{
  "abstract": "FINDING: Search results conflate Maynard–Tao sieve theory with golden-ratio geometry; no direct evidence links sieve weights to 0.618 optimality. | MATH: Maynard–Tao sieve uses multidimensional weights \\(W(n) = \\sum_{d_i | n+h_i} \\lambda_{d_1,\\dots,d_k}\\) with \\(\\lambda\\) chosen to maximize \\(\\sum_{n\\le x} \\left(\\sum_{i=1}^k \\mathbf{1}_{n+h_i \\text{ prime}} - \\rho \\right) W(n)^2\\), yielding \\(k\\)-tuples with \\(\\liminf (p_{n+k}-p_n) \\ll k e^{k}\\) (Maynard 2013). No constant 0.618 appears in the sieve construction; optimal smoothing is polynomial (e.g., \\(P(\\log x)\\)), not golden. | CONNECTION: The golden ratio appears only in unrelated Numberphile videos and a paper on self-application (arXiv:2510.08934) — no mathematical bridge to sieve theory. The only shared feature is the number 1.618 as a ratio, but sieve weights are optimized via linear programming and Selberg's \\(\\Lambda^2\\), not via geometric proportion. | DEPTH: 2 — The search query itself is a false premise; the results are a\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,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/7h0fsekeefxt5.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465032",
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  "id": "7h0fsekeefxt5",
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  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7h0fsekeefxt5.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:49Z",
      "native_id": "23465032",
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  "subjects": [],
  "title": "Debunking the False Link Between Maynard–Tao Sieve and Golden Ratio — E8 Intelligence Research",
  "title_text": "Debunking the False Link Between Maynard–Tao Sieve and Golden Ratio — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:49Z",
  "url": "https://research.draconitic.com/paper/7h0fsekeefxt5",
  "venue": "Zenodo",
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