"Standard Model Parameters from Geometric Derivation." Paper V in MEF Series.

We derive the absolute magnitudes of the Standard Model gauge couplings, the Higgs vacuum expectation value and boson mass, the top quark Yukawa coupling, and the electroweak-to-Planck hierarchy from the Kaluza–Klein reduction of the twelve-dimensional Master Equation framework over the internal eight-manifold K₈ = [(CP² × S²) ×w (T²/Z₂)]Spinᶜ. The derivation employs zero continuous free parameters. Every input is a topological invariant (χ(K₈) = 12, χ(S²) = 2), a discrete Spinᶜ charge, or a geometric ratio dynamically locked by flux stabilisation. Three principal results emerge: (i) the Gauss–Bonnet theorem rigorously forbids the Higgs mass term from the internal Ricci scalar, forcing the Mexican hat potential to arise instead from the competition between bulk tension and topologically quantised Spinᶜ monopole flux on S², yielding μ² and λ as geometric functions of the weak sector radius Rw; (ii) the gauge coupling ratio αₛ/αw = τ₂² follows exactly from the Killing vector overlap integrals on CP² and S² respectively, with the aspect ratio τ₂ = Rw/Rc dynamically stabilised by the moduli potential; (iii) the gravitational hierarchy MPl/Mweak = e12π ≈ 2.3 × 10¹⁶ is a direct consequence of the topologically derived warp exponent ζ = 12π. Combined with the companion CKM, PMNS, and cosmological constant papers, the K₈ manifold now accounts for all 22+ parameters of the Standard Model from pure geometry, with one empirical anchor (αₛ) setting the overall mass scale.