The E2Xs511/E2Vs511 doubling conjecture for minimally 3-rigid graphs

Let $G$ be a minimally 3-rigid graph, and let $G'$ be obtained from $G$ by a 1-extension of type E2Xs511 or E2Vs511. Let $\mathbf{c}_{3}(G)$ denote the three-dimensional realization count. The E2Xs511/E2Vs511 doubling conjecture. Then

$$\frac{\mathbf{c}_{3}(G')}{\mathbf{c}_{3}(G)}=2.$$

The claim is supported by computations for graphs with at most nine vertices, where these extension types always produced a factor of two. Its unrestricted validity is not established in the supplied text.