The node-count conjecture for factoriality of nodal threefolds

Let $X\subset\mathbb{P}(1^{4},r)$ be the nodal double-cover threefold described above, and let $V\subset\mathbb{P}^{4}$ be a nodal hypersurface of degree $n$ as described above. The notation $\operatorname{Sing}(X)$ and $\operatorname{Sing}(V)$ denotes their singular loci, and a threefold is $\mathbb{Q}$-factorial if every Weil divisor has a positive multiple that is Cartier.

Node-count conjecture. The inequalities

$$|\operatorname{Sing}(X)|<(2r-1)r$$

and

$$|\operatorname{Sing}(V)|<(n-1)^{2}$$

respectively imply the $\mathbb{Q}$-factoriality of the threefolds $X$ and $V$.

The claim proposes that the examples immediately preceding it are asymptotically sharp: at the displayed node counts, the corresponding threefolds can fail to be $\mathbb{Q}$-factorial, while strict improvement of those bounds should force $\mathbb{Q}$-factoriality. The supplied text gives no resolution of this expectation.