Generalized Wright conjecture on the global attractor

Let $\alpha>0$ and let $U(\alpha)$ be the forward extension by the semiflow of a local unstable manifold at zero for Wright's equation. Write

$$Wright's equation: \quad x'(t)=-\alpha f(x(t-1)).$$

Let $\overline{U(\alpha)}$ denote the closure of $U(\alpha)$. Generalized Wright conjecture. For every $\alpha>0$, the set $\overline{U(\alpha)}$ is the global attractor for Wright's equation. This question was proposed in the cited work and is presented as unresolved in the source.