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 (K₈) = 12 and zero continuous free parameters. The Weinberg angle follows from Spinᶜ holonomy on the pillowcase orbifold and equals 1 / (1 + ₂²) 0. 224 at the compactification scale, where ₂ is the pillowcase aspect ratio fixed by the gauge coupling ratio w / ₛ. Three fermion generations follow from the Dolbeault cohomology dimension h^0, 2 (CP², O (-4) ) = 3. The Planck–weak hierarchy follows from the warp exponent = 12 fixed by tadpole cancellation. The Cabibbo parameter |Vₔₒ| 0. 225 follows from D4 path holonomy on the same pillowcase, yielding the structural identity |Vₔₒ| = ² W which is parameter-free and falsifiable. A discovered fourth fermion generation, or a measured ² W deviating from |Vₔₒ| 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.
Dhiren Jashwant MASTER (Mon,) studied this question.