Equivalence of virtual knot theory and virtual mosaic theory

Let $L_1$ and $L_2$ be virtual knots or links, and let virtual mosaics represent them. Two virtual mosaics are equivalent when they represent equivalent virtual knots or links. Virtual mosaic equivalence conjecture. Virtual knot theory is equivalent to virtual mosaic theory: $L_1$ and $L_2$ are equivalent if and only if any two virtual mosaics that represent $L_1$ and $L_2$ are equivalent. This conjecture seeks to establish that virtual mosaics capture exactly the equivalence theory of virtual knots and links; the source describes it as an open question in the developing study of virtual mosaic knots.