Hutchings's Ruelle-invariant conjecture for ECH error terms

Let $(X,\omega)$ be a nice star-shaped domain in $\mathbb{R}^4$, let $e_k(X,\omega)$ be its ECH error terms, and let $\operatorname{Ru}(X,\omega)$ denote its Ruelle invariant.

Hutchings's Ruelle-invariant conjecture. If $(X,\omega)$ is generic, then

$$\lim_{k\to\infty}e_k(X,\omega)=-\frac{1}{2}\operatorname{Ru}(X,\omega).$$

The statement is described in the paper as a conjecture of Hutchings, alongside a theorem; its resolution status is not specified in the supplied text.