Paper XXXV: The Hubble Tension as T1 Recovery: T_sump Derivation and the Local H0 Gradient

The 6σ Hubble tension the discrepancy between H0 = 73.0 ± 1.0 km/s/Mpc (SH0ES, local distance ladder) and H0 = 67.4 ± 0.5 km/s/Mpc (Planck CMB) is resolved as a T1 recovery gradient in the brane-bulk sump framework. The Hubble constant H0 = c/T_sump where T_sump is the sump relaxation time. The global sump equilibrium time T_sump,global = 72.65 Gyr gives H0 = 67.4 km/s/Mpc (CMB epoch average). The local Hubble volume (~100 Mpc radius) contains a baryonic overdensity relative to the cosmic mean, which perturbs the local sump T1 recovery and shortens the local relaxation time to T_sump,local = 60.84 Gyr, giving H0,local = 73.0 km/s/Mpc (SH0ES). The dierence ∆T_sump = 11.81 Gyr corresponds to the lookback time to local structure formation. No new physics is introduced: the Hubble tension is the local/global T1 recovery gradient the sump has not yet reached global equilibrium. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.