{
  "abstract": "We establish a comprehensive, non-perturbative mathematical framework that unifies the three foundational pillars of theoretical physics:\n\n1. The Einstein Field Equations of General Relativity: G_{\\mu\\nu} + \\Lambda g_{\\mu\\nu} = \\frac{8\\pi G}{c^4} T_{\\mu\\nu}\n\n2. The Schrödinger Wave Equation of Quantum Mechanics: i\\hbar \\frac{\\partial \\Psi}{\\partial t} = -\\frac{\\hbar^2}{2m}\\nabla^2\\Psi + V\\Psi\n\n3. The Governing Equation of Classical Nonlinear Dynamics: \\frac{d^2 \\mathbf{r}}{dt^2} + \\mathbf{f}\\left(\\frac{d\\mathbf{r}}{dt}, \\mathbf{r}, t\\right) = 0\n\nWe prove that these three formulations arise as exact, asymptotic projections of a single underlying master spectral system: the derived noncommutative spectral scheme \\mathcal{U} \\equiv \\operatorname{Spec}(\\mathcal{A}_{\\text{eff}}) defined over the global adèle class space \\mathbb{X}_{\\mathbb{Q}} \\equiv \\mathbb{A}_{\\mathbb{Q}}/\\mathbb{Q}^\\times, governed by the four-sector coordinate Dirac operator \\mathbf{D} = \\mathbf{D}_M + \\mathbf{D}_L + \\mathbf{D}_G + \\mathbf{D}_F on the zero-mean adèlic Hilbert space \\mathcal{H}_{\\mathbb{A}} = L_0^2(\\mathbb{X}_{\\mathbb{Q}}, d\\mu).\n\nThe architectural synthesis resolves the foundational obstructions of quantum gravity, macroscopic cat-state superpositions, dissipation, and continuum divergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "August Tudor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6emre21xr9x2w.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23515229",
  "fulltext_url": null,
  "id": "6emre21xr9x2w",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23515229",
  "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": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6emre21xr9x2w.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:27Z",
      "native_id": "23515229",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23515229"
    }
  ],
  "subjects": [],
  "title": "A Multi-Scale Spectral Framework for General Relativity, Quantum Mechanics, and Classical Nonlinear Dynamics",
  "title_text": "A Multi-Scale Spectral Framework for General Relativity, Quantum Mechanics, and Classical Nonlinear Dynamics",
  "type": "preprint",
  "updated_at": "2026-11-03T12:20:27Z",
  "url": "https://research.draconitic.com/paper/6emre21xr9x2w",
  "venue": "Zenodo",
  "versions": []
}