{
  "annotation_id": "c537b783-08c2-4759-bdd8-6e97f75671b2",
  "date_created": "2026-03-02T18:02:30.936000Z",
  "date_modified": "2026-03-02T18:02:30.936000Z",
  "file_hash": "36053a55c8f0c6cb32432a4dfb9b9fe0e12566f5951c3afe2f4a51ec2bfeb03e",
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  "record": {
    "abstract": "In this paper fields of quantum reference frames based on gauge\ntransformations of rational string states are described in a way that,\nhopefully, makes them more understandable than their description in an earlier\npaper. The approach taken here is based on three main points: (1) There are a\nlarge number of different quantum theory representations of natural numbers,\nintegers, and rational numbers as states of qubit strings. (2) For each\nrepresentation, Cauchy sequences of rational string states give a\nrepresentation of the real (and complex) numbers. A reference frame is\nassociated to each representation. (3) Each frame contains a representation of\nall mathematical and physical theories that have the representations of the\nreal and complex numbers as a scalar base for the theories. These points and\nother aspects of the resulting fields are then discussed and justified in some\ndetail. Also two different methods of relating the frame field to physics are\ndiscussed.",
    "arxiv_id": "quant-ph/0611139",
    "authors": [
      "Paul Benioff"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1742-6596/70/1/012003",
    "journal_ref": "Journal of Physics: Conference Series 70 (2007) 012003",
    "title": "Fields of quantum reference frames based on different representations of   rational numbers as states of qubit strings",
    "url": "https://arxiv.org/abs/quant-ph/0611139"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "097d489a-9aa8-4cd3-b260-689ff3789927",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}