{
  "abstract": "FINDING: No proof of the twin prime conjecture exists in these sources; the closest rigorous result is Maynard's theorem on bounded prime gaps, while the arXiv paper claims a flawed sieve-based \"proof\" with no peer review. | MATH: Twin primes: \\(p, p+2\\) both prime. Maynard (2013): \\(\\liminf_{n\\to\\infty} (p_{n+1}-p_n) \\le 246\\) (unconditional, without Elliott–Halberstam). Zhang (2013): gap < 70,000,000 → later improved to 246. arXiv:1708.07884v1 claims: for \\(n\\) increasing by 1, at least 3 new twin pairs appear below \\((6n+5)^2\\) — this is unverified and contradicts known density heuristics (Hardy–Littlewood: \\(\\pi_2(x) \\sim 2C_2 \\int_2^x dt/\\ln^2 t\\), \\(C_2 \\approx 0.66016\\)). | CONNECTION: No direct geometric harmony. However, the modulus 6 in the arXiv claim (\\(6n\\pm1\\) forms for all primes > 3) links to the hexagonal lattice (A₂ root system) — primes > 3 live on two of six rays of the Eisenstein integer lattice, a crystallographic symmetry of order 6. The constant \\(C_2 = \\prod_{p\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"
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  "author_total": 1,
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      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/90ebbt5a7mxry.bib",
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  "doi": "10.5281/zenodo.23409717",
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  "published": "2026-10-16",
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      "first_seen": "2026-10-30T12:18:27Z",
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  "title": "Twin Prime Proof Unsubstantiated; Maynard's 246 Bound Remains Strongest — E8 Intelligence Research",
  "title_text": "Twin Prime Proof Unsubstantiated; Maynard's 246 Bound Remains Strongest — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:26Z",
  "url": "https://research.draconitic.com/paper/90ebbt5a7mxry",
  "venue": "Zenodo",
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