Kauffman–Przytycki conjecture on detection of minimal-genus surfaces by the surface bracket polynomial

A virtual knot $L$ is an equivalence class of virtual knot diagrams under Reidemeister and virtual Reidemeister moves; a diagram is realized in a surface when it is represented by a link diagram in that closed oriented surface. The surface bracket polynomial is the polynomial invariant obtained from surface states of such a diagram.

Kauffman–Przytycki conjecture. For a virtual knot $L$, if a diagram of $L$ is realized in a surface of the minimal genus, then this fact is detected by the surface bracket polynomial.

This conjecture concerns whether the surface bracket polynomial detects minimal-genus realizations of virtual knots. The supplied source does not state a resolution, so its status remains open.