{
  "annotation_id": "e8a8726c-75d9-4d84-92c4-829dc8d18481",
  "date_created": "2026-03-02T18:01:17.573000Z",
  "date_modified": "2026-03-02T18:01:17.573000Z",
  "file_hash": "1edfcb79c571702d0d137b6f342aea7d222fb2f450ccef39bf091a5f5110a52d",
  "private": false,
  "record": {
    "abstract": "The spectral test of random number generators (R.R. Coveyou and R.D.\nMcPherson, 1967) is generalized. The sequence of random numbers is analyzed\nexplicitly, not just via their n-tupel distributions. We find that the mixed\nmultiplicative generator with power of two modulus does not pass the extended\ntest with an ideal result. Best qualities has a new generator with the\nrecursion formula X(k+1)=a*X(k)+c*int(k/2) mod 2^d. We discuss the choice of\nthe parameters a, c for very large moduli 2^d and present an implementation of\nthe suggested generator with d=256, a=2^128+2^64+2^32+62181, c=(2^160+1)*11463.",
    "arxiv_id": "physics/9610004",
    "authors": [
      "Oliver Schnetz"
    ],
    "categories": [
      "physics.comp-ph"
    ],
    "title": "Harmonic analysis of random number generators",
    "url": "https://arxiv.org/abs/physics/9610004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f1fc3cc7-185a-4e9c-94a8-c3caa32c4a10",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}