Geometric Origin of Dark Matter Density: A Kaluza-Klein Ansatz via Action Minimization in Bosonic String Theory

We propose a phenomenological model deriving the ratio of Dark Matter to Baryonic Matter
density (Ωc/Ωb) from the dimensionality of Bosonic String Theory (D = 26). By applying the
Principle of Least Action to the compactification process (M26 → M4 × K22), we postulate that
the vacuum energy is distributed according to an Equipartition Principle. We identify the energy
content of the 22 hidden dimensions with Dark Matter via the Kaluza-Klein mechanism. The
resulting geometric ratio (26 − 4)/4 = 5.5 aligns with Planck 2018 observations (∼ 5.36) with high
precision (< 2.6% deviation). This suggests that Dark Matter is not a particulate WIMP, but the
gravitational manifestation of the compactified geometry required to preserve Lorentz invariance
and cancel the Weyl anomaly.