Adiprasito–Schmidt stability conjecture for slice rank of subspaces

Let $d\geq 2$, let $\mathbb{K}$ be a field, and let $\mathsf{W}\subseteq\mathbb{K}^{n_1}\otimes\cdots\otimes\mathbb{K}^{n_d}$ be a linear subspace. Write $\overline{\mathbb{K}}$ for an algebraic closure of $\mathbb{K}$, and let $\operatorname{SR}_{\mathbb{K}}(\mathsf{W})$ denote the slice rank. Stability conjecture for slice rank of subspaces. There is a constant $C\coloneqq C(d)>0$ such that

$$\operatorname{SR}_{\mathbb{K}}(\mathsf{W})\leq C\operatorname{SR}_{\overline{\mathbb{K}}}(\mathsf{W}\otimes\overline{\mathbb{K}}).$$

The conjecture was introduced in the cited work; the paper discusses stronger stability results for related slice-rank questions but does not state that this conjecture itself is resolved.