Spectral construction of time in ZEBTS via a flightron network

This paper presents a spectral construction of global time within the Zero‑Entropy Background Topological Structure (ZEBTS) framework, realized through the dynamics of a flytron network on an evolving discrete graph. We demonstrate how space emerges as a metric structure defined by flytron amplitudes, and prove that under spectral control conditions the sequence of discrete geometries converges to a continuum Riemannian geometry in the Gromov–Hausdorff sense (Section 2, Section 6). Time is defined operationally as a measurable quantity derived from the collective accumulation of flytron phases; its global step Δt(t)\Delta t(t)Δt(t) is expressed in terms of directly observable network averages (Section 3). We show that gravity is encoded in the gravitational potential and manifests through its influence on local time rates and energy spectra, while quantum behavior arises from the wave‑like interpretation of flytrons, path‑sum probabilities, and a spectral uncertainty principle (Section 4, Section 5). A central result is the intrinsic avoidance of geometric degeneracies and singularities via a dynamically maintained spectral gap condition λ2(LGt)≥δmin⁡\lambda_2(L_{G_t}) \ge \delta_{\min}λ2(LGt)≥δmin. We prove that this condition prevents edge collapse and connectivity loss, and verify its persistence numerically in the ZEBTS‑SUPER implementation (Section 3, Appendix A). The same platform is used to confirm gravity‑induced time dilation and the modification of interference patterns under gravitational influence (Section 7). We construct a discrete analogue of the Schrödinger equation governed by the Flytronus operator, yielding a unified dynamical description where kinetic, potential, and internal flytron contributions are consistently combined (Section 4). The computational realizability of ZEBTS is demonstrated through reproducible scripts, control tests, and convergence studies (Section 7, Appendix B). The paper positions ZEBTS within the broader landscape of quantum gravity and discrete geometry approaches, highlighting its distinctive features: unification around a single dynamical object (the flytron), an operational definition of time tied to measurable phases, explicit coupling between geometry and quantum coherence, and built‑in singularity avoidance via spectral control. We outline open questions and future directions, including the inclusion of spin and fermions, refinement of the continuum limit, and potential experimental tests via quantum simulators and synthetic gauge fields. The results establish ZEBTS as a coherent and testable framework that offers a novel perspective on the unity of fundamental physical laws.