{
  "abstract": "FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve methods and a claimed arXiv proof (1708.07884) that is not peer-validated. | MATH: Twin primes: pairs \\((p, p+2)\\). Maynard's theorem: \\(\\liminf_{n\\to\\infty} (p_{n+1}-p_n) \\le 246\\) (unconditional, Zhang–Maynard–Polymath). The arXiv paper claims at least 3 new twin pairs per increment of \\(n\\) when setting \\((6n+5)^2\\) as a sieve bound — but this is not accepted mathematics. No exact constant for twin prime density; conjectured asymptotic \\(\\sim \\frac{2C_2 x}{(\\ln x)^2}\\), with \\(C_2 = \\prod_{p>2} \\frac{p(p-2)}{(p-1)^2} \\approx 0.66016\\). | CONNECTION: The constant \\(C_2\\) is not a golden-ratio family number, but note \\(C_2 \\approx 0.660\\) — close to \\(2/\\pi \\approx 0.6366\\) and \\(1/\\phi \\approx 0.618\\) but not equal. No base-60 or crystallographic symmetry appears in the valid mathematics. The sieve structure is arithmetic, not geometric. | DEPTH: 3 — The valid result (gap ≤ 246) is deep but does not\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": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/4waxxx6hcctw6.bib",
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  "doi": "10.5281/zenodo.23490649",
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  "id": "4waxxx6hcctw6",
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  "published": "2026-10-20",
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  "ris": "https://research.draconitic.com/paper/4waxxx6hcctw6.ris",
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      "first_seen": "2026-11-03T12:21:27Z",
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  "title": "Twin Prime Conjecture: Unproven, With Recent Sieve Progress and Unverified Claim — E8 Intelligence Research",
  "title_text": "Twin Prime Conjecture: Unproven, With Recent Sieve Progress and Unverified Claim — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:27Z",
  "url": "https://research.draconitic.com/paper/4waxxx6hcctw6",
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