Generic uniqueness of the artery in the Handel–Mosher axis bundle

Let $F_r$ be a free group, let $\operatorname{Out}(F_r)$ be its outer automorphism group, and let $\varphi\in\operatorname{Out}(F_r)$ have axis bundle $\mathcal{A}_\varphi$. A reasonable random walk on $\operatorname{Out}(F_r)$ is a random walk satisfying the hypotheses implicit in the source.

Generic uniqueness conjecture. For a reasonable random walk on $\operatorname{Out}(F_r)$, having that $\mathcal{A}_\varphi$ has a unique artery is generic.

The claim proposes that the unique-artery property is typical for random walks, consistent with the authors' observation that nongeometric fully irreducible elements are generic in relevant random-walk settings. The precise meaning of “reasonable” and the status of this expectation are not established in the supplied text.