Virtual transverse finite type invariants detect braided type and self-linking number

Let $VTK$ denote the set of virtual transverse knots and let $U_n(VTK)$ be its finite type group of order at most $n$. For virtual transverse knots $x$ and $y$, suppose that they have the same braided virtual knot type and the same self-linking number.

Virtual transverse triviality conjecture. Then $x$ and $y$ represent the same element of $U_n(VTK)$ for all $n$.

The conjecture proposes that these finite type groups cannot distinguish virtual transverse knots having the same braided virtual knot type and self-linking number. The source reports no counterexample and notes that the corresponding statement for ordinary transverse knots is known, while the virtual case remains open.