Article 15: Galactic Rotation Curves from Hopf Vortex Topology: PEW Prediction vs SPARC Dataset (175 Galaxies)

The PEW (Primordial Energy Waves) dark halo profile V²DM (r) = V²_∞ · (r/rₛ) · K₁ (r/rₛ) · 1−e^ (−r/rₛ), derived from the Hopf vortex opercule geometry (Article 7), is applied to the SPARC dataset of 175 late-type galaxies with resolved rotation curves. With three free parameters per galaxy (V_∞, rₛ, Υdisk), the PEW profile achieves a median χ²ᵣed = 0. 965 (90. 1% of galaxies with χ²ᵣed < 5), a factor ~200 better than MOND in median fit quality. The optimal scale radii satisfy rₛ, opt/Rₘax ≈ φ (golden ratio, median 1. 374), consistent with the KAM stability result of Article 14. With the PEW-motivated constraint rₛ = φ·Rₘax (two free parameters), the median χ²ᵣed rises to 1. 381 (82. 7% with χ²ᵣed < 5), still 156× better than MOND. Open problem PO-SPARC is partially closed at level B: the profile shape is derived, but the derivation of rₛ from the PEW Lagrangian without free parameters (via the galactic harmonic level Ngal) is deferred to Articles 16–17.