Nonuniqueness of negative stabilization for virtual transverse knots

A virtual transverse knot is an equivalence class of one-component virtual braid closures modulo conjugation and positive stabilization. A negative stabilization is an operation on a virtual transverse knot obtained by adjoining a negative classical crossing in a stabilization move; the source considers the possible choices of such an operation.

Negative stabilization nonuniqueness conjecture. Negative stabilization is not a unique operation on virtual transverse knots. That is, there are two ways to negatively stabilize some virtual transverse knot such that the two results are no longer the same virtual transverse knot.

For ordinary transverse knots, finite type relations can relate sufficiently negative stabilizations in the setting discussed in the source. The conjecture predicts genuinely different outcomes for negative stabilization in the virtual setting.