Results from the 3D disk-halo decomposition applied to the mock MUSE cube of the simulated galaxy ID3. Panel (a): Mock MUSE white-light image with flux intensity contours overlaid. Panel (b): Position velocity diagram. The observed velocity profiles as measured with GALPAK^3D and MPDAF (Bacon et al. 2016) are overlaid in red and green, respectively. The dotted black line shows the region beyond which the S/N of the emission line falls below unity, whereas the white contours show the flux intensity. Panels (c) and (d): Observed velocity field obtained using a traditional 2D line fitting code and the modelled velocity field obtained from 3D disk-halo decomposition with GALPAK^3D. Panel (e): Contribution of the different components (stars-orange, gas-blue, DM-green curve) to the RC (dot-dashed curve; corrected for pressure support). Panel (f): Measured DM density profile (in green) compared to the true DM density profile (in red). The light shaded regions in these two panels show the 95% confidence interval. Panel (g): Posterior distributions (in blue) for a subset of the parameters we fit for: log(X) = log(M_★/M_halo), the virial velocity, the concentration, and the disk inclination. Panel (h): Posterior distributions for parameters derived from the fitted ones, including the DM density profile shape parameters α, β, and γ (computed using Eqs. (A.2), (A.3), and (A.4), respectively), as well as the stellar mass log(M_★/M_⊙). The recovered values are shown as the dark blue lines, while the values used as inputs for the simulation are shown as the red lines.