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

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.