On the coupled Ding stability and the Yau--Tian--Donaldson correspondence for Fano manifolds

We interpret the coupled Ding semistability and the reduced coupled uniform Ding stability of log Fano pairs in the notion of coupled stability thresholds and reduced coupled stability thresholds. As a corollary, we solve a modified version of the conjecture by Hultgren and Witt Nyström for coupled Kähler–Einstein metrics on Fano manifolds.