{
  "abstract": "Jananthan and Simpson asked in Conjecture~4.5 whether every pseudo-hyperjump $\\operatorname{HJ}_e(X)=X\\oplus V_e^X$, with $V_e^X$ uniformly $Π^1_1(X)$, admits Turing-degree inversion above Kleene's $\\mathcal{O}$. We settle their conjecture in the negative. We construct one index $e_*$ such that $X<_{\\mathrm T}\\operatorname{HJ}_{e_*}(X)$ for every real $X$, while the range of $\\operatorname{HJ}_{e_*}$ omits every Turing degree $\\mathbf d$ such that $°_{\\mathrm T}(\\mathcal{O})\\leq\\mathbf d<°_{\\mathrm T}(\\mathcal{O}^{\\mathcal{O}})$. Thus Conjecture~4.5 fails even for an operator which strictly raises the Turing degree of every input. Each of Properties~4.6--4.8 implies Conjecture~4.5; consequently, the accompanying class-characterisation problems collapse: no class of reals, even without a definability assumption, satisfies any one of these properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37478",
  "author_total": 1,
  "authors": [
    {
      "name": "Patrizio Cintioli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9vefb3d4j1dbc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37478",
  "fulltext_url": null,
  "id": "9vefb3d4j1dbc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37478",
  "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",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7214950161",
  "pdf_url": "https://arxiv.org/pdf/2609.37478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vefb3d4j1dbc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Pseudo-Hyperjump Inversion Fails for Turing Degrees",
  "title_text": "Pseudo-Hyperjump Inversion Fails for Turing Degrees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/9vefb3d4j1dbc",
  "venue": "arXiv",
  "versions": []
}