{
  "schema_version": 1,
  "problem_number": "OWR-16930-001",
  "title": "High-Density Canonical Hard Disks Percolate",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We derive high-density percolation for uniform canonical hard-disk packings from Georgii's equivalence of ensembles and Magazinov's high-activity percolation theorem. For every epsilon > 0, every weak limit of uniform square-torus packings sufficiently close to the maximum number density 1/(2 sqrt(3)) has an infinite component when centers at distance at most 2+epsilon are joined. The parameter conversion uses the explicit bound rho <= 1/(2 sqrt(3)) - exp(-4 pi lambda)/9 for stationary Gibbs packings of activity lambda. We give the ensemble argument for arbitrary square sizes and treat the maximum-density endpoint separately. The conclusion addresses the canonical percolation question of Bowen, Lyons, Radin and Winkler; it is not a crystallization theorem. Separated triangular patches show why the uniform sampling hypothesis cannot be replaced by high density alone. This AI-assisted research note is self-audited and unrefereed, credits its published theorem inputs, and makes no absolute priority claim.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.PR",
    "math.MP",
    "math.MG"
  ],
  "keywords": [
    "hard disks",
    "canonical ensemble",
    "continuum percolation",
    "Gibbs measure",
    "equivalence of ensembles",
    "packing density",
    "OWR-16930-001"
  ],
  "manuscript_version_date": "2026-10-19",
  "publication_date": "2026-10-19",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-19",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-16930-001/",
  "pdf_url": "https://eulersolve.org/papers/owr-16930-001/paper.pdf?v=d00a956a9e46",
  "doi": "10.5281/zenodo.23463294",
  "zenodo_record_url": "https://zenodo.org/records/23463294",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete analytic proof of the high-density uniform canonical percolation statement, derived from credited published results of Georgii, Magazinov, and Bowen-Holton-Radin-Sadun. The uniform sampling model is essential: arbitrary high-density packings need not percolate. The broader shortened dataset prompt remains PARTIAL_RESULT; no crystallization, optimal density threshold, unrestricted whole-record closure, or dataset-maintainer acceptance is claimed. The 44,085 finite exact checks are sanity checks of analogues and distance formulas, not a computational proof of the continuum theorem. AI-assisted, self-audited and unrefereed; no external review, formal verification or absolute priority claim.",
  "files": {
    "paper.pdf": {
      "sha256": "d00a956a9e46b86ed5ba15bddf407254fa8449654d5ba269b1bd79363550243d"
    },
    "source.zip": {
      "sha256": "4f8b093f055e7ee0b3d53a6981d61effb2adb5d61c50e6f5d7de408dcd57e8a0"
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    "verification_report.md": {
      "sha256": "b1aab9f0f54214165a69374d6d23e05d72ffc11cc65b69e716c9c67e6dc51ab9"
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  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}