4 problems

Free welded non-triviality conjecture. The knot $S$ shown in Figure $19$ is non-trivial in free welded theory.

Upsilon-move conjecture. Except for some very specific cases, the Upsilon moves are not induced by the usual welded moves. Consequently, they provide a large class of nontrivial mo…

A welded knot is an equivalence class of virtual knot diagrams under welded moves, and a diagram is minimal crossing when it realizes the least possible number of classical crossin…

The $w_k$-equivalence conjecture. Two welded string links are $w_k$-equivalent if and only if they cannot be distinguished by finite type invariants of degree $<k$.