Directed Burr–Erdős conjecture for oriented hypercubes

Let $\vv{Q_d}$ denote the oriented $d$-dimensional hypercube, and let $\vv{r}(\vv{Q_d})$ be its oriented Ramsey number. Directed Burr–Erdős conjecture. There is an absolute constant $C>0$ such that

$$\vv{r}(\vv{Q_d})\leq C2^d$$

for all $d\geq 1$.

This conjecture predicts a linear-in-the-order bound for oriented hypercubes, paralleling the Burr–Erdős conjecture for undirected hypercubes. The source gives no resolution status.