{
  "annotation_id": "3185f9ce-2f8d-439d-b8a6-eef9a6311483",
  "date_created": "2026-02-17T05:53:20.181000Z",
  "date_modified": "2026-02-17T05:53:20.181000Z",
  "file_hash": "f2ece7fb46416a3f7a0043b52f522f3092f4034b99121958503c73cc11297cba",
  "private": false,
  "record": {
    "abstract": "We prove universality for cokernels of random integral matrices with symmetries via an approach different from the classical surjection moment method introduced by Wood (arXiv:1402.5149). In the symmetric case, we reprove Hodges\u0027 universality theorem (arXiv:2311.07078), i.e. the version incorporating the canonical pairing from Wood\u0027s setting, and in the alternating case we reprove the local universality theorem of Nguyen-Wood (arXiv:2210.08526). A key advantage of our method is that it is quantitative: we obtain explicit error bounds, which are exponentially small in most regimes, thereby addressing Wood\u0027s question on effective convergence rates. Our argument is inspired by Maples\u0027 exposure-process and coupling viewpoint (arXiv:1301.1239) and uses a generalized form of Fourier-analytic estimates in the exponentially sharp style of Ferber-Jain-Sah-Sawhney (arXiv:2106.04049).",
    "arxiv_id": "2601.09704",
    "authors": [
      "Jiahe Shen"
    ],
    "categories": [
      "math.PR",
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Quantative universality for cokernels of matrices with symmetries",
    "url": "https://arxiv.org/abs/2601.09704",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c7c6ab1e-5ae6-4f95-bb8d-b4a4fb5c74b5",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}