{
  "abstract": "This record contains 11 visual posters from the Villaber Universe Formula Collection by Ruel Villaber, Mandaluyong City, Philippines, 2026.\n\nContents:\n\n1. Millennium Prize Overview & Villaber Invariant (0.5+0.5=1)\n\n2. MSC2020 Classification Study (All=1)\n\n3. Riemann Hypothesis - Visual Study\n\n4. P vs NP - Visual Study\n\n5. Navier-Stokes Existence and Smoothness - Visual Study\n\n6. Yang-Mills Existence and Mass Gap - Visual Study\n\n7. Birch and Swinnerton-Dyer (BSD) Conjecture - Visual Study\n\n8. Hodge Conjecture - Visual Study\n\n9. Collatz Conjecture (3n+1) - Visual Study\n\n10. Collatz Generalization (k·n+1) - Visual Study\n\n11. Front Cover / Main Collection Poster\n\nEach poster presents the standard statement of the problem, key formulas (Riemann zeta, P vs NP, Navier-Stokes equations, Yang-Mills field strength F_mn, L-function rank, Hodge decomposition, Collatz map C_k(n)), worked examples (e.g., Collatz 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1), and the author's speculative framework summarized as All=1 and 0.5+0.5=1.\n\nNote: This is a personal artistic and exploratory collection for visualization and discussion. It does not contain peer-reviewed proofs that the Millennium Problems or Collatz Conjecture are solved. The six Millennium Problems (Riemann, P vs NP, Navier-Stokes, Yang-Mills, BSD, Hodge) and the Collatz Conjecture remain open as of 2026. The C_k generalization does not converge to 1 for all k; for example, k=5 has a known cycle 13 -> 66 -> 33 -> 166 -> 83 -> 416 -> 208 -> 104 -> 52 -> 26 -> 13.\n\nAuthor: Ruel Villaber\n\nLocation: Mandaluyong City, Metro Manila, Philippines\n\nYear: 2026",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Ruel Villaber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2yrhjah49j417.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23641728",
  "fulltext_url": null,
  "id": "2yrhjah49j417",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23641728",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
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  "pmcid": null,
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2yrhjah49j417.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:14Z",
      "native_id": "23641728",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23641728"
    }
  ],
  "subjects": [],
  "title": "Villaber Universe Formula Collection: A Visual Study of Millennium Prize Problems, Collatz Maps, and the All=1 Framework - 11 Posters",
  "title_text": "Villaber Universe Formula Collection: A Visual Study of Millennium Prize Problems, Collatz Maps, and the All=1 Framework - 11 Posters",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:14Z",
  "url": "https://research.draconitic.com/paper/2yrhjah49j417",
  "venue": "Zenodo",
  "versions": []
}