{
  "schema_version": 1,
  "problem_number": "OWR-16412-006",
  "title": "A Bounded Convex Hilbert Domain with Vanishing Squeezing",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We construct a bounded convex balanced domain in the complex Hilbert space C direct-sum ell^2 that is not holomorphic homogeneous regular. The domain is Omega = {(z,w): |z| + ||w||_infinity < 1, ||w||_2 < 1}. Its squeezing function at (t,0) is bounded above and below by positive constant multiples of 1-t as t increases to 1. The upper bound follows from explicit holomorphic retractions onto polydiscs of increasing dimension and an elementary Hilbert-space Schwarz argument. This gives a negative answer to Question 5 in Kim's 2018 Oberwolfach report. No boundary smoothness is claimed, and the separate Question 6 about squeezing constants of arbitrary bounded homogeneous domains is not addressed. This is an AI-assisted, self-audited, unrefereed preprint; no external review, formal verification or absolute priority is claimed.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.CV",
    "math.FA"
  ],
  "keywords": [
    "squeezing function",
    "Hilbert space",
    "bounded convex domain",
    "holomorphic retract",
    "OWR-16412-006"
  ],
  "manuscript_version_date": "2026-10-19",
  "publication_date": "2026-10-19",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-19",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-16412-006/",
  "pdf_url": "https://eulersolve.org/papers/owr-16412-006/paper.pdf?v=ee9c3a26d59c",
  "doi": "10.5281/zenodo.23461147",
  "zenodo_record_url": "https://zenodo.org/records/23461147",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Question 5 is answered completely negatively by an explicit bounded convex balanced Hilbert domain whose squeezing tends to zero linearly. This is the current cleaned Hugging Face target. Question 6 on arbitrary bounded homogeneous domains is not resolved, so the older combined statement in our frozen v1.6 corpus remains only partially resolved. No smoothness is claimed. The classical ball-polydisc norm obstruction is credited. AI-assisted, self-audited and unrefereed; no independent review, formal certification or absolute-priority claim.",
  "files": {
    "paper.pdf": {
      "sha256": "ee9c3a26d59c6895c17196518dcb8f23ccd3ec1afaf03f036061bbfd90fe4859"
    },
    "source.zip": {
      "sha256": "3afbe33d2a79a207f6deca7a8e5e702a3093744c2a33b124e53d433332e6c6c2"
    },
    "verification_report.md": {
      "sha256": "9cc997b03c6bc2057e9526d0f9c9ce70365ac412a4786e440b290d74ea12523b"
    }
  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}