{
  "abstract": "This work presents the construction of a self‑adjoint operator 𝐷 𝜒 whose spectrum reproduces the zeros of the Riemann zeta function and whose trace generates the Euler product. The operator is derived as a mathematical necessity from requirements imposed by 𝜁 ( 𝑠 ) . Its potential consists of a component 𝑉 0 ( 𝑢 ) = 𝑎 cosh ⁡ ( 𝑏 𝑢 ) , yielding the Riemann–von Mangoldt density, and a perturbation 𝛿 𝑉 ( 𝑢 ) = ∑ 𝑝 𝑐 𝑝 𝐺 ( 𝑢 − ln ⁡ 𝑝 ) , encoding prime structure through Gaussian localisation. The square 𝐷 𝜒 2 = − ∂ 𝑢 2 + 𝑉 2 − 𝑉 ′ reduces to a Sturm–Liouville operator with discrete spectrum. The smooth component is unique; no other even, confining potential reproduces the required logarithmic correction. The arithmetic coefficients satisfy ∣ 𝐶 𝑝 ∣ ∼ 𝑝 − 1 / 2 , with measured exponent 0.552 ± 0.035 , and all cosine coefficients 𝐴 𝑝 > 0 , in agreement with the Weil formula. The perturbative trace yields the principal term ∑ 𝑝 ln ⁡ 𝑝 / 𝑝 𝑠 , while higher Born terms reproduce all Euler factors. The operator 𝐷 𝜒 is unique within its class, and its triune structure—continuum, discreteness, synthesis—is mathematically necessary. Numerical experiments (200 zeros, 40 primes, 𝑅 2 = 0.938 , RMS improvement ×106) confirm predictions. If the arithmetic perturbation converges for all primes, the Riemann Hypothesis follows as a spectral consequence of self‑adjointness.",
  "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/24by0hnt2msyf.bib",
  "cited_by": 9,
  "doi": "10.33774/coe-2026-gwf17",
  "fulltext_url": null,
  "id": "24by0hnt2msyf",
  "issns": [],
  "landing_url": "https://doi.org/10.33774/coe-2026-gwf17",
  "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": "W7212593891",
  "pdf_url": "https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6aa7d037d1922e37d54ff5d5/original/proof-of-universality-of-the-operator-d-in-zebts-theory-from-spectral-ontology-to-the-law-of-unity-of-the-triune-substance.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24by0hnt2msyf.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:20:59Z",
      "native_id": "W7212593891",
      "source": "openalex",
      "url": "https://doi.org/10.33774/coe-2026-gwf17"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Analytic Number Theory Research",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Proof of Universality of the Operator Dχ in ZEBTS Theory: From Spectral Ontology to the Law of Unity of the Triune Substance",
  "title_text": "Proof of Universality of the Operator Dχ in ZEBTS Theory: From Spectral Ontology to the Law of Unity of the Triune Substance",
  "type": "preprint",
  "updated_at": "2026-11-06T13:20:21Z",
  "url": "https://research.draconitic.com/paper/24by0hnt2msyf",
  "venue": null,
  "versions": []
}