{
  "abstract": "Building on OpenAI's preprint, we construct, for every real number $r\\in(0,1)$, a finitely generated discrete group $G_r$ and a projection $e_r\\in C_r^*(G_r)$ whose canonical trace is $r$. The construction encodes the geometry of expanders in the dynamics of a semidirect product of groups. For irrational $r$, the $K$-theory class $[e_r]$ is not in the image of the reduced Baum--Connes map. The groups $G_r$ have torsion and satisfy the maximal strong Novikov conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35674",
  "author_total": 1,
  "authors": [
    {
      "name": "Guoliang Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/as7am6rqt6hpg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35674",
  "fulltext_url": null,
  "id": "as7am6rqt6hpg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35674",
  "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.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223895970",
  "pdf_url": "https://arxiv.org/pdf/2610.35674",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/as7am6rqt6hpg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.35674",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35674"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Projections in reduced group C*-algebras with prescribed trace values in (0,1)",
  "title_text": "Projections in reduced group C*-algebras with prescribed trace values in (0,1)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/as7am6rqt6hpg",
  "venue": "arXiv",
  "versions": []
}