{
  "abstract": "FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve bounds gaps, but no proof exists. One arXiv claim (1708.07884v1) asserts a constructive proof via sieve of Eratosthenes, but is not peer-validated. | MATH: Twin primes: pairs \\((p, p+2)\\) with \\(p\\) prime. Maynard's theorem: \\(\\liminf_{n\\to\\infty} (p_{n+1} - p_n) \\le 246\\) (unconditionally; 6 with Elliott–Halberstam). Conjecture: infinitely many \\(n\\) with \\(p_{n+1} - p_n = 2\\). The arXiv paper claims: for each \\(n\\), at least three new twin pairs appear between \\((6n+5)^2\\) and \\((6(n+1)+5)^2\\) — a density claim, not a proof of infinitude. | CONNECTION: Twin primes modulo 6: all pairs > 3 are \\((6k-1, 6k+1)\\). This is a residue class symmetry in \\(\\mathbb{Z}/6\\mathbb{Z}\\) — a cyclic group of order 6, related to hexagonal lattice symmetry (root system \\(A_2\\)). The gap 2 is the smallest nonzero difference in the even lattice \\(2\\mathbb{Z}\\). No direct golden-ratio or base-60 link appears in the given s\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
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  "author_total": 1,
  "authors": [
    {
      "affs": [
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      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/0btbd837yjkj8.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635252",
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  "published": "2026-10-25",
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  "ris": "https://research.draconitic.com/paper/0btbd837yjkj8.ris",
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      "first_seen": "2026-11-08T12:21:56Z",
      "native_id": "23635252",
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  "subjects": [],
  "title": "Twin Prime Proof Claim Unverified; Maynard's Bound Remains Best — E8 Intelligence Research",
  "title_text": "Twin Prime Proof Claim Unverified; Maynard's Bound Remains Best — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:56Z",
  "url": "https://research.draconitic.com/paper/0btbd837yjkj8",
  "venue": "Zenodo",
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