{
  "schema_version": 1,
  "problem_number": "AIM-SEVERAL_COMPLEX_VARIABLES-0021",
  "title": "A Nonremovable Meromorphic Map into a Ball on a Codimension-Two Wedge",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We construct a meromorphic germ in C^3 that is holomorphic from an attached wedge into the open unit ball, extends continuously to its real-algebraic generic edge with values on the unit sphere, and nevertheless has no holomorphic extension to a full neighborhood of the edge point. The edge has real codimension two and CR dimension one. An explicit rational sphere identity is combined with a holomorphic factor that is unimodular on the edge and suppresses interior norm growth. The boundary limit holds along every wedge approach, not just normal rays. This gives a negative answer to the arbitrary-generic-edge question posed by Meylan in the 2010 AIM CR-mapping problem list, with convergence understood from inside the ball. The example is nonminimal and has a continuous but nondifferentiable boundary map; it makes no claim about strengthened minimal-source or smooth-boundary-map formulations. The manuscript is AI-assisted, self-audited and unrefereed. No independent review, formal verification or absolute priority is claimed.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.CV"
  ],
  "keywords": [
    "several complex variables",
    "CR geometry",
    "meromorphic mapping",
    "wedge extension",
    "unit ball",
    "counterexample",
    "AIM-SEVERAL_COMPLEX_VARIABLES-0021"
  ],
  "manuscript_version_date": "2026-10-10",
  "publication_date": "2026-10-10",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-10",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-several-complex-variables-0021/",
  "pdf_url": "https://eulersolve.org/papers/aim-several-complex-variables-0021/paper.pdf?v=bdc65c95be98",
  "doi": "10.5281/zenodo.23272827",
  "zenodo_record_url": "https://zenodo.org/records/23272827",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "A real-algebraic generic nonminimal codimension-two edge in C^3 admits a meromorphic germ holomorphic into the unit ball on a full attached wedge, continuous on the wedge together with its edge with unit-norm values at every edge point, yet having no holomorphic extension to a full neighborhood of the origin. This refutes the arbitrary-generic-edge AIM question with the explicit all-approaches from-inside boundary interpretation; it makes no minimal-source or smooth-boundary-map claim. AI-assisted, self-audited and unrefereed; no independent review, formal verification or certified priority is claimed.",
  "files": {
    "paper.pdf": {
      "sha256": "bdc65c95be981cf236fc18f56e6d74ea977079bc7c725a1341f93c3f76a2ddac"
    },
    "source.zip": {
      "sha256": "be7e2789dfb2a0e87a87c518fbfdd9c48a05bac88df24da871e7492580041e18"
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    "verification_report.md": {
      "sha256": "b341d435cb4629c5cf7ffe14919050e50a5cb5a5458fbbb248e6d2b7ade0f13d"
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  },
  "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."
}