Odd-genus nonorientable normalized liminf conjecture

Let $N_g$ be the closed nonorientable surface of genus $g$, and let $\delta^+(N_g)$ be the minimal stretch factor among pseudo-Anosov homeomorphisms of $N_g$ with an orientable invariant foliation. The notation $\liminf$ is taken along odd genera.

Odd-genus normalized liminf conjecture.

$$\liminf_{\substack{g\to\infty\\ g\text{ odd}}}(\delta^+(N_g))^g>(1+\sqrt{2})^2=(\text{silver ratio})^2.$$

The authors expect different asymptotic behavior along other genus sequences and give this strict lower bound as an example. No proof or resolution is supplied in the source.