Graph-change conjecture for virtual broken surface diagrams

A virtual broken surface diagram (VBSD) is a broken surface diagram for a virtual $2$-link. A graph change is a diagram change preserving the Gauss code of the double point curves while passing one double point curve through another or changing its induced framing. Graph-change conjecture. Virtual broken surface diagrams modulo the surface diagram Roseman moves, virtual Roseman moves, and graph changes represent virtual $2$-links. The proposed move set is intended to resolve the ambiguity in placing and framing double point curves; the source does not establish that these moves give a complete representation theory.