Rainbow clique saturation conjecture

Let $K_r$ be the complete graph on $r$ vertices, and let $\operatorname{sat}_{t}\left(n,\mathfrak{R}(K_r)\right)$ denote the minimum number of edges in an $n$-vertex graph whose edges are coloured from a palette of $t$ colours and which is rainbow-saturated with respect to $K_r$. Rainbow clique saturation conjecture. For any integers $r$ and $t$ with $t\geq {r \choose 2}$,

$$\operatorname{sat}_{t}\left(n,\mathfrak{R}(K_r)\right)=\Theta(n\log n).$$

This conjecture predicts that the lower bound matches the known logarithmic upper bound for rainbow saturation of complete graphs, resolving the remaining gap in the asymptotic order.