# Virtual diagrams from oriented Gauss codes

Suppose that $D_1$ and $D_2$ are virtual diagrams of oriented virtual knots with the same oriented Gauss code (each crossing in the code contains the following information: crossing number, over/under, crossing type - "+/-"). Is it true that $D1$ and $D_2$ are the same with respect to generalized Reidemeister moves (classical + virtual)? - i. e. they represent the same virtual knot?

A way to think of virtual crossings is that they are merely artifacts of trying to draw on the plane a not-necessarily-planar $4$-regular graph with a rotation system, where the vertices are classical crossings. A Gauss code is a convenient way of capturing the data of the kinds of $4$-regular graphs we see from knot diagrams. In the history of the subject, general Gauss codes are virtual knots.