The conjecture on immortal Ricci flows from quotients of Bryant's soliton

Let the Bryant steady soliton be quotiented by a subgroup of $\operatorname{SU}(2)$, and let a hyperkähler Ricci-flat ALE metric be given. An immortal Ricci flow is a Ricci flow defined on a time interval extending to $+\infty$.

Bryant-quotient conjecture. There exist immortal Ricci flows approaching any quotient of Bryant's steady soliton by a subgroup of $\operatorname{SU}(2)$, bubbling off any hyperkähler Ricci-flat ALE metric.

The conjecture echoes the paper's four-dimensional constructions and proposes a broad existence theory for immortal flows with orbifold soliton limits and ALE bubbles.