{
  "annotation_id": "442b93e9-1248-4638-bfa0-2073fb021b2b",
  "date_created": "2026-03-02T18:02:20.075000Z",
  "date_modified": "2026-03-02T18:02:20.075000Z",
  "file_hash": "734270b15cedc8bde6e417eb12f80373fdc37e3815fc74ac569ddff432695e5b",
  "private": false,
  "record": {
    "abstract": "A binary representation of complex rational numbers and their arithmetic is\ndescribed that is not based on qubits. It takes account of the fact that $0s$\nin a qubit string do not contribute to the value of a number. They serve only\nas place holders. The representation is based on the distribution of four types\nof systems, corresponding to $+1,-1,+i,-i,$ along an integer lattice. Complex\nrational numbers correspond to arbitrary products of four types of creation\noperators acting on the vacuum state. An occupation number representation is\ngiven for both bosons and fermions.",
    "arxiv_id": "quant-ph/0508038",
    "authors": [
      "Paul Benioff"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S021797920603425X",
    "journal_ref": "International Journal of Modern Physics B Vol 20, 1730-1741 (2006)",
    "title": "Complex Rational Numbers in Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0508038"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8c10a840-6704-4476-8a4e-64d692423d10",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}