Distribution of the tertiary mass-ratio ($\frac{M_3}{M_1+M_2}$), the tertiary period (P₂), and the eccentricity (e₂) of the outer orbit for CHTs with metallicity estimates. The left panel shows the distribution of $\frac{M_3}{M_1+M_2}$ and P₂. The right panel shows the distribution of $\frac{M_3}{M_1+M_2}$ with e₂ of the outer orbit. The points have colours according to their systemic metallicity, where metal-poor (< −0.15 dex) systems are purple, near solar-metallicity (−0.15 dex < [Fe/H] < 0.15 dex) ones are red, and metal-rich (> 0.15 dex) CHTs are yellow. The narrow panels on each axes represent the histograms of the respective parameters, with the coloured histograms representing the distributions for each metallicity group.