{
  "abstract": "FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve bounds gaps, but a claimed \"definitive proof\" (arXiv:1708.07884v1) is not peer-validated and likely flawed. | MATH: Twin primes: \\(p_{x+1}=p_x+2\\). Maynard–Tao: \\(\\liminf_{n\\to\\infty}(p_{n+1}-p_n)\\le 246\\) (unconditionally; 6 with Elliott–Halberstam). The arXiv paper claims: for \\(n\\) increasing by 1, at least 3 new twin pairs appear in interval up to \\((6n+5)^2\\), implying infinite pairs — but this step lacks rigorous sieve control. | CONNECTION: No direct geometric ratio appears. However, the sieve structure \\((6n\\pm1)\\) reflects modular lattice \\(\\mathbb{Z}/6\\mathbb{Z}\\) — the crystallographic root lattice \\(A_2\\) (hexagonal) — where primes >3 live in two residue classes ±1 mod 6. This is a 2D hexagonal symmetry, not golden-ratio based. | DEPTH: 4 — The Maynard bound is profound (narrowing prime gaps from infinity to finite 246), but the \"proof\" claim is not credible. The lattice connection to \\(A_2\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"
    }
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  "bibtex": "https://research.draconitic.com/paper/brzjerbxdk588.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553672",
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  "id": "brzjerbxdk588",
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  "language": "eng",
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  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brzjerbxdk588.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:21:20Z",
      "native_id": "23553672",
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  "subjects": [],
  "title": "Twin Prime Proof Claim Flawed; Maynard's Bound Remains Best — E8 Intelligence Research",
  "title_text": "Twin Prime Proof Claim Flawed; Maynard's Bound Remains Best — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:20Z",
  "url": "https://research.draconitic.com/paper/brzjerbxdk588",
  "venue": "Zenodo",
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