Jahanbekam–West anti-Ramsey conjecture for edge-disjoint rainbow spanning trees

For positive integers $n$ and $t$, let $r(n,t)$ be the maximum number of colors in an edge-coloring of $K_n$ that has no $t$ edge-disjoint rainbow spanning trees. Jahanbekam–West conjecture. Whenever $n\geq 2t+2\geq 6$,

$$r(n,t)=\binom{n-2}{2}+t.$$

This is an anti-Ramsey extremal problem. The source states that the conjecture is resolved by the paper's main theorem, so the displayed formula holds in the indicated range.