Inferred spatial origin within the Galactic plane for five selected objects (upper row; see Fig. A.1 for all program stars). The most likely plane-crossing point is marked by a black cross, while the shaded areas visualize the corresponding 1σ (light red) and 2σ (light blue) contours. Circles centered at the GC (black plus sign) with radii of 1 kpc (dotted black line), 8.3 kpc (solar circle; dashed red line), and 25 kpc (solid blue line) are shown for reference. The galactocentric coordinate system is Cartesian and right-handed, with the Sun (red square) on the negative x-axis and the z-axis pointing to the Galactic north pole. The panels in the lower row show the same, except that proper motions from Gaia DR2 are used as input, demonstrating the improved precision of EDR3.