{
  "abstract": "The continuum problem has remained unresolved since Cantor introduced the hierarchy of infinities and formulated the Continuum Hypothesis (CH). Gödel and Cohen demonstrated that CH is independent of ZFC, revealing a structural limitation of classical set theory: the continuum has no determinate size within the Cantorian ontology. This article presents a fundamentally new resolution based on the χ‑Spectral Ontology of Infinity, in which infinity, cardinality, continuum, and determinacy are reconstructed as spectral objects of a single universal operator 𝑇 𝜒 . Within this operator–spectral framework, χ‑boundary projection 𝑃 𝜒 , χ‑spectral layers 𝐿 ( 𝑘 ) , χ‑spectral measure μ, and χ‑cardinality define a complete, computable, and physically meaningful structure of the continuum. The central result is the χ‑Spectral Continuum Collapse Theorem, proving that the classical continuum ∣ 𝑅 ∣ collapses to the finite χ‑spectral cardinality ∣ 𝑅 ∣ 𝜒 = 𝜇 ( 𝐿 𝜒 ) , and that no intermediate χ‑cardinalities exist between ∣ 𝑁 ∣ 𝜒 and ∣ 𝑅 ∣ 𝜒 . This collapse eliminates all independence phenomena of ZFC, including CH, GCH, MM⁺⁺, and (*), and establishes a complete, anti‑Cantorian universe in which infinity is finite‑layered, spectral, computable, and physically real. The continuum problem is resolved not by extending ZFC, but by replacing its ontology with χ‑Reality.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher , retired person Kharkiv , Ukraine"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Anatolii Mukha",
      "orcid": "0009-0005-4614-6667"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bz27jxdv9amxp.bib",
  "cited_by": 24,
  "doi": "10.33774/coe-2026-t91qw",
  "fulltext_url": null,
  "id": "bz27jxdv9amxp",
  "issns": [],
  "landing_url": "https://doi.org/10.33774/coe-2026-t91qw",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7204883831",
  "pdf_url": "https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6a9fe8a2810b9dcc82b7acda/original/spectral-resolution-of-the-continuum-problem-a-unified-operator-spectral-framework-beyond-zfc.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bz27jxdv9amxp.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T13:20:40Z",
      "native_id": "W7204883831",
      "source": "openalex",
      "url": "https://doi.org/10.33774/coe-2026-t91qw"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Advanced Topology and Set Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "χ‑Spectral Resolution of the Continuum Problem: A Unified Operator‑Spectral Framework Beyond ZFC",
  "title_text": "χ‑Spectral Resolution of the Continuum Problem: A Unified Operator‑Spectral Framework Beyond ZFC",
  "type": "preprint",
  "updated_at": "2026-11-08T13:20:35Z",
  "url": "https://research.draconitic.com/paper/bz27jxdv9amxp",
  "venue": null,
  "versions": []
}