{
  "annotation_id": "d3fa4ccf-f2a5-44e1-94ba-a8020c4b9bf2",
  "date_created": "2026-02-17T05:53:19.349000Z",
  "date_modified": "2026-02-17T05:53:19.349000Z",
  "file_hash": "8b6ebbbc00fa7d1ecfbb80d6c41b7f918db53025b1e1b894002cbf8e3ea8e58b",
  "private": false,
  "record": {
    "abstract": "Let $\\mathcal{E}=\\text{Rep}(G)$ be a Tannakian fusion category. For a braided fusion category $\\mathcal{C}$ over $\\mathcal{E}$ we give sufficient and necessary conditions that characterize the Witt relation $[\\mathcal{C}]=[\\mathcal{E}]$. Then we show the Witt group $\\mathcal{W}(\\mathcal{E})$ is naturally a direct sum of Witt group $\\mathcal{W}:=\\mathcal{W}(\\text{Vec})$ and the group $\\text{H}^4(G,\\mathbb{K}^\\times)$. Consequently, for any non-degenerate fusion category $\\mathcal{C}$ over $\\mathcal{E}$, there is a positive integer $n$ (e.g. $n=|G|$) such that $\\mathcal{C}^{\\boxtimes_\\mathcal{E}^n}$ admits a minimal extension.",
    "arxiv_id": "2601.09060",
    "authors": [
      "Theo Johnson-Freyd",
      "Victor Ostrik",
      "Zhiqiang Yu"
    ],
    "categories": [
      "math.CT",
      "math.KT",
      "math.QA"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "title": "On the structure of Witt groups and minimal extension conjecture",
    "url": "https://arxiv.org/abs/2601.09060",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "034d7091-acdf-44f6-88b4-014c49fdc8c3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}