Radial profiles of surface density Σ_g (top panel) and aspect ratio h = H/R (bottom panel) of α = 0.1 disks, under different numerical treatments. The thin cyan line shows the original SG profile as published in Sirko & Goodman 2003, valid only for log M_•/M_⊙ = 8.0 and α = 0.01. Thicker colorful lines are extensions of the model to different SMBH masses (orange: log M_•/M_⊙ = 6.0; purple: 7.0; black: 8.0). Different line-styles distinguish the numerical method: solid lines are self-consistent solutions of the SG equations computed with pAGN, while dashed and dotted lines represent power-law scaling approximations from Vaccaro et al. (2024) and Grishin et al. (2024) respectively. The dot-dashed gray line is a Shakura & Sunyaev (1973) disk for comparison. Solid lines should be regarded as the most physically consistent profiles within this framework.