Cieliebak–Mohnke's presentation conjecture for the normalized Lagrangian capacity in all dimensions

Let $\bar c_L$ be the normalized Lagrangian capacity on $2n$-dimensional ellipsoids, let $P(1/n,\dots,1/n)$ denote the cube with all $n$ radius parameters equal to $1/n$, and let $c_{P(1/n,\dots,1/n)}$ be the corresponding embedding capacity. Cieliebak–Mohnke's presentation conjecture. The restriction of $\bar c_L$ to $\operatorname{Ell}^{2n}$ equals

$$c_{P(1/n,\dots,1/n)},$$

the embedding capacity of the cube of radius $1/\sqrt n$.

This is the higher-dimensional analogue of the preceding four-dimensional presentation conjecture for the normalized Lagrangian capacity; the source does not give a resolution.