{
  "abstract": "ZEBTS is an operator-spectral framework in which all domains of reality — quantum, geometric, gravitational, cosmological, informational, and cognitive — are postulated to arise from a single self-adjoint elliptic operator T_chi acting on a compact 2-dimensional Riemannian manifold S2_chi (the chi-sphere). The mathematical apparatus is proven: the spectral theorem (von Neumann, 1929) guarantees self-adjointness and real discrete spectrum; the Rellich lemma guarantees compact resolvent; Weyl asymptotics, Agmon localization, Kato-Rellich perturbation theory, and heat-kernel spectral geometry provide the functional-analytic foundation. The physical interpretation is postulated (the chi-Principle): all phenomena correspond to spectral properties of T_chi, partial geometric reconstruction via spectral invariants, and boundary stability governed by a self-adjoint operator S_chi. This article introduces four new mathematical structures that strengthen the framework to publication-ready rigour: (1) a generalized trace formula linking spectral sums to geometric integrals; (2) a zeta-regularized determinant det_zeta(T_chi) with meromorphic continuation of the spectral zeta function zeta_chi(s); (3) a postulated determinant-zeta correspondence identifying the Riemann zeta function as a derived invariant of T_chi; (4) an arithmetic Frobenius structure linking spectral weights to multiplicative number theory. Variational spectral bounds, numerical protocols with guaranteed error estimates, and experimental falsifiability criteria are provided throughout. For the canonical chi-sphere, numerical verification confirms: Weyl asymptotics (lambda_n ~ C * n, R^2 > 0.9999), convergence of zeta_chi(s) for Re(s) > 1, heat-kernel recovery of scalar curvature (R = 2), and trace-formula volume-term dominance. All postulates are explicitly identified; the mathematical foundation is proven independently of them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anatolii Mukha",
      "orcid": "0009-0005-4614-6667"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qzsm6b4jzqxt.bib",
  "cited_by": 6,
  "doi": "10.5281/zenodo.22896277",
  "fulltext_url": null,
  "id": "6qzsm6b4jzqxt",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.22896277",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214026557",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/6qzsm6b4jzqxt.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T13:20:40Z",
      "native_id": "W7214026557",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.22896277"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Analytic Number Theory Research",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Operator–Spectral Framework of ZEBTS: A Unified Structure for Geometry, Arithmetic, and the Riemann Hypothesis",
  "title_text": "The Operator–Spectral Framework of ZEBTS: A Unified Structure for Geometry, Arithmetic, and the Riemann Hypothesis",
  "type": "preprint",
  "updated_at": "2026-11-06T13:20:22Z",
  "url": "https://research.draconitic.com/paper/6qzsm6b4jzqxt",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}