The free abelian link-group conjecture for welded links

Let $L$ be a welded link diagram, let $\pi_1(L)$ denote its fundamental group, and let $G(L)$ denote its link group. Suppose that

$$\pi_1(L) \cong \mathbb{Z} \oplus \ldots \oplus \mathbb{Z}.$$

Free abelian link-group conjecture. Then $L$ is welded equivalent to the unlink.

The conjecture proposes that a free abelian fundamental group detects the welded unlink, despite the fact that the fundamental group does not determine the virtual homotopy class in general; the source gives no resolution.