ZEBTS: From Flytron Networks to Quantum Physics

This paper presents the ZEBTS (Zero‑parameter, Emergent, Bound‑state, Topological, Spectral) framework—a unified construction in which quantum principles, the Yang–Mills mass gap, and structural links to arithmetic are derived from discrete spectral geometry and topology, without introducing free parameters or external postulates. The core object is the spectral Flytronus operator OFly(N)=(DF(N))2\mathcal{O}_{\mathrm{Fly}}^{(N)} = (D_F^{(N)})^2OFly(N)=(DF(N))2, built from a discrete Dirac operator DF(N)D_F^{(N)}DF(N) on a finite graph GNG_NGN equipped with holonomies and cluster structure. Through the APS‑triunity TN=(ΣN,GN,Eχ(N))T_N = (\Sigma_N, G_N, E_\chi^{(N)})TN=(ΣN,GN,Eχ(N)), the framework combines geometry, topology, and boundary conditions to control the spectrum and ensure stability of the Atiyah–Patodi–Singer (APS) index I0I_0I0 and a topological‑curvature spectral gap γTC>0\gamma_{\mathrm{TC}} > 0γTC>0. Key results include: (i) a rigorous derivation of quantum features (noncommutativity, discreteness of the spectrum, superposition, geometric correlations) from the underlying discrete geometry; (ii) an analytical proof of the mass gap via positive curvature estimates and spectral stability; (iii) a structural correspondence between arithmetic data (encoded in the operator ΘN\Theta_NΘN) and spectral resonances, pointing to a geometric realization of number‑theoretic patterns. Small‑network examples (N=3,4N=3,4N=3,4) illustrate how these effects manifest concretely, while asymptotic relations to standard quantum mechanics clarify the continuum limit. The ZEBTS framework differs from existing approaches by constructing geometry and dynamics simultaneously via spectral operators on networks, rather than imposing quantization on classical structures or building models “on top” of known theories. Matter, void, and physical laws emerge as aspects of a single topological‑spectral construction, offering a logically closed, parameter‑free foundation for fundamental physics.