{
  "annotation_id": "75998708-a7c5-46be-b87c-ce49af973ae2",
  "date_created": "2026-02-17T05:53:19.555000Z",
  "date_modified": "2026-02-17T05:53:19.555000Z",
  "file_hash": "af2a283dc16f10a804b926987e5d75451ca560d425c979342419c1dbe62ff912",
  "private": false,
  "record": {
    "abstract": "We establish a non-ergodic version of the Host-Kra-Ziegler structure theorem for measure-preserving $\\mathbb{Z}^d$-actions. Our argument reduces the non-ergodic case to the ergodic theorem (for $d\\ge 2$ due to Candela and Szegedy) via a measurable selection procedure.",
    "arxiv_id": "2601.09553",
    "authors": [
      "Asgar Jamneshan",
      "Simon Machado"
    ],
    "categories": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The non-ergodic Host-Kra-Ziegler structure theorem for $\\mathbb{Z}^d$-actions via measurable selections",
    "url": "https://arxiv.org/abs/2601.09553",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f6299675-6d13-4140-b51c-e9f20b8440dc",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}