{
  "annotation_id": "2abb6fd3-4929-45be-96ff-883d4edf706d",
  "date_created": "2026-03-02T18:00:39.532000Z",
  "date_modified": "2026-03-02T18:00:39.532000Z",
  "file_hash": "e1e4aa6a97966ab7eff8dbd41c6551f28bc4edef36fd1b21ccf4cc2804d2f359",
  "private": false,
  "record": {
    "abstract": "We present a new computational scheme, GRIP (Geometric Random Inner\nProducts), for testing the quality of random number generators. The GRIP\nformalism utilizes geometric probability techniques to calculate the average\nscalar products of random vectors generated in geometric objects, such as\ncircles and spheres. We show that these average scalar products define a family\nof geometric constants which can be used to evaluate the quality of random\nnumber generators. We explicitly apply the GRIP tests to several random number\ngenerators frequently used in Monte Carlo simulations, and demonstrate a new\nstatistical property for good random number generators.",
    "arxiv_id": "physics/0209032",
    "authors": [
      "Shu-Ju Tu",
      "Ephraim Fischbach"
    ],
    "categories": [
      "physics.comp-ph"
    ],
    "doi": "10.1103/PhysRevE.67.016113",
    "title": "Geometric Random Inner Products: A New Family of Tests for Random Number   Generators",
    "url": "https://arxiv.org/abs/physics/0209032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1a6b1c84-3ef9-4f1b-add4-d40fa3fbe600",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}