{
  "abstract": "FINDING: The 2011 IMO windmill problem (P2) is the standout mathematical structure — a combinatorial geometry problem about rotating lines through point sets, revealing deep symmetry in finite point configurations.\n\nMATH: The problem: Given a set \\(S\\) of \\(n\\) points in general position, a \"windmill\" process rotates a line \\(l\\) through a pivot point \\(p \\in S\\). When \\(l\\) hits another point \\(q \\in S\\), the pivot switches to \\(q\\), and the line continues rotating. The key result: there exists a starting line such that every point in \\(S\\) is a pivot infinitely often. The proof uses a parity/balance invariant — the number of points on each side of \\(l\\) changes by \\(\\pm 1\\) at each switch, and the total \"winding number\" forces periodicity. The critical constant is the **half-count** \\(k = \\lfloor (n-1)/2 \\rfloor\\) — the line must always have exactly \\(k\\) points on one side and \\(n-1-k\\) on the other (for odd \\(n\\), \\(k = (n-1)/2\\) exactly).\n\nCONNECTION: The windmill process is a dis\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/2ynhyqz37yge0.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465129",
  "fulltext_url": null,
  "id": "2ynhyqz37yge0",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23465129",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ynhyqz37yge0.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:47Z",
      "native_id": "23465129",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23465129"
    }
  ],
  "subjects": [],
  "title": "Symmetry in Motion: The 2011 IMO Windmill Problem — E8 Intelligence Research",
  "title_text": "Symmetry in Motion: The 2011 IMO Windmill Problem — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:47Z",
  "url": "https://research.draconitic.com/paper/2ynhyqz37yge0",
  "venue": "Zenodo",
  "versions": []
}