Newton's constant G is derived as the baseline brane-bulk interface trans- mission coecient: the ratio of the bulk curvature amplitude induced by a unit brane mass to the resulting force on a test mass. The brane thickness equals the Planck length ℓ_P = p ℏG/c3 this is not a coincidence but a consequence of the brane stiness equation (Paper XXV). The hierarchy between the electroweak scale and the Planck scale H_hierarchy = E_nuc/E_Pl ∼6×1019 is the ratio of the nuclear strong-force closure scale to the brane thickness. The T2* coherence radius r_T2* = p GMBH/a0 is derived here as a zero-free-parameter prediction from G, M_BH, and a0. The ve-zone black hole structure (Paper V) is embedded in this derivation.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.