{
  "annotation_id": "1c73f0af-d7f4-45f1-95d4-c3fe76792c89",
  "date_created": "2026-03-02T18:02:51.557000Z",
  "date_modified": "2026-03-02T18:02:51.557000Z",
  "file_hash": "42ae323dd7627adcd63341b051c1401d427e706d5bbef5460315996c88728010",
  "private": false,
  "record": {
    "abstract": "A discrete analogue of the holomorphic map z^a is studied. It is given by a\nSchramm\u0027s circle pattern with the combinatorics of the square grid. It is shown\nthat the corresponding immersed circle patterns lead to special separatrix\nsolutions of a discrete Painleve equation. Global properties of these\nsolutions, as well as of the discrete $z^a$ are established.",
    "arxiv_id": "solv-int/9909002",
    "authors": [
      "Sergey I. Agafonov",
      "Alexander I. Bobenko"
    ],
    "categories": [
      "solv-int",
      "math.CV",
      "nlin.SI"
    ],
    "journal_ref": "International Math. Research Notices 2000:4 165-193",
    "title": "Discrete Z^a and Painleve equations",
    "url": "https://arxiv.org/abs/solv-int/9909002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0180976a-d14d-4bf3-a27b-f516651c9672",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}