Resonance identification procedure based on semimajor axis. The horizontal axis represents the final semimajor axis, a_f, of the particles, while the vertical axis represents their mean semimajor axis, a, during the final 0.5 Myr. The figure shows the region near the 4:7 MMR in the simulation with ȧ_N = 0.2 au/Myr. In the upper panel, black crosses indicate objects excluded during the initial filtering, green crosses represent resonant candidates that were subsequently excluded during clustering, and orange dots denote particles finally identified as resonators. Horizontal dashed lines mark the positions of several MMRs. The lower panel provides a magnified view of the dotted rectangular region in the upper panel, where all particles residing in the 4:7 MMR are identified based on the libration of their resonant angles, with colors indicating the corresponding libration amplitudes.