Soft-Haired Primordial Black Holes as Dynamical Dark Energy: A Fully Patched Model with Skyrmion Topological Hair, DESI DR2 Implications and Euclid Tests (V5)

V5 fully patched model: PBH antimatter stored as Skyrmion topological hair (B=-1), phase transition at zt=0.32 to dynamical dark energy, log-normal mass function M0=5e14 g sigma=1.0 to satisfy Fermi-LAT f_PBH limits (f_PBH=1e-9 today <7.2e3 pc^-3 yr^-1), while integrated energy xi f_PBH,init~0.68 explains Omega_de. BMS soft hair retained only as information channel, baryon number conservation provided by Skyrmion hair following Dvali & Gussmann (2016), addressing criticism that BMS soft hair cannot encode baryon number, effective degrees proportional to area, cannot affect hard S-matrix due to Weinberg soft theorem. hi_class implementation path w(z)= -1 + Delta w/[1+exp((z-zt)/Delta z)] and coupling Q=Gamma(z) rho_p consistent with DESI DR2 2025 w0=-0.827±0.063 wa=-0.75±0.29 z_cross~0.30. Magnetized QGP shell tau_gamma~4.2 provides shielding and photon-ALP conversion P~0.1 unifying Fermi EGB non-excess and GRB 221009A BOAT 18 TeV survival at 2 Gly (z=0.151). Four falsifiable predictions: (1) Omega_b(z=1)/Omega_b(z=0)=1.15±0.03, (2) 15-20% broad bump in 100 MeV-1 GeV EGB, (3) scale-dependent S8(k): 0.76 at k=0.1 to 0.90 at k=1.0 h/Mpc for Euclid weak lensing 12.5 sigma test, (4) stochastic GW background Omega_GW h^2~1e-9 at 10 nHz for NANOGrav/PTA. M51 Whirlpool galaxy small-scale excess and 【entity-BOAT¦canonical_name=BOAT】 downgraded to qualitative analogues in Discussion. This upload contains searchable PDF (pure English fixed font) and figures w(z) and S8(k). V5 Fully Patched Version September 2026 - Leung Tsz Chun Jacky - Independent Researcher, Hong Kong