{
  "annotation_id": "4ded228c-a5e8-4a4b-a2b8-c0d373353b1d",
  "date_created": "2026-03-02T18:02:51.141000Z",
  "date_modified": "2026-03-02T18:02:51.141000Z",
  "file_hash": "75ac4a4db463d2d68a876f564f6b206197e8d9b72e6ce62143ed0b464e4df1ac",
  "private": false,
  "record": {
    "abstract": "The local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is a\nproper generalization to 3 dimensions of the zero curvature relation. Recently,\nKorepanov has constructed an infinite set of integrable 3-dimensional lattice\nmodels, and has related them to solutions to the local YBE. The simplest\nKorepanov\u0027s model is related to the star-triangle relation in the Ising model.\nIn this paper the corresponding discrete equation is derived. In the continuous\nlimit it leads to a differential 3d equation, which is symmetric with respect\nto all permutations of the three coordinates. A similar analysis of the\nstar-triangle transformation in electric networks leads to the discrete\nbilinear equation of Miwa, associated with the BKP hierarchy. Some related\noperator solutions to the tetrahedron equation are also constructed.",
    "arxiv_id": "solv-int/9512005",
    "authors": [
      "R. M. Kashaev"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1007/BF01815521",
    "title": "On Discrete 3-Dimensional Equations Associated with the Local   Yang-Baxter Relation",
    "url": "https://arxiv.org/abs/solv-int/9512005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "45117516-451d-412a-a942-165399242920",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}