  We introduce a classification conjecture for $\kappa$-solutions in 4d Ricci
flow. Our conjectured list includes known examples from the literature, but
also a new 1-parameter family of $\mathbb{Z}_2^2\times \mathrm{O}_3$-symmetric
bubble-sheet ovals that we construct. We observe that some special cases of the
conjecture follow from recent results in the literature. We also introduce a
stronger variant of the classification conjecture for ancient asymptotically
cylindrical 4d Ricci flows, which does not assume smoothness and nonnegative
curvature operator a priori. Assuming this stronger variant holds true, we
establish a canonical neighborhood theorem for 4d Ricci flow through
cylindrical singularities, which shares some elements in common with Perelman's
canonical neighborhood theorem for 3d Ricci flow as well as the mean-convex
neighborhood theorem for mean curvature flow through neck-singularities.
Finally, we argue that quotient-necks lead to new phenomena, and sketch an
example of non-uniqueness for 4d Ricci flow through singularities.
