{
  "abstract": "Naryshkin recently proved that a free action of a countably infinite discrete amenable group $G$ on a compact metrizable space $X$ with the uniform Rokhlin property and comparison (URPC) admits an equivariant embedding into $([0,1]^m)^G$ whenever $\\mathrm{mdim}(X,G)<m/2$. We strengthen this result from existence to genericity by a substantially different method: the set of observables $f\\in C(X,[0,1]^m)$ whose orbit maps are equivariant embeddings into $([0,1]^m)^G$ is a dense $G_δ$ subset of $C(X,[0,1]^m)$. The proof combines an adaptation of the Kakutani skyscraper construction used by Gutman--Tsukamoto with a new polynomial perturbation method, departing from the predominantly linear perturbation approaches used in earlier equivariant embedding literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31735",
  "author_total": 2,
  "authors": [
    {
      "name": "Yonatan Gutman"
    },
    {
      "name": "Chunlin Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fs74sdv8g5pn0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31735",
  "fulltext_url": null,
  "id": "fs74sdv8g5pn0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31735",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214737720",
  "pdf_url": "https://arxiv.org/pdf/2609.31735",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fs74sdv8g5pn0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31735"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Generic Sharp Shift Embedding for Amenable Group Actions with the Uniform Rokhlin Property and Comparison",
  "title_text": "Generic Sharp Shift Embedding for Amenable Group Actions with the Uniform Rokhlin Property and Comparison",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/fs74sdv8g5pn0",
  "venue": "arXiv",
  "versions": []
}