{
  "annotation_id": "2acbeacf-9ec2-460d-9dac-6ba08265151b",
  "date_created": "2026-03-02T18:02:23.824000Z",
  "date_modified": "2026-03-02T18:02:23.824000Z",
  "file_hash": "a342549f40653727a068b07dfbbbc1df1f074c9c7e3baba2c53d24b2b10e197f",
  "private": false,
  "record": {
    "abstract": "In this work we define an universal arithmetical algorithm, by means of the\nstandard quantum mechanical formalism, called universal qm-arithmetical\nalgorithm. By universal qm-arithmetical algorithm any decidable arithmetical\nformula (operation) can be decided (realized, calculated. Arithmetic defined by\nuniversal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds\nto decidable part of the usual arithmetic. We prove that in the qm-arithmetic\nthe undecidable arithmetical formulas (operations) cannot exist (cannot be\nconsistently defined). Or, we prove that qm-arithmetic has no undecidable\nparts. In this way we show that qm-arithmetic, that holds neither Church\u0027s\nundecidability nor Godel\u0027s incompleteness, is decidable and complete. Finally,\nwe suggest that problems of the foundation of the arithmetic, can be solved by\nqm-arithmetic.",
    "arxiv_id": "quant-ph/0602009",
    "authors": [
      "Vladan Pankovic",
      "Milan Predojevic"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A Quantum Gate as a Physical Model of an Universal Arithmetical   Algorithm without Church\u0027s Undecidability and Godel\u0027s Incompleteness",
    "url": "https://arxiv.org/abs/quant-ph/0602009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2dea44f7-2ed4-4672-b22a-0330c594133a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}