{
  "annotation_id": "dd6135f6-8c9a-4031-81de-4076b01f7ab0",
  "date_created": "2026-03-02T18:01:11.091000Z",
  "date_modified": "2026-03-02T18:01:11.091000Z",
  "file_hash": "7051e96615a6ed1e7b37ee6024cf5bd1b651f9f29c840f08ad2750a1ff2cee7f",
  "private": false,
  "record": {
    "abstract": "We report the proof that the expression of extended Gibrat\u0027s law is unique\nand the probability distribution function (pdf) is also uniquely derived from\nthe law of detailed balance and the extended Gibrat\u0027s law. In the proof, two\napproximations are employed that the pdf of growth rate is described as\ntent-shaped exponential functions and that the value of the origin of growth\nrate is constant. These approximations are confirmed in profits data of\nJapanese companies 2003 and 2004. The resultant profits pdf fits with the\nempirical data with high accuracy. This guarantees the validity of the\napproximations.",
    "arxiv_id": "physics/0607217",
    "authors": [
      "Atushi Ishikawa"
    ],
    "categories": [
      "physics.soc-ph",
      "q-fin.GN"
    ],
    "title": "The uniqueness of the profits distribution function in the middle scale   region",
    "url": "https://arxiv.org/abs/physics/0607217"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "261be8b8-74ef-429f-9a59-ed174257735f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}