Identification of X₄ orbits: (I) frequency map, f_y/f_z vs f_x/f_z, showing the bar-supporting stars (blue), the X₄ orbits (red), and the non-bar stars (black); (II) distribution of the net angular momentum parameter (L_zni) in the non-inertial reference frame; (III) distribution of the X_max/Y_max ratio for the X₄ orbits. The inset shows the same for the bar stars. (IV) V_φ vs V_Z distribution for the X₄ and the bar stars shown as contour plots, along with mean velocities, galactocentric velocities, and their respective dispersions. The non-bar stars are shown as black points.