{
  "title": "A proof of the positive density conjecture for integer Apollonian circle packings",
  "authors": [
    "Jean Bourgain",
    "Elena Fuchs"
  ],
  "arxiv_id": "1001.3894v1",
  "version_date": "2010-01-21",
  "preparation_date": "2026-10-15",
  "pages": 20,
  "abstract_url": "https://arxiv.org/abs/1001.3894v1",
  "pdf_url": "https://arxiv.org/pdf/1001.3894v1",
  "source_url": "https://arxiv.org/src/1001.3894v1",
  "pdf_sha256": "a426aec23eb1532c64c3858743462672bb3282102b3f54dd27e0b34c4b9b6fe2",
  "original_source_sha256": "8f882b7c433f205dbed62c20dd5379c3a9206b06408a10079aca00dfccce2993",
  "native_sha256": "803e26afc4c48a289769131a5b512a8d371607181bdef83b156a5b3ea4e444a8",
  "source_preparation": "Exact native source bytes preserved. MacRoman decoding maps two bibliography page-range D0 bytes to en dashes; no mathematical character changes. Identifying front matter and acknowledgements withheld line-for-line. No proof correction, expansion, TeX execution or bundled-code execution.",
  "changed_lines": [
    {
      "line": 56,
      "original": "\\title{A proof of the positive density conjecture for integer Apollonian circle packings}\n",
      "review": "\\title{Manuscript}\n"
    },
    {
      "line": 57,
      "original": "\\author{Jean Bourgain}\n",
      "review": "% Withheld identifying front matter.\n"
    },
    {
      "line": 58,
      "original": "\\address{Institute for Advanced Study, School of Mathematics, Einstein Drive, Princeton, NJ 08540 USA}\n",
      "review": "% Withheld identifying front matter.\n"
    },
    {
      "line": 59,
      "original": "\\thanks{The first author is supported in part by NSF}\n",
      "review": "% Withheld identifying front matter.\n"
    },
    {
      "line": 61,
      "original": "\\email{bourgain@math.ias.edu}\n",
      "review": "% Withheld identifying front matter.\n"
    },
    {
      "line": 62,
      "original": "\\author{Elena Fuchs}\n",
      "review": "% Withheld identifying front matter.\n"
    },
    {
      "line": 63,
      "original": "\\address{Princeton University, Department of Mathematics, Fine Hall, Washington Rd, Princeton, NJ 08544-100 USA}\n",
      "review": "% Withheld identifying front matter.\n"
    },
    {
      "line": 64,
      "original": "\\email{efuchs@math.princeton.edu}\n",
      "review": "% Withheld identifying front matter.\n"
    },
    {
      "line": 126,
      "original": "{\\bf Acknowledgements:}  We thank Peter Sarnak and Jeffrey Lagarias for introducing this problem to us, and for many insightful comments and conversations.  We thank Alex Kontorovich for sharing his program for drawing Apollonian circle packings.\n",
      "review": "% Withheld identifying acknowledgements.\n"
    }
  ],
  "figure_limit": "The two supplied figure PDFs are preserved separately; the text panel does not receive figure pixels. Captions and mathematical prose remain unchanged.",
  "blinding_limit": "References, mathematical content and filenames remain recognizable. Not fully blind or an unseen-capability evaluation.",
  "edition_limit": "The 20-page arXiv v1 is the primary panel input. A distinct 25-page author-hosted copy is retained for later version checks, not silently substituted or certified as the journal typesetting.",
  "journal_reference": {
    "journal": "Journal of the American Mathematical Society",
    "volume": 24,
    "year": 2011,
    "pages": "945–967",
    "doi": "10.1090/S0894-0347-2011-00707-8",
    "source": "https://www.math.ucdavis.edu/~efuchs/research.html",
    "journal_text_inspected": false
  },
  "author_copy": {
    "path": "sources/paper-author.pdf",
    "pages": 25,
    "url": "https://www.math.ucdavis.edu/~efuchs/posdensbourgain.pdf",
    "sha256": "10447d219eb8669db869c3099e3ea62a3b833f9b1e6b58e8616bca0928f56ddd",
    "pdf_creation_metadata": "2011-02-20; not treated as a manuscript revision date"
  },
  "files": {
    "paper-author.txt": "c7ad63a5fc29c3a2f2a8257da07a554f570a31c2d418c12cb0ccedbe954f2788",
    "manuscript-review.tex": "803e26afc4c48a289769131a5b512a8d371607181bdef83b156a5b3ea4e444a8",
    "original.tex": "8f882b7c433f205dbed62c20dd5379c3a9206b06408a10079aca00dfccce2993",
    "paper-arxiv-v1.txt": "aa173d800a301e34d1aac470d5d83cfb326a165dad012312bc6e4033c8859ad2",
    "paper.pdf": "a426aec23eb1532c64c3858743462672bb3282102b3f54dd27e0b34c4b9b6fe2",
    "paper-arxiv-v1.pdf": "a426aec23eb1532c64c3858743462672bb3282102b3f54dd27e0b34c4b9b6fe2",
    "paper-author.pdf": "10447d219eb8669db869c3099e3ea62a3b833f9b1e6b58e8616bca0928f56ddd",
    "source.download": "3e26a53ed16db7c69b1b4799ec9d3a5255588534a8f921fc6a2fc8911eb310e5",
    "native-arxiv-v1/1223.pdf": "8b19de3446a3d6f5d1224739b29ebdc38d53ce55d52fe94a3dbbd022a55d6c39",
    "native-arxiv-v1/posdensbourgain.tex": "8f882b7c433f205dbed62c20dd5379c3a9206b06408a10079aca00dfccce2993",
    "native-arxiv-v1/packingcircles.pdf": "e91d1e716da5fcb7054e9c1e9a636b437260162fc876f05d890339219619a198"
  }
}