{
  "abstract": "Can random real carry arbitrary information. In terms of (Turing) computability, Kučera and Gács addressed this question in affirmative. i.e., Every real $x\\in 2^ω$ is computable from some Martin-Löf random real. This result motivated quantitative versions of coding into random reals. i.e., How many bits of the random oracle are needed to compute the first $n$ bits of $x$. Barmpalias and Lewis-Pye obtained a coding that uses $n+O(\\log n)$ many bits. Is it possible for the coding to use $n$ bits exactly? This is equivalent to say, if every real is $rK$-reducible to a Martin-Löf random real. In this paper, we prove that such a coding does not exist. i.e., There exists some real that is not $rK$-reducible to any Martin-Löf random real.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39174",
  "author_total": 2,
  "authors": [
    {
      "name": "George Barmpalias"
    },
    {
      "name": "Lu Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ersd6kfjpqxs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39174",
  "fulltext_url": null,
  "id": "0ersd6kfjpqxs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39174",
  "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.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39174",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ersd6kfjpqxs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39174",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39174"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Martin-Löf randomness and rK-reducibility",
  "title_text": "Martin-Löf randomness and rK-reducibility",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0ersd6kfjpqxs",
  "venue": "arXiv",
  "versions": []
}