{
  "abstract": "In a tracial von Neumann algebra M, two subsets X and Y are said to be N-independent if alternating products of length at most N of trace zero words from X and Y have trace zero. We show that two approximately 2N-independent finite tuples can be perturbed, in operator norm, to be exactly N-independent. Consequently, we are able to generalize Theorem 5.1 and Theorem H of Houdayer-Ioana and resolve Problem 31 of Kunnawalkam Elayavalli in the positive.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10087",
  "author_total": 2,
  "authors": [
    {
      "name": "Gregory Patchell"
    },
    {
      "name": "Austin Shiner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9pxyqf154qnfr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10087",
  "fulltext_url": null,
  "id": "9pxyqf154qnfr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10087",
  "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"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7212140313",
  "pdf_url": "https://arxiv.org/pdf/2609.10087",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9pxyqf154qnfr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10087",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10087"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Lifting for N-independent sets in II1 factors",
  "title_text": "Lifting for N-independent sets in II1 factors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/9pxyqf154qnfr",
  "venue": "arXiv",
  "versions": []
}