The Hubble Tension necessitates New Physics in the early universe. While our previous sub mission validated the Unified Applicable Time (UAT) framework observationally (kearly ≈ 0.967), this manuscript rigorously tests the UAT’s core theoretical coherence: the hypothesis that **Dark Energy (ΩΛ) is not a free component but an emergent consequence of the universal temporal struc ture**. We impose the physical constraint of a flat universe (ΩTotal = 1) and utilize χ2 minimiza tion against Baryon Acoustic Oscillation (BAO) data, fixing H0 = 73.00 km/s/Mpc. This ”UAT Pure” scenario yields an optimal quantum correction parameter kearly = 0.95501 and an emergent ΩΛ =0.69909. Crucially, the fit quality improves by 39.6% (χ2 = 53.708) compared to standard ΛCDM (χ2 =88.860), providing decisive evidence. The consistency between this theoretically rigid result and the previous observational MCMC findings confirms the UAT framework’s internal el egance and supports the conclusion that the vacuum energy we observe is the required geometric manifestation of the UAT quantum correction at large scales. miguel_percudani@yahoo.com.ar (+5411) 2923 463661