Kosaka's conjecture on virtual bridge number and primary data

A virtual knot diagram has primary data consisting of the sequence of over- and undercrossings, equivalently the unsigned chords of its Gauss diagram. Let $\operatorname{vb}(K)$ denote the virtual bridge number of a virtual knot $K$.

Kosaka's conjecture. Virtual knots have the same virtual bridge number if they have the same primary data.

In the classical setting, a pseudo-knot may admit only two realizable crossing-sign assignments, whereas in the virtual setting a diagram with $n$ crossings can have $2^n$ sign assignments. The conjecture, cited as Problem 6.3 in HKK, asks whether changing this secondary sign data while preserving the primary data leaves virtual bridge number unchanged; no resolution is supplied here.