Completeness of virtual broken surface diagrams with graph changes

A virtual broken surface diagram (VBSD) is a broken surface diagram for a virtual $2$-link; a graph change is a modification that preserves the Gauss code of the double-point curves while passing one such curve through another or changing its induced framing. The surface diagram Roseman moves and virtual Roseman moves are the diagrammatic moves described in the paper. VBSD completeness conjecture. Virtual broken surface diagrams modulo the surface diagram Roseman moves, virtual Roseman moves, and graph changes represent virtual $2$-links. This would give a complete diagrammatic model for virtual $2$-links, while the preceding discussion explains why graph changes are needed to account for choices of framed double-point graphs.