The non-degeneracy conjecture for the realizable generic Enriques surface $Y_{158}$

Let $Y_{158}$ be the realizable $(\tau,\overline{\tau})$-generic Enriques surface associated with the family indexed by $158$, and let $\mathrm{nd}(Y_{158})$ denote its non-degeneracy invariant. Non-degeneracy conjecture. The realizable $(\tau,\overline{\tau})$-generic Enriques surface $Y_{158}$ satisfies

$$\mathrm{nd}(Y_{158})=9.$$

Theorem cited in the source gives the lower bound $\mathrm{nd}(Y_{158})\geq 9$, while computational experiments with large finite samples of smooth rational curves consistently yield the value $9$. No proof of the equality is given, so the conjecture remains open.