4 problems

Kinoshita's problem. Every $P^2$-knot is $P^2$-reducible, that is, every $P^2$-knot is a connected sum of a standard $P^2$-knot and a surface-knot homeomorphic to the 2-sphere…

Shadow-diagram move conjecture. The diagrams $\mathfrak D^1$ and $\mathfrak D^2$ can be related by a finite sequence of moves, each of which is one of the listed types.

Classification conjecture. Every $(2,0;2)$-bridge trisection is diffeomorphic to one of those described in Example and Figure.

Classification conjecture. There are exactly three, up to mirroring, totally irreducible $(2,0;1)$-bridge trisections.