[28]Connectivity Geometry: Topological Frustration of Dark Energy and the Evolution of the Equation of State

Current high-precision survey data have preliminarily indicated that the dark energy equation of state w may not be strictly equal to -1. Based on the framework of connectivity geometry, this paper starts from the first principles of the underlying discrete spin network and demonstrates that the accelerated expansion of the universe is a geometric relaxation effect during macroscopic coarse-graining. By introducing the odd-even topological frustration mechanism of network sub-chains, we derive the evolution law of the residual vacuum energy density and strictly solve the fluid continuity equation. The core conclusion is that the dark energy equation of state exhibits a tiny but extremely deterministic redshift evolution, yielding a parameter-free exact prediction w ≈ -0.980 at z=0. This analytical solution provides a Decisive Test for future high-precision surveys.