The connected-sum conjecture for non-classical weakly prime virtual links

Let $V_1$ and $V_2$ be non-classical, weakly prime virtual links. A connected sum is formed by joining diagrams of two links along chosen arcs; for virtual links this operation can depend on the choices. Connected-sum conjecture. There are infinitely many distinct virtual links that decompose as a connected sum of $V_1$ and $V_2$. For alternating virtual links, this phenomenon is established by the flyping theorem; the conjecture is that the same construction works without the alternating hypothesis.