Classification conjecture for ancient asymptotically cylindrical 4-dimensional Ricci flows

Consider an ancient asymptotically cylindrical 4-dimensional Ricci flow, meaning a Ricci flow existing for all sufficiently negative times and asymptotic at negative infinity to a cylindrical model. Classification conjecture for ancient asymptotically cylindrical 4-dimensional Ricci flows. Any ancient asymptotically cylindrical 4d Ricci flow is, up to scaling, either $\mathbb{R}\times S^3$, $\mathbb{R}^2\times S^2$, or one of the steadies or ovals listed in the classification conjecture for 4-dimensional Ricci-flow $\kappa$-solutions. This is presented as a more ambitious generalization of the preceding classification conjecture and remains open; the source mentions partial progress for steady solitons asymptotic to $\mathbb{R}\times S^3$.