Nontriviality conjecture for bucklings of spatial theta-graphs

Let $G$ be a $\theta$-graph in $S^3$. A belt $B$ is an oriented annulus intersecting the edges of $G$ in intervals, and $G(B)$ denotes the spatial graph obtained by buckling $G$ along $B$. Buckling nontriviality conjecture. There is no $\theta$-graph $G$ in $S^3$ and no belt $B$ intersecting all the edges of $G$ such that $G(B)$ is either the trivial $\theta$-graph or the Kinoshita graph. This would rule out the simplest possible outcomes for buckling along a belt meeting every edge; the surrounding discussion notes that little is known about how buckling affects spatial graphs, although buckling preserves the Brunnian property when the original graph is Brunnian and the belt intersects every edge.