Uniqueness conjecture for the belief-propagation fixed-point equation

In the large-degree regime, let $\mu$ and $\alpha$ be the parameters appearing in the scalar density-evolution recursion, and let $h(v)$ be the function defined by that recursion. Fixed-point uniqueness conjecture.

$$v=\frac{\mu^2 h(v)}{4}$$

has a unique fixed point for all $|\mu| \ge 2$ and $\alpha \in (0,1/2)$. The paper proves uniqueness when $|\mu|<2$ and reports numerical evidence beyond that range, so the stated extension remains open.