{
  "annotation_id": "577270c7-df70-4716-9d1c-ed3603f0a659",
  "date_created": "2026-03-02T18:02:09.391000Z",
  "date_modified": "2026-03-02T18:02:09.391000Z",
  "file_hash": "b2272a1c4cb21d600f32457f5011c31be55e9262755492326b60e071505b9f3e",
  "private": false,
  "record": {
    "abstract": "We continue the development of a so called contextual statistical model (here\ncontext has the meaning of a complex of physical conditions). It is shown that,\nbesides contexts producing the conventional trigonometric $\\cos$-interference,\nthere exist contexts producing the hyperbolic $\\cos$-interference. Starting\nwith the corresponding interference formula of total probability we represent\nsuch contexts by hyperbolic probabilistic amplitudes or in the abstract\nformalism by normalized vectors of a hyperbolic analogue of the Hilbert space.\nThere is obtained a hyperbolic Born\u0027s rule. Incompatible observables are\nrepresented by noncommutative operators.",
    "arxiv_id": "quant-ph/0408188",
    "authors": [
      "A. Yu. Khrennikov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1931042",
    "journal_ref": "J. Math. Phys., 46, N.6, 062111 (2005)",
    "title": "Representation of the contextual statistical model by hyperbolic   amplitudes",
    "url": "https://arxiv.org/abs/quant-ph/0408188"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "15eab1ca-9447-471f-a86f-bd0800a38673",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}