Smith and Wright's global stability conjecture for scalar delay differential equations

Consider the scalar delay differential equation

$$x'(t)=-ax(t)+w(x(t-h)),$$

under conditions (W), with the trivial solution and its local asymptotic stability understood as in the paper. Smith and Wright's conjecture. Under conditions (W), the trivial solution of Eq. is globally attracting if it is locally asymptotically stable. This conjecture concerns whether local asymptotic stability suffices for global attraction in the class of scalar delay differential equations considered, extending the relationship suggested by the stability boundaries for the Nicholson equation. The supplied text gives no resolution.