Cube-normalized capacity uniqueness conjecture for convex domains

Let $X$ be a convex domain in $\mathbb{C}^n$. A symplectic capacity is cube normalized when its value on the relevant polydisc and cube-cylinder model domains agrees with the cube normalization.

Cube-normalized capacity uniqueness conjecture. All cube-normalized symplectic capacities coincide on $X$.

The conjecture is motivated by the preceding theorem for monotone toric domains. The source gives no resolution status for convex domains.