{
  "abstract": "We develop the χ‑Unified Operator Law, Lχ = Ord(Tχ), as a complete non‑commutative operator‑spectral framework underlying all physical phenomena. In this formulation, spacetime geometry, gauge fields, quantum states, classical interactions, cosmological expansion, and informational measures arise strictly as low‑dimensional GNS‑projections of the universal operator Tχ acting on an ultrametric substrate Mχ. The full operator chain Mχ → Tχ → Φχ → Pχ → Hχ → Aχ → Bχ → Iχ constitutes a mathematically closed C\\*-algebraic hierarchy incorporating Connes spectral triples, Tomita–Takesaki modular flow, non‑commutative curvature, and χ‑boundary invariants. We show that classical and quantum theories—Newtonian mechanics, Maxwell electrodynamics, Schrödinger dynamics, quantum field theory, and Einstein gravity—emerge as smooth‑phase, linear, or low‑spectral‑curvature limits of χ‑operator dynamics. Singularities, vacuum divergences, and measurement collapse are resolved through χ‑phase gradients, χ‑boundary tension, and modular automorphisms. Cosmological acceleration arises from χ‑phase pressure rather than ΛCDM, predicting a dynamic equation‑of‑state wχ(z) ≠ −1. The framework yields five falsifiable predictions: (1) discrete χ‑phase jumps ΔΦχ = nπ in ballistic Dirac materials; (2) boundary‑driven transparency collapse at Bχcrit; (3) deterministic spectral branching in ultra‑high‑Q vacuum cavities; (4) χ‑modulated non‑thermal horizon emission channels; (5) log‑oscillatory modulations in the primordial power spectrum. These signatures span condensed matter, quantum optics, astrophysics, and cosmology. Our results establish Ord(Tχ) as a unified, non‑perturbative operator foundation for physical law, replacing geometric and field‑theoretic ontologies with a single spectral‑operator architecture.",
  "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/1k8z0pm0gry4e.bib",
  "cited_by": 11,
  "doi": "10.5281/zenodo.21722101",
  "fulltext_url": null,
  "id": "1k8z0pm0gry4e",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.21722101",
  "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",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7171953369",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-31",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/1k8z0pm0gry4e.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:20:59Z",
      "native_id": "W7171953369",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.21722101"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Advanced Operator Algebra Research",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "χ‑Spectral Reconstruction of the Klein Paradox: Operator‑Topological Origin of χ‑Current in Strong Fields",
  "title_text": "χ‑Spectral Reconstruction of the Klein Paradox: Operator‑Topological Origin of χ‑Current in Strong Fields",
  "type": "preprint",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/1k8z0pm0gry4e",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}