Gas surface density maps (g cm^-2, log units) in the fiducial model shown at nine times since the formation of the central protostar. Only the inner 600 × 600 au² box is shown. The total computational region extends to 14 000 au in the r-direction. The contour lines in the top-left panel outline the regions where the Toomre Q-parameter is less than unity and the red arrows point to the identified fragments in the disk. Fragment IF1 is marked by the yellow arrows in the middle row of panels; its dynamics is considered in detail in Sect. 4.