{
  "schema_version": 1,
  "problem_number": "OWR-720-006",
  "title": "Parameter Holes in Bessel Wave Packet Systems",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We prove that a Bessel wave packet system generated by a nonzero L2 function, with an arbitrary discrete parameter set in the affine Weyl-Heisenberg group, has a parameter set missing a left translate of every compact set. Hence all lower densities in the Czaja-Kutyniok-Speegle convention vanish and the lower Beurling dimension is zero. The proof uses explicit left Folner averaging of translated counting measures and the known divergent continuous coefficient integral. No product structure or extra generator regularity is assumed. The necessary nonzero-generator qualification and the degenerate zero exception are explicit. This is an unrefereed preprint with an originating-researcher self-audit, not independent review, formal verification or a certified priority claim. The manuscript was developed with OpenAI Codex assistance. Source dataset record: OWR-720-006 (ulamai/UnsolvedMath v1.6.0). The manuscript discloses OpenAI Codex assistance.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "keywords": [
    "OWR-720-006",
    "Bessel wave packet system",
    "Beurling density",
    "Folner averaging"
  ],
  "manuscript_version_date": "2026-10-24",
  "publication_date": "2026-10-24",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-24",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-720-006/",
  "pdf_url": "https://eulersolve.org/papers/owr-720-006/paper.pdf?v=b4753c7e2134",
  "doi": "10.5281/zenodo.23621541",
  "zenodo_record_url": "https://zenodo.org/records/23621541",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "For every nonzero L2(R) generator, a Bessel wave packet system with arbitrary discrete parameter set has an empty left translate of every compact set, hence every source lower density and its lower dimension are zero. The literal unqualified source wording is false for the zero generator; the explicit log-grid exception supplies the complete case distinction. The substantive theorem assumes a nonzero generator. The degenerate zero-generator exception is explicit. This preprint is AI-assisted, self-audited and unrefereed; no independent or formal verification or certified novelty or absolute-priority claim is made.",
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      "sha256": "b4753c7e213459e2c1b7f8ced3372a27d7b83d795cea6a710644f02108570736"
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    "source.zip": {
      "sha256": "4cd1ca4830cb0086b962c313eadb63aff1bd106d47913c4e1660121df8df2a3c"
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    "verification_report.md": {
      "sha256": "24c91401918a40d6b737a1094aa4c36676df2e6446eb1ed4dc36786b77b3d194"
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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."
}