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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.
Michel ALdon (Tue,) studied this question.