Higgs and Yukawa in the Geometric Ladder: Curvature-Corrected Bulk Derivation of the Scalar Sector

We present a complete derivation of the Higgs boson and fermion Yukawa couplings in the Operator-Derived Dimension (ODD) framework, using the 5-dimensional curved hyperspherical bulk established in the flagship Geometric Ladder paper.By explicitly including bulk curvature, we demonstrate:1. The Higgs scalar emerges as the lowest bound state of the 5D domain wall.2. Its mass is determined by the bulk curvature scale k ∼ 173 GeV and the geometric phase alignment along the hypersphere, naturally producing mH ≈ 125GeV.3. Fermion Yukawa couplings arise directly from the wavefunction overlap of the Higgs mode with the corresponding fermion ladder states.4. Only one light scalar appears; higher modes are pushed to the multi-TeV scale by curvature and boundary conditions.This paper provides a fully explicit, curvature-corrected Higgs sector derivation, explaining mass hierarchies, Yukawa structure, and the scalar spectrum entirely from geometry, with no free parameters.