Injectivity conjecture for classical spatial graphs in virtual spatial graph theory

Let classical spatial graphs be embeddings of abstract graphs in three-dimensional space, and regard classical diagrams as virtual graph diagrams with no virtual crossings. Two such graphs are virtually equivalent if their diagrams are related by virtual graph moves, and classically equivalent if they are related by classical spatial graph isotopy.

Injectivity conjecture. If two classical spatial graphs are virtually equivalent, then they are classically equivalent.

This asks whether the inclusion of spatial graph theory into virtual spatial graph theory is injective. The analogous statement is known for knots, but the spatial-graph case is not yet known.