Non-trivial realization conjecture for virtual link diagrams with zero intersection pairs

Let $(F,L)$ be a minimal genus representation of a virtual link diagram, where an intersection pair records the relevant intersection data of $L$ with the surface $F$. If every intersection pair is of the form

$$\lbrace 0,0\rbrace,$$

Non-trivial realization conjecture. Then there exists a minimal genus representation resulting in a non-trivial realization.

This conjecture concerns when a virtual link diagram admits a non-trivial realization despite all intersection pairs being trivial. The source gives no resolution, so its status remains open.