6\\) in the arXiv claim ties to residue classes mod 6: all primes >3 are \\(6k\\pm1\\). Twin primes are \\(6k-1, 6k+1\\). This is a lattice/residue structure, but **no** golden-ratio, base-60, or crystallographic symmetry appears in any of the cited work.\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/efp92szfn1n9x.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490625",
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  "id": "efp92szfn1n9x",
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  "landing_url": "https://zenodo.org/records/23490625",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efp92szfn1n9x.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:27Z",
      "native_id": "23490625",
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  "subjects": [],
  "title": "Twin Prime Proof Claim Unverified; Bounded Gaps Remain Best Result — E8 Intelligence Research",
  "title_text": "Twin Prime Proof Claim Unverified; Bounded Gaps Remain Best Result — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:27Z",
  "url": "https://research.draconitic.com/paper/efp92szfn1n9x",
  "venue": "Zenodo",
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}