{
  "abstract": "Proof theorists developed various frameworks to analyze impredicative systems like $Π^1_1\\text{-}\\mathsf{CA}_0$ or $\\mathsf{KP}$; One is an operator-controlled derivation system, and the other is Girard's dilator-based $β$-logic. In this paper, we provide a functorial formulation of operator-controlled analysis of $\\mathsf{KP}$, thereby unifying the two approaches into a single framework. As an application, a new proof of Girard's boundedness theorem is also provided, which states that every $Σ_1$-over-$L_{ω_1^{\\mathsf{CK}}}$-definable function $ω_1^\\mathsf{CK}\\to ω_1^\\mathsf{CK}$ is bounded by a recursive dilator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29157",
  "author_total": 1,
  "authors": [
    {
      "name": "Hanul Jeon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a5jp5xm7tyfmc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29157",
  "fulltext_url": null,
  "id": "a5jp5xm7tyfmc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29157",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7204906617",
  "pdf_url": "https://arxiv.org/pdf/2608.29157",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a5jp5xm7tyfmc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2608.29157",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29157"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Dilator-based analysis of KP",
  "title_text": "Dilator-based analysis of KP",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/a5jp5xm7tyfmc",
  "venue": "arXiv",
  "versions": []
}