Skip to content
DraconiticResearch
Search Sources API
203,952 studies31 sourcesUpdated 28 min ago
PreprintCC BY 4.0Zenodo

Spectral‑Cluster Ontology in ZEBTS: Flytron Geometry, Axiomatic Framework, and Implications for RH, P vs NP, and the Mass Gap

  • Anatolii Mukha
Open at sourcePDFDOICite

Abstract

This paper presents a rigorous mathematical formulation of the Zero‑Entropy Boundary‑Topological Structure (ZEBTS) as a self‑consistent axiomatic framework unifying arithmetic, discrete geometry, and spectral theory. The central result is the Law of Unity — an exact triune isomorphism between arithmetic constraints, flytron network geometry, and the spectrum of a self‑adjoint operator HχH_\chiHχ, which encodes the Riemann xi‑function via a regularized determinant identity. We establish the existence of a finite, positive Yang–Mills–type mass gap ΔYM=log⁡2/LP\Delta_{\mathrm{YM}} = \log 2 / L_PΔYM=log2/LP as a structural consequence of the arithmetic rigidity axiom (ZA5) and prove its stability in the continuum limit and independence from regularization schemes. The framework yields a deterministic spectral realization of the Riemann zeros with exact multiplicities and provides a no‑go architecture: any classical construction that relaxes the integer weight condition or ignores the TC‑measure cannot reproduce the spectral data or maintain the mass gap. Numerical verifiability is ensured by explicit finite‑NNN algorithms and convergence criteria. The work closes key logical gaps in spectral approaches to the Riemann Hypothesis and the mass gap problem and positions ZEBTS as a classification theorem for such models.

Keywords: ZEBTS; Riemann Hypothesis; Hilbert–Pólya conjecture; mass gap; spectral realization; arithmetic–geometric–spectral isomorphism; no‑go theorem; flytron network; TC‑measure; regularized determinant.

Related

  1. The Extended Quantum Information Geometry System (EQIGS): A Deductive Framework Unifying Petz Monotone Metrics, Thermodynamic Length Dissipation Bounds, and Tensor-Network Curvature Transitions within the ZFC Axiomatic Bridge
    Seonggil Lee
    ZenodoPreprintCC BY 4.0Full textZenodo
  2. ZEBTS: An Axiomatic Framework for Spectral Arithmetic and the Riemann Hypothesis
    Anatolii Mukha
    ZenodoPreprintCC BY 4.0Full textZenodo
  3. The Operator–Spectral Framework of ZEBTS: A Unified Structure for Geometry, Arithmetic, and the Riemann Hypothesis
    Anatolii Mukha
    Zenodo (CERN European Organization for Nuclear Research)PreprintCC BY6 citedAlgebra & number theoryOpenAlex
  4. 无边之动的几何:形态的公理化构造 / Geometry of Boundless Motion: An Axiomatic Construction of Form
    Chao Qin
    Zenodo (CERN European Organization for Nuclear Research)Peer-reviewedCC BY8 citedGeometry & topologyOpenAlex
  5. The Profile Calculus: An Axiomatic Certification Framework for the ω ≤ 9/4 Matrix-Multiplication Exponent
    Mark Winston
    ZenodoPreprintCC BY 4.0Full textZenodo

Cite

BibTeXRIS
BibTeX
@misc{mukha2026spectralcluster,
  title = {{Spectral‑Cluster Ontology in ZEBTS: Flytron Geometry, Axiomatic Framework, and Implications for RH, P vs NP, and the Mass Gap}},
  author = {Anatolii Mukha},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23537859},
  url = {https://zenodo.org/records/23537859},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spectral‑Cluster Ontology in ZEBTS: Flytron Geometry, Axiomatic Framework, and Implications for RH, P vs NP, and the Mass Gap
AU  - Anatolii Mukha
PY  - 2026
DA  - 2026/10/21
PB  - Zenodo
DO  - 10.5281/zenodo.23537859
UR  - https://zenodo.org/records/23537859
AB  - This paper presents a rigorous mathematical formulation of the Zero‑Entropy Boundary‑Topological Structure (ZEBTS) as a self‑consistent axiomatic framework unifying arithmetic, discrete geometry, and spectral theory. The central result is the Law of Unity — an exact triune isomorphism between arithmetic constraints, flytron network geometry, and the spectrum of a self‑adjoint operator HχH_\chiHχ, which encodes the Riemann xi‑function via a regularized determinant identity. We establish the existence of a finite, positive Yang–Mills–type mass gap ΔYM=log⁡2/LP\Delta_{\mathrm{YM}} = \log 2 / L_PΔYM=log2/LP as a structural consequence of the arithmetic rigidity axiom (ZA5) and prove its stability in the continuum limit and independence from regularization schemes. The framework yields a deterministic spectral realization of the Riemann zeros with exact multiplicities and provides a no‑go architecture: any classical construction that relaxes the integer weight condition or ignores the TC‑measure cannot reproduce the spectral data or maintain the mass gap. Numerical verifiability is ensured by explicit finite‑NNN algorithms and convergence criteria. The work closes key logical gaps in spectral approaches to the Riemann Hypothesis and the mass gap problem and positions ZEBTS as a classification theorem for such models.  Keywords: ZEBTS; Riemann Hypothesis; Hilbert–Pólya conjecture; mass gap; spectral realization; arithmetic–geometric–spectral isomorphism; no‑go theorem; flytron network; TC‑measure; regularized determinant.
ER  -