Theoretical S-curves at the λ_Edd–Σ plane, at the literature black hole mass of Mkn 590 and at R = 6, 20, 100 R_Schw, color-coded by α_B. The shaded band marks the empirical CL transition Eddington ratios from A. Jana et al. (2025), and the cross-hatched strip those from B. Palit et al. (2026).The empirical thresholds intersect the theoretical knees only for α_B ≈ 0.5–0.55 at the inner radii. Black dashed lines correspond to S-curves predicted from standard accretion theory prescribed with α = 0.1.