Resolution of Dark Matter-Free Galaxies NGC 1277 and NGC 1052-DF2 in Twistor-EBIKK-β Gravity

We demonstrate that Twistor-Entropic-Born-Infeld-Kaluza-Klein gravity with β-regularization(Twistor-EBIKK-β) naturally explains the observed dynamics of dark matter-free galaxies NGC1277 and NGC 1052-DF2 without invoking dark matter. The model predicts: (1) suppression of nonNewtonian effects in compact high-density systems (ρ > 109M⊙/kpc3) through topological quenching of twistor fields, and (2) scale-dependent gravity modifications emerging at r > 2 kpc. For NGC1277, we derive the rotation curve v(r) = pGM(r)/r(1 + κ(r)/2r2)−1/4 with κ(r) = κ0e−r/0.5kpc,matching observations within 5%. For NGC 1052-DF2, the velocity dispersion σ = 8.5+2.3−3.1 km/s isreproduced when Tent = 0.015 ± 0.004 eV. The theory makes testable predictions for ultra-diffusegalaxies in cluster environments.