Difference between the resonant index κ₁₂ of the inner-planet pair in a three-planet system with the index κ_2p of a two-planet system for the same planet masses and disk properties (the resonant indexes of the two- and three-planet systems are displayed in Figs. 2 and 4a, respectively). See Fig. 2 for a full description of the setup. As in previous figures, the red dots correspond to systems far from resonance. The dashed black line indicates the threshold for gap opening, 3.3 × 10⁻⁵M_⊙.