Exact formula conjecture for the rainbow-saturation coefficient

For each integer $k\geq 4$, let $f(k)$ be the auxiliary extremal function from the paper and let $\alpha_{k+2}$ be the coefficient in the asymptotic formula for rainbow saturation, so that $\operatorname{sat}(n,\mathcal{R}(K_{k+2}))=\alpha_{k+2}n+O(1)$. Exact coefficient conjecture. For every $k\geq 4$,

$$\alpha_{k+2}=f(k)=k+\left\lceil\frac{-1+\sqrt{4k-3}}{2}\right\rceil.$$

This conjecture is proposed as a way to close the gap between the lower and upper bounds for rainbow saturation by determining the auxiliary function $f(k)$ exactly. The supplied text does not state whether it has been resolved.