Future-edge algorithm conjecture for balanced independent sets

Let $G$ be the graph in the paper's online model, let $\mathcal{A}(G)$ be the set selected by an online algorithm $\mathcal{A}$, and let $E$ be the set of all future edges ever revealed to the algorithm. Let $b$ and $n,p$ be the parameters used in the definition of the computational threshold. Future-edge algorithm conjecture. For any $\epsilon$, there exists a constant $c_\epsilon>0$ and an online algorithm $\mathcal{A}$ that finds a $\gamma$-balanced independent set of size at least $(1+\epsilon)\alpha_{\rm COMP}$ whp, provided

$$\left|E\cap \binom{\mathcal{A}(G)}{2}\right|\le c_\epsilon\log_b^2(np).$$

This conjecture asks whether limited access to future edges can allow online algorithms to exceed the computational threshold; the source presents it as an open direction and does not claim a resolution.