Total inflow of material through a cylinder of radius R_shell = 30 AU and height h = 16 AU throughout the simulation’s duration post-sink formation for runs R1 (≈58 kyr, first row) and R2 (≈27 kyr, second row), computed by integrating Eq. (3) (first column) and Eq. (4) (second and third columns) in time. The red circles in the second and third columns correspond to the minimum and maximum semimajor axis of the disk throughout each simulation’s duration, and thus represent the locations where material has landed in the disk.