Unified Framework of Space, Time, Gravity and Quantum Phenomena in ZEBTS: A Topological and Spectral Construction via Flytron Dynamics

This paper presents the Zero‑Entropy Background Topological Structure (ZEBTS) framework — a unified paradigm for fundamental physics in which space, time, gravity, and quantum phenomena emerge from a single dynamical object: the flytron on an evolving discrete graph. We rigorously establish the geometric foundations of ZEBTS, demonstrating how a discrete metric defined by flytron amplitudes converges to a continuum Riemannian geometry in the Gromov–Hausdorff sense under spectral control conditions. Time is reinterpreted as an observable quantity derived from collective phase accumulation, directly linking quantum measurement to the evolution of the network. We derive a discrete analogue of the Schrödinger equation governed by the Flytronus operator and show how quantum interference, uncertainty, and localization arise naturally from the path‑sum formulation on the graph. A key result is the intrinsic avoidance of singularities via a spectral gap condition (λ2≥δmin⁡λ_2 ≥ δₘᵢₙλ2≥δmin) that is maintained dynamically, without external cutoffs or ad hoc regularization. This mechanism is numerically verified in the ZEBTS‑SUPER implementation, where we confirm the persistence of the spectral gap, observe gravity‑induced time dilation, and demonstrate the modification of interference patterns under gravitational influence. The paper further positions ZEBTS within the broader landscape of quantum gravity and discrete geometry approaches, highlighting its distinctive features: unification around a single object, operational definition of time, explicit coupling between geometry and quantum coherence, and computational realizability. We outline open questions and future directions, including the inclusion of spin and fermions, the 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.