Article 16: Topological Quantization of Galactic Scale Radii — Hopf Resonance, Fibonacci Closure and the 1/φ Fractional Level

This article derives the topological constraints on galactic dark halo scale radii in the Primordial Energy Waves (PEW) framework. We prove that the Hopf vortex on the golden torus T²_φ induces an exact phase twist of 1/φ along the meridional cycle, leading to the universal fractional harmonic level N_gal = N_0 + 1/φ. The Opercule-Shell identity 1/φ + 1/φ² = 1 shows that the complete galactic vortex (baryonic disk + dark halo) occupies an integer level, while the baryonic component observed in SPARC corresponds to the fractional offset 1/φ ≈ 0.618. Analysis of 175 SPARC galaxies confirms this prediction to 3.3%. New falsifiable predictions for weak-lensing virial radii are formulated.