``The Dark Matter Ratio from Spinᶜ Phase Structure.'' Paper~VIII in MEF Series

The observed ratio of dark matter to visible matter density, ΩDM/Ωb ≈ 5.36, is one of the outstanding unexplained quantities in cosmology. No Standard Model mechanism predicts this ratio; every dark matter candidate either introduces free parameters to accommodate it or leaves it unexplained. This paper derives a geometric mechanism for the approximate 5:1 ratio from the broken mirror symmetry between the Quantum-wall and Anti-Quantum-wall boundaries of the T²/Z₂ orbifold sector of the K₈ manifold of the Master Equation Framework. The Spinᶜ holonomy phase φ_ψ = 5π/12 accumulated across the ψ-axis of the orbifold pillowcase — derived topologically in Paper V [15], §8 as Wbase + Wfibre = π/12 + π/3 from χ(K₈) = 12 and the Z₃ centre of SU(3), and the same phase that generates the CKM CP-violation phase δCKM derived in Paper II [12] — acts exclusively on the U(1)Y determinant line bundle, leaving the SU(3) and SU(2) gauge fields unaffected. This shifts the effective electroweak mixing angle at the Anti-Quantum-wall from θQ ≈ 28.2^∘ to θAQ = 103.2^∘, giving: sin² θW(AQ) = sin²(103.2^∘) ≈ 0.948. The resulting electromagnetic coupling of the dark sector is αEMAQ/αEMQ ≈ 4.23 times stronger than the visible sector (Derived). Through an asymmetric baryogenesis mechanism mediated by sphaleron transitions at the orbifold fixed points, this coupling asymmetry predicts ΩDM/Ωb ≈ 4--5, consistent with the observed 5.36 value (Motivated). The framework further predicts dark disk formation, dark hydrogen with binding energy ~ 18× that of visible hydrogen, and a self-interaction cross-section consistent with the self-interacting dark matter programme. The freeze-out argument is clearly labelled Motivated throughout; the Anti-Quantum-wall angle derivation is Derived.