  An old conjecture in delay equations states that Wright's equation \[ y'(t)=
- \alpha y(t-1) [ 1+y(t)], \alpha \in \mathbb{R} \] has a unique slowly
oscillating periodic solution (SOPS) for every parameter value $\alpha>\pi/2$.
We reformulate this conjecture and we use a method called validated
continuation to rigorously compute a global continuous branch of SOPS of
Wright's equation. Using this method, we show that a part of this branch does
not have any fold point nor does it undergo any secondary bifurcation,
partially answering the new reformulated conjecture.
