{
  "annotation_id": "d5bc42cb-e5a9-494f-a88d-2183ddf615de",
  "date_created": "2026-03-02T18:01:48.341000Z",
  "date_modified": "2026-03-02T18:01:48.341000Z",
  "file_hash": "c08a12c72747ee1ad4cbc395f1b7caef0548e252422ecc1314d1c1cfdc916e70",
  "private": false,
  "record": {
    "abstract": "A class of Clebsch-Gordan coefficients are derived from the properties of\nconditional probability using the binomial distribution. In particular, in the\ncase of $l=l_1+l_2$ it is shown that $$[\u003cl_1/2-k_1, l_2/2-k_2|l/2,\nk=k_1+k_2]\u003e^2 =\\frac{(\\begin{array}{c} l_1 k_1\\end{array}) (\\begin{array}{c}l_2\nk_2\\end{array})}{(\\begin{array}{c}l k \\end{array})}$$",
    "arxiv_id": "quant-ph/0112096",
    "authors": [
      "Paul O\u0027Hara"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "title": "Clebsch-Gordan coefficients and the binomial distribution",
    "url": "https://arxiv.org/abs/quant-ph/0112096"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ac99ba36-47c1-4f54-9c35-43e4ca5476ff",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}