Summary plot showing the kinematics and derived properties for one source in the CORE sample (G75.78). Top left panel: Intensity-weighted mean velocity (first moment) map of CH₃CN (12₅−11₅) in colour with 1.37 mm continuum contours. The blue and red arrows correspond to the estimated directions of bipolar blueshifted and redshifted molecular outflows, respectively. The dotted line indicates the position of the strongest velocity gradient tracing the disk, i.e. perpendicular to the rotation axis. The edges of the assumed disk extent are marked with an ×. Top right panel: PV plot of CH₃CN (12₅−11₅) along the cut in the direction of rotation as depicted by the dotted line in the top left panel. The contours correspond to the 6σ level increasing in steps of 24σ. Yellow lines show the Keplerian rotation curves for an enclosed mass of 19 M_⊙. The cross in the bottom right corner corresponds to the spatial and spectral resolutions. Bottom left panel: Rotational temperature maps obtained by fitting CH₃CN(12_K−11_K) K = 0–6 and CH₃¹³CN(12_K−11_K) K = 0–3 lines with XCLASS in colour and 1.37 mm continuum contours. Bottom right panel: Toomre Q map assuming a protostar is located at the position of the continuum peak as depicted by a star and accounting for the self-gravity of the disk, with 1.37 mm continuum contours. Regions outside of 6σ continuum contours are masked out. The synthesised beam and a scale bar are shown in the bottom of the panels.