The n-determined product conjecture for generically stable measures

Let $T$ be an $m$-distal theory, and let $n>m>0$. For global generically stable measures $\mu_0(x_0),\ldots,\mu_{n-1}(x_{n-1})$, write

$$\mu:=\mu_1\otimes\ldots\otimes\mu_{n-1}.$$

A tuple of measures is $m$-determined when its product is determined by the Boolean algebra of formulas involving at most $m$ of the variables. The n-determined product conjecture. The product $\mu$ is $m$-determined. This would extend the stated type-theoretic determinacy phenomenon to generically stable Keisler measures and connect $m$-distality with hypergraph regularity; the source does not indicate whether the conjecture is resolved.