{
  "annotation_id": "36e75c9d-6791-4d18-a2db-5b986451e1e0",
  "date_created": "2026-03-02T18:01:42.263000Z",
  "date_modified": "2026-03-02T18:01:42.263000Z",
  "file_hash": "f3380b72f548eddbd7f5877c5c5f44f232deb3f868fa099fc4541a1d2e2a8d1e",
  "private": false,
  "record": {
    "abstract": "It is shown that in two-state quantum theory, a generic quantum state can be\ndescribed by a non-computable real number. In terms of this, the criterion for\nmeasurement outcome is simply and deterministically defined. This demonstration\nis based on a construction of the Riemann sphere whose points represent, not\ncomplex numbers, but divergent sequences with bivalent elements. Complex\nstructure arises from self-similar properties of a set of operators which\ngenerate these sequences. In general, a rotation of (the coordinates of) the\nsphere maps a computable real to a non-computable real. This is interpreted\nphysically as a mapping of a physically-measurable state to a counterfactual\nstate. Implications for non-locality, null measurements, many worlds and so on,\nare discussed. The possible role of the Euler equation as the counterpart of\nthe Schrodinger equation for real-number quantum state evolution is also\noutlined.",
    "arxiv_id": "quant-ph/0101007",
    "authors": [
      "T. N. Palmer"
    ],
    "categories": [
      "quant-ph",
      "nlin.CD"
    ],
    "title": "Formulation of Quantum Theory Using Computable and Non-Computable Real   Numbers",
    "url": "https://arxiv.org/abs/quant-ph/0101007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f3db8ae0-1375-4cba-8e4e-f72ab59a1e54",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}