Standard Model Parameters from a Twelve-Dimensional Compactification

A specific twelve-dimensional Kaluza–Klein compactification, M₁₂ = (S¹ × S³) × K₈ with internal manifold K₈ = [(CP² × S²) ×w (T² / Z₂)]Spinᶜ, predicts four Standard Model parameters from a single topological invariant χ(K₈) = 12 and zero continuous free parameters. The Weinberg angle follows from Spinᶜ holonomy on the pillowcase orbifold and equals 1 / (1 + τ₂²) ≈ 0.224 at the compactification scale, where τ₂ is the pillowcase aspect ratio fixed by the gauge coupling ratio αw / αₛ. Three fermion generations follow from the Dolbeault cohomology dimension h0,2(CP², O(-4)) = 3. The Planck–weak hierarchy follows from the warp exponent ζ = 12π fixed by tadpole cancellation. The Cabibbo parameter |Vᵤₛ| ≈ 0.225 follows from D4 path holonomy on the same pillowcase, yielding the structural identity |Vᵤₛ| = sin² θW which is parameter-free and falsifiable. A discovered fourth fermion generation, or a measured sin² θW deviating from |Vᵤₛ| at the compactification scale by more than RG running can account for, would falsify the framework. Full derivations are given in the comprehensive treatment, deposited separately.