Paper XXVII of the Brane-Bulk Series The Sump, the Higgs Field, the Equivalence Principle, and the Yukawa Hierarchy B. D. Jagadeesan, MD

Paper XXVI identied the sump mechanism as the constant inward pressure Λ_opp(t) from the ongoing H−extrusion collapse. This paper shows that the same mechanism resolves three deep puzzles of the Standard Model. (1) the Fano Higgs condensation mechanism: the sump pressure creates a standing wave at the brane-bulk interface, selecting a preferred vacuum conguration the Higgs vev v(t) ∝H(t){7/2}. (2) The Equivalence Principle: both gravitational and inertial mass are focal deceleration resistance (Paper V), making them equal by construction. (3) The Yukawa hierarchy: the coupling of each fermion to the Higgs standing wave is proportional to its focal deceleration amplitude divided by v(t0). The top quark couples maximally (deepest focal zone); the electron couples minimally (shallowest focal zone). No ne-tuning. 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.