Empirical Verification of TTDS Evolving Gravity (G_σ) Against JWST High-Redshift Galaxy Formation and the Hubble Tension (TTDS-p.V)

Two of the most severe anomalies confronting contemporary ΛCDM cosmology are the "Hubble Tension" (the discrepancy between early and late-universe expansion rates) and the discovery by the James Webb Space Telescope (JWST) of massive, fully formed galaxies at extreme redshifts (z > 10) that defy classical structure formation timelines. This fifth paper in the Topological Theory of Deformed Space (TTDS) series provides a strict, parameter-free analytical resolution to both crises without postulating Dark Matter or modified Dark Energy. By enforcing cellular budget conservation within a 100% elastic, discrete 3D+1D vacuum lattice (V + Mtot·KT = Vmax), this work derives the exact functional dependence of the effective gravitational constant Gσ(V, z) and the vacuum relaxation rate Hσ(z). The paper analytically proves that in the volume-depleted early universe, the topological scattering cross-section scaled as (V/V₀)¹/³, linearly amplifying effective gravity according to the law Gσ(z) = G₀(1+z), while logarithmically damping photon relaxation. This evolving gravity mechanism drastically compresses early baryonic free-fall timescales, accurately predicting the rapid assembly of extreme JWST milestones (e.g., JADES-GS-z14-0) within ~294 Myr, and smoothly bridges the CMB (67.0 km/s/Mpc) and local (73.0 km/s/Mpc) Hubble expansion rates.