Delta-matroid invariance conjecture for ML degrees

Let $C_1,C_2\in\mathbb{C}^{d\times d}$ be scaling matrices, with associated delta-matroids, and let $c_1,c_2$ be the corresponding scalings. Delta-matroid invariance conjecture. If the delta-matroids associated to $C_1$ and $C_2$ are isomorphic, then

$$\operatorname{MLdeg}(V_d^{c_1})=\operatorname{MLdeg}(V_d^{c_2}).$$

The source proves this statement in the range $2\le d\le6$; its validity beyond that range is not established here.