{
  "abstract": "We determine the Borel-reducibility comparison of each pair of $\\mathbfΠ^0_3$ benchmark equivalence relations in Gao's monograph. The additional comparisons we prove are $E_\\infty\\leq_B c_0$, $E_\\infty\\nleq_B\\ell_p$ for $2<p<\\infty$, $\\ell_p\\nleq_B{\\equiv_m}$ for $2<p<\\infty$, $c_0\\nleq_B{\\equiv_m}$, $c_0\\nleq_B\\ell_\\infty^+$ and $\\equiv_m\\nleq_B\\ell_\\infty^+$. Together with the previous positive direction, these give $\\ell_p\\leq_B{\\equiv_m}$ if and only if $p\\leq2$. These answer several questions in Gao's monograph and Kanovei' monograph. We also prove that unitary equivalence of all bounded linear operators is not Borel reducible to $\\equiv_m$. This answers a question of Ding and Gao. Equivalently, unitary equivalence of arbitrary representations of $F_\\infty$ is strictly more complicated than that of arbitrary representations of $\\mathbb Z$. This answers a question of Thomas.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35025",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruijun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/azvrg7w5eahdv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35025",
  "fulltext_url": null,
  "id": "azvrg7w5eahdv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35025",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7223822146",
  "pdf_url": "https://arxiv.org/pdf/2610.35025",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/azvrg7w5eahdv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35025",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35025"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Comparisons of benchmark equivalence relations",
  "title_text": "Comparisons of benchmark equivalence relations",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/azvrg7w5eahdv",
  "venue": "arXiv",
  "versions": []
}