"The Cosmological Constant from K₈ Topology: ₄₅₅ = V_ e^-96. " Paper IV in MEF Series

We derive the effective four-dimensional cosmological constant ₄₅₅ from the topology of the twelve-dimensional manifold M₁₂ = (S¹ₒ₎₋ S³) K₈, where K₈ = (CP² S²) w (T²/Z₂) ^Spinᶜ is the internal compactification manifold of the Master Equation framework. The derivation proceeds without free parameters. Two factors combine to produce the observed value: (i) Topological suppression. The Euler characteristic (K₈) = 12 fixes the quantum coherence coupling constant = 12 via tadpole cancellation. Dimensional reduction from 12D to 4D introduces a warp factor exponent n = 8 (six from the fibre volume, two from Einstein-frame Weyl rescaling), giving: e^-8 = e^-96 10^-131. (ii) Geometric prefactor. The unwarped fibre volume Vol (CP² S²) = 2³ ₂² Rc⁶ and the Planck-to-compactification scale ratio contribute a prefactor V_ 10⁹ M₏₋⁴, where ₂ 1. 86 is the orbifold aspect ratio derived from ²W = 0. 224 via ₂² = (1 - ²W) /²W. The product yields: ₄₅₅ = V_ e^-96 10⁹ 10^-131 = 10^-122 M₏₋⁴, in precise agreement with the observed value ₎₁ₒ 10^-122 M₏₋⁴. The positive sign (de Sitter) is a structural prediction: the Spinᶜ gauge flux energy on the T²/Z₂ orbifold stabilises the Quantum Coherence Dilaton and provides geometric uplift from the Anti-de Sitter flux vacuum. Additionally, the same Spinᶜ holonomy that stabilises the vacuum generates a broken mirror symmetry between visible and dark sectors: the -cycle holonomy phase _ = 5/12—derived from SU (3) centre symmetry and the Euler characteristic—shifts the effective Weinberg angle at the AQ-wall to ²W^ (AQ) 0. 948, producing a 4. 2 enhancement of dark electromagnetic coupling and providing a geometric mechanism for the observed ₃₌/b 5 ratio. The result is overconstrained: the same topological integer (K₈) = 12 simultaneously determines three fermion generations, the electroweak mixing angle, the Planck–weak hierarchy, the cosmological constant, and the dark-to-visible matter coupling ratio. Altering would cascade into violations of all these observables.