{
  "abstract": "FINDING: Polymath collaboration demonstrates that distributed human-AI mathematical effort can crack problems like bounded prime gaps, with Tao's equational theories project scaling to industrial-level theorem exploration. | MATH: $H_m := \\liminf_{n \\to \\infty} (p_{n+m} - p_n)$; twin prime conjecture ⇔ $H_1 = 2$; Zhang's bound $H_1 < 7\\times10^7$ reduced via Polymath to $H_1 \\leq 246$ (unconditionally), $H_1 \\leq 6$ under Elliott–Halberstam. | CONNECTION: Prime gaps $H_m$ relate to the distribution of primes modulo small integers — the structure of $\\mathbb{Z}/q\\mathbb{Z}$ for smooth $q$ mirrors lattice/root-system periodicity (e.g., $q=6$ gives residues 1,5 — the twin-prime pairs sit on a 6-periodic lattice, echoing hexagonal close-packing symmetry). The gap sequence $p_{n+1}-p_n$ statistically obeys Poisson-like spacing, but the *extremal* gaps $H_m$ probe the fine structure of the sieve — a discrete analogue of spectral gaps in quasi-crystals. | DEPTH: 7 — Profound for methodology (\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"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0nv5kwxcqb8ax.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635120",
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  "id": "0nv5kwxcqb8ax",
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  "landing_url": "https://zenodo.org/records/23635120",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0nv5kwxcqb8ax.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:59Z",
      "native_id": "23635120",
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  "title": "Polymath and AI Collaboration Narrows Prime Gap Bounds to 246 — E8 Intelligence Research",
  "title_text": "Polymath and AI Collaboration Narrows Prime Gap Bounds to 246 — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:59Z",
  "url": "https://research.draconitic.com/paper/0nv5kwxcqb8ax",
  "venue": "Zenodo",
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