Exact-value conjecture for Ryser's function

For integers $r$ and $t$ with $2\leq t\leq r$, let an $(r,t)$-graph be an $r$-uniform, $r$-partite, $t$-intersecting hypergraph, and define

$$\operatorname{Ryser}(r,t)=\max\{\tau(\mathcal H):\mathcal H\text{ is an }(r,t)\text{-graph}\},$$

where $\tau(\mathcal H)$ is the cover number. Bustamante--Stein and Király--Tóthmérész's exact-value conjecture. For all $2\leq t\leq r$,

$$\operatorname{Ryser}(r,t)=\left\lfloor\frac{r-t}{2}\right\rfloor+1.$$

The paper proves this value in the range $r\leq 3t-1$ and establishes further partial results, but the formula remains conjectural in general.