{
  "abstract": "FINDING: The corpus reveals no single \"hardest problem\" but a cluster of structurally distinct challenges — Putnam's elegant-combinatorics, IMO's windmill (dynamic geometry), Collatz (iterative arithmetic), and the MATH dataset (benchmarking) — with the deepest mathematical content in the windmill problem's hidden projective symmetry. MATH: - **Windmill (IMO 2011 P2):** For odd \\(n\\), a finite set \\(S\\) of points in general position. A \"windmill\" is a line through a pivot point \\(p \\in S\\), rotating continuously; when it hits another point \\(q \\in S\\), the pivot switches to \\(q\\) (line passes through \\(q\\) and continues rotating). **Key result:** There exists a starting line such that every point of \\(S\\) is a pivot infinitely often. The proof uses a parity/involution argument: the number of points on each side of the rotating line changes by \\(\\pm 1\\) at each pivot switch, and for odd \\(n\\), the line must pass through exactly one point at all times (since \\(n-1\\) is even, sides ba\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/e1t8kbz08pf6t.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587065",
  "fulltext_url": null,
  "id": "e1t8kbz08pf6t",
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  "landing_url": "https://zenodo.org/records/23587065",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1t8kbz08pf6t.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:53Z",
      "native_id": "23587065",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587065"
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  "subjects": [],
  "title": "The Hidden Projective Symmetry Behind IMO's Windmill Problem — E8 Intelligence Research",
  "title_text": "The Hidden Projective Symmetry Behind IMO's Windmill Problem — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:53Z",
  "url": "https://research.draconitic.com/paper/e1t8kbz08pf6t",
  "venue": "Zenodo",
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}