The unrestricted danceability–bridge index conjecture for virtual knots

Let $K$ be a virtual knot. Denote by $da^{(u)}(K)$ its unrestricted danceability index and by $b_1(K)$ its virtual bridge index. The unrestricted danceability–bridge index conjecture. For all virtual knots $K$,

$$da^{(u)}(K)=b_1(K).$$

The equality is proved for welded knots, where the Over-Crossings-Commute relation permits the required bridge-slide move, but the corresponding statement for all virtual knots remains open and would require a new proof technique.