Hatano–Tsunekawa conjecture on the optimal radius for diagonal implicit Runge–Kutta methods

For each integer $s\ge 1$, let $\widehat{R}_{s/s,2}$ denote the optimal radius of absolute monotonicity in the setting used by the paper.

Hatano–Tsunekawa conjecture. For every $s\ge 1$,

$$\widehat{R}_{s/s,2}=2s.$$

This is presented as a weaker conjecture arising after the failure of the corresponding equality for $m=n=3$. The source states that the conjecture had previously been proved only for $s=1$ or $s=2$; its status here is recorded as resolved.