{
  "abstract": "This paper establishes a rigorous proof of the Riemann Hypothesis by constructing a densely defined, self-adjoint operator ABT on a weighted Hilbert space HBT\n\nwhose spectrum is in bijective correspondence with the non-trivial zeroes of the Riemann\n\nZeta function. By anchoring the algebraic center of inversion at the exact fractional\n\ncoordinates C(︁−1/2, −1/2)︁ under a stratified linear pencil of odd slopes km = 2m + 1, we\n\nconstruct a geometric sieve that maps grid positions p yielding composite odd integers\n\nN = 2p + 1 onto the lattice grid Z2. The prime locations are isolated as a strict topological\n\ncomplement variety Mprime. Utilizing the U(1) local gauge symmetries of the resulting\n\nMittag-Leffler meromorphic derivative M(z) and applying the Guinand-Weil trace formula,\n\nwe demonstrate that the eigenvalue spectrum satisfies strict spectral completeness against\n\nthe von Mangoldt density. The self-adjointness of the core operator forces all non-trivial\n\neigenvalues to be strictly real, mapping the non-trivial zeroes ρn identically onto the critical\n\nline Re(s) = 1/2.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Silvio Gabbianelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3pevtecvzhnae.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23480087",
  "fulltext_url": null,
  "id": "3pevtecvzhnae",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23480087",
  "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,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3pevtecvzhnae.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:58Z",
      "native_id": "23480087",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23480087"
    }
  ],
  "subjects": [],
  "title": "ON THE SPECTRAL REALIZATION OF THE GEOMETRIC SIEVE VIA CENTERED LINEAR PENCILS AND SELF-ADJOINT OPERATORS",
  "title_text": "ON THE SPECTRAL REALIZATION OF THE GEOMETRIC SIEVE VIA CENTERED LINEAR PENCILS AND SELF-ADJOINT OPERATORS",
  "type": "preprint",
  "updated_at": "2026-11-02T12:20:58Z",
  "url": "https://research.draconitic.com/paper/3pevtecvzhnae",
  "venue": "Zenodo",
  "versions": []
}