5 problems

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

Kraaijevanger–MacDonald–Gottlieb conjecture. For every such method,

Let a vector-valued explicit or implicit Runge–Kutta method have order $p$, and let the conditions in the sufficiency theorem referred to in the source be imposed on such a method.…

Implicitness conjecture. Every symmetric resonance-based scheme is necessarily implicit.

Let an $s$-stage fully implicit Runge–Kutta method have order conditions … and let $r>0$ satisfy the absolute-monotonicity conditions … with $I+rA$ invertible and…