Adversarial binary interactive capacity conjecture without shared randomness

Consider fully adversarial binary error channels without shared randomness, with noise rate $\epsilon\to0$. Let $R$ denote the interactive channel capacity, namely the maximal asymptotically achievable communication rate. Adversarial binary interactive capacity conjecture.

$$R=1-\Theta\left(\sqrt{\epsilon\log\log\frac{1}{\epsilon}}\right).$$

This conjecture concerns the fully adversarial binary setting without shared randomness; the source notes that the corresponding bound does not extend to larger alphabets.