Theorem on the Evolution of Emergent Time in a Coherently Frustrated Topological Phase: Analytical Derivation of weff and Prediction for the Sandage-Loeb Test

This letter formalizes the mathematical apparatus for the evolution of macroscopic time within the framework of the Coherently Frustrated Topological Phase (CFTP) of the vacuum with a discrete local symmetry H₄. An exact equation for the evolution of time is derived, from which the effective equation of state for the illusory “dark energy” w_eff ≈−0.992 analytically follows, consistent with the latest DESI survey data. As an absolute test of the theory’s falsifiability, a modified equation for redshift drift (the Sandage-Loeb test) is derived, mathematically unifying the effects of topological time drift and kinematic mass dissipation. It is shown that the combined action of these geometric effects mimics positive acceleration across the entire cosmological range; however, CFTP predictions radically differ from the standard ΛCDM model in both the amplitude and sign of the drift at high redshifts. This provides a clear, quantitative criterion for verifying the theory at next-generation observatories (ELT, SKA).