Metric dimension formula for Villarceau grids

Let $VG^1_{m,n}$ and $VG^2_{m,n}$ be the two Villarceau grids, and let $\dim(G)$ denote the metric dimension of a graph $G$. For integers $m,n$ satisfying

$$n>2m+1,$$

Metric dimension conjecture.

$$\dim(VG^1_{m,n})=\dim(VG^2_{m,n})=\left\lceil \frac{n-1}{m} \right\rceil+1.$$

The preceding theorem establishes the corresponding value for $VG^2_{m,n}$ when $n\leq 2m+1$; the displayed formula concerns the complementary range and is presented as a conjectural claim in the source.