{
  "abstract": "Real Betti realization is a symmetric monoidal functor from the category of motivic spectra to that of topological spectra, extending the functor that associates to a scheme over $\\mathbb{R}$ the space of its real points. In this article, we identify the $\\mathcal{E}_1$-ring structure on the real realization of $\\mathsf{ko}$, the very effective cover of Hermitian K-theory $\\mathsf{KO}$, by an explicit 2-local fracture square, as being equivalent to $\\mathsf{L}(\\mathbb{R})_{\\geq 0}$, the connective L-theory spectrum of $\\mathbb{R}$. Along the way, we also compute the real realization of other motivic ring spectra: motivic cohomology $\\mathsf{H}\\mathbb{Z}$ and $\\mathsf{H}\\mathbb{Z}/2$, the variant $\\widetilde{\\mathsf{H}\\mathbb{Z}}$, $\\mathsf{KO}$, the very effective cover $\\mathsf{kgl}$ of algebraic K-theory $\\mathsf{KGL}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20688",
  "author_total": 1,
  "authors": [
    {
      "name": "Julie Bannwart"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5t2x7kst6d2xp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20688",
  "fulltext_url": null,
  "id": "5t2x7kst6d2xp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20688",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7222500002",
  "pdf_url": "https://arxiv.org/pdf/2610.20688",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5t2x7kst6d2xp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.20688",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20688"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The real Betti realization of very effective Hermitian K-theory",
  "title_text": "The real Betti realization of very effective Hermitian K-theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/5t2x7kst6d2xp",
  "venue": "arXiv",
  "versions": []
}