Picard-rank-one smoothing conjecture for the reconstructed Fano threefolds

For each of the seven specified Noether--Lefschetz divisors in the degree-$22$ moduli space, let $X$ be the Gorenstein canonical Fano threefold constructed from a general polarized K3 surface in that divisor. Picard-rank-one smoothing conjecture. The constructed threefold $X$ has Picard rank $1$ and admits a $\mathbb{Q}$-Gorenstein smoothing to $V_{22}$. Explicit computations verify the conjecture for several of the seven divisors, but it is not resolved in full and is left for future investigation.