Finiteness conjecture for low-volume knot complements with hidden symmetries

For $R>0$, consider hyperbolic knot complements in $\mathbb{S}^3$ with hidden symmetries and volume less than $R$. Finiteness conjecture. For any $R>0$, at most finitely many hyperbolic knot complements in $\mathbb{S}^3$ have hidden symmetries and volume less than $R$. This conjecture asserts that knot complements with hidden symmetries are sparsely distributed by volume. It is presented as still open; the paper also asks separately whether infinitely many such complements exist.