{
  "abstract": "We introduce the definition of a weakly $X$-uniformly $Y$-computably categorical structure, relativizing a definition of Kudinov (1996), and show that this relativized notion is closely related to the 2-dimensional complexity of the pairs of partial functions $(f,g)$ with the property that the composition $g\\circ f$ simulates convergent $\\emptyset'$-oracle computations. We develop a general theory for computing via composition and use it to prove results about the surprisingly complex weakly uniform categoricity spectrum of the structure $(ω,S)$ where $S(n)=n+1$. Namely, that $(ω,S)$ is w.$X$.u.$Y$.c.c. for some $X\\not\\geq_T\\emptyset'$ and $Y<_T\\emptyset'$, but $(ω,S)$ is not w.$X$.u.$Y$.c.c. for any $X<_T\\emptyset'$ and $Y\\not\\geq_T\\emptyset'$. We also construct a computably categorical structure that is not w.$\\emptyset'$.u.c.c., but is w.$X$.u.c.c. for a set $X$ that is $\\leq_T$-incomparable with $\\emptyset'$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24422",
  "author_total": 1,
  "authors": [
    {
      "name": "Joey Lakerdas-Gayle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5qzx8zpgenm8t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24422",
  "fulltext_url": null,
  "id": "5qzx8zpgenm8t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24422",
  "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.LO"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7223060474",
  "pdf_url": "https://arxiv.org/pdf/2610.24422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5qzx8zpgenm8t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24422"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Weakly uniform computable categoricity and function composition",
  "title_text": "Weakly uniform computable categoricity and function composition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/5qzx8zpgenm8t",
  "venue": "arXiv",
  "versions": []
}