Article 18: Topological Origin of $ \log_\varphi(3/2) $ in the PEW Galactic Hierarchy — Hopf Fibration Dimensional Ratio and Closure of PO-log32 & PO-Cosmo-dyn

We derive analytically the fractional galactic harmonic level n_gal^frac = log_φ(3/2) = 0.8426 from the topology of the Hopf fibration S³ → S², without any cosmological input. The ratio 3/2 is the dimensional ratio dim S³ / dim S², where S³ is the total space of the complete galactic vortex and S² is the base onto which the baryonic disk projects. This completes the derivation of n_gal = 25 + log_φ(3/2). A remarkable numerical coincidence 1 - log_φ(3/2) ≈ Ω_M/2 (0.15% agreement) is also discussed. PO-log32 and PO-Cosmo-dyn are closed at level [A] for the topological argument.