Definable $(p,q)$-conjecture for NIP theories

Let $T$ be an NIP theory and let $M\models T$. Let $\phi(x;d)\in L(\mathcal U)$ be a formula that is non-forking over $M$. Definable $(p,q)$-conjecture. There is $\theta(y)\in \operatorname{tp}(d/M)$ such that the partial type

$$\{\phi(x;d'):d'\in \theta(\mathcal U)\}$$

is consistent. This is the central conjecture of the paper's discussion of the definable $(p,q)$-theorem and is listed among the open problems.