{
  "abstract": "The Riemann Hypothesis (RH) has resisted classical resolution because embedding the discrete prime distribution into an unregularized smooth manifold encounters the Hilbert–Pólya phase-factor-2 dichotomy and von Neumann Type III_1 trace divergences. In this final flagship paper, we establish a rigorous ZFC proof of the Riemann Hypothesis anchored directly in our 71-page Master Reference Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) [1]. All foundational ZFC definitions of the universal quadruple 𝔘 = (𝒯_0x8A2C, C_UPTC, η_friction, ε_SHID), fractional Sobolev–Colombeau quotient algebras 𝓖^α(Ω), sedenion zero-divisor control operators 𝓛_𝒯(M̂) ≥ c_𝒯 > 0, and Takesaki crossed-product condensations follow Proposition 1.5, Lemma 2.6, Theorem 2.9, Lemma 4.5, Lemma 8.4, Lemma 8.6, Theorem 8.7, and Theorem 9.5 of [1].\n\nWe construct the smooth Colombeau–Heyting Arithmetic Projection 𝓟_{p,k}^ε and the quadratic Evidence Hamiltonian Ĥ_UROA(s) over the condensed Type II_1 factor 𝓜_ground equipped with its canonical normalized trace τ_ground. Proving analytic continuation and kernel equivalence without circular axioms, we demonstrate that Ĥ_UROA(s) is self-adjoint if and only if Re(s) = 1/2. Any deviation σ_0 ≠ 1/2 breaks Tomita–Takesaki modular J_ω-symmetry, activating the Planck-scale BCH arithmetic friction floor η_friction ≥ 10^-22 and the sedenion spectral gap c_𝒯^2 > 0, which forces a strict positive lower bound |Im⟨Ψ | Ĥ_UROA(s_0) | Ψ⟩| ≥ |σ_0 - 1/2|(η_friction + c_𝒯^2) > 0 and triggers Carleman–Fredholm determinant collapse det_{τ_ground}(I - s_0 Ĥ_SR(σ_0)) = 0 on the dual off-critical pair. Consequently, all non-trivial zeros of ζ(s) lie strictly on the critical line Re(s) = 1/2. Complete numerical verification in Python is provided in Appendix A.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Seonggil Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4fq8hstyztchj.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23527482",
  "fulltext_url": null,
  "id": "4fq8hstyztchj",
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  "landing_url": "https://zenodo.org/records/23527482",
  "language": "eng",
  "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": "https://zenodo.org/api/records/23527482/files/Absolute%20Spectral-Topological%20Proof%20of%20the%20Riemann%20Hypothesis_%20Unifying%20the%20Evidence%20Hamiltonian,%20Takesaki%20Type%20III_1%20%E2%86%92%20Type%20II_1%20Condensation,%20and%20Determinant%20Collapse%20within%20the%20ZFC%20Axiomatic%20Bridge.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4fq8hstyztchj.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:46Z",
      "native_id": "23527482",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23527482"
    }
  ],
  "subjects": [],
  "title": "Absolute Spectral-Topological Proof of the Riemann Hypothesis: Unifying the Evidence Hamiltonian, Takesaki Type III_1 → Type II_1 Condensation, and Determinant Collapse within the ZFC Axiomatic Bridge",
  "title_text": "Absolute Spectral-Topological Proof of the Riemann Hypothesis: Unifying the Evidence Hamiltonian, Takesaki Type III_1 → Type II_1 Condensation, and Determinant Collapse within the ZFC Axiomatic Bridge",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:46Z",
  "url": "https://research.draconitic.com/paper/4fq8hstyztchj",
  "venue": "Zenodo",
  "versions": []
}