{
  "schema_version": 1,
  "problem_number": "OWR-17464-019",
  "title": "Independent Sets in Two-Regular Uniform Hypergraphs",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For every integer r >= 2, we prove the Balogh-Bollobas-Narayanan independent-set bound for finite simple r-uniform, 2-regular hypergraphs. If such a hypergraph has n vertices, its number of weak independent sets is at most (2^(2(r-1)) + 3(2^(r-1)-1)^2)^(n/(2r)). The proof uses the edge-cover dual and regional entropy inequalities of Sarantis, Tetali and Zheng. An edge-and-odd-cycle factor can be chosen with all its odd cycles induced, by reducing chords. A uniform transfer-matrix estimate handles the remaining closed cycles. This extends the previously stated degree-two cases, odd r and r = 4, to all uniformities without a finite rooted-region enumeration. The general-degree conjecture for d >= 3 is not resolved. This is a self-audited, AI-assisted, unrefereed preprint; no independent review, formal certification or exhaustive priority determination is asserted.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.CO"
  ],
  "keywords": [
    "independent sets",
    "regular hypergraphs",
    "edge covers",
    "entropy",
    "odd-cycle factor",
    "OWR-17464-019"
  ],
  "manuscript_version_date": "2026-10-18",
  "publication_date": "2026-10-18",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-18",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-17464-019/",
  "pdf_url": "https://eulersolve.org/papers/owr-17464-019/paper.pdf?v=8799bd763e2b",
  "doi": "10.5281/zenodo.23457189",
  "zenodo_record_url": "https://zenodo.org/records/23457189",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "The complete theorem covers finite simple r-uniform, 2-regular hypergraphs for every integer r >= 2. The general-degree conjecture for d >= 3 is not resolved; no whole-source closure is claimed. The dual edge-cover, entropy, pair and doubling methods of Sarantis, Tetali and Zheng are credited. AI-assisted, self-audited and unrefereed; no independent review, formal certification or absolute-priority claim.",
  "files": {
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      "sha256": "8799bd763e2b5dbcbcf54a0dbea1bf754a0deb41d6b96c395fa815d946d57042"
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    "source.zip": {
      "sha256": "92b0e83bf49a2f415a99c97b3abf943c8a3ac422593a367f580db2d6f0d0e81a"
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    "verification_report.md": {
      "sha256": "cced0bbd7a51cbf7dffaa032d528a22088b5b0767317513692a3738b742e8f30"
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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."
}