Surjectivity conjecture for saddle cobordisms between braid diagrams

Let $D_{n,m}^i$ and $E_{n,m}^i$ be the diagrams defined in the paper, and consider the saddle cobordism

$$D_{n,n-1}^i\longrightarrow D_{n,n-1}^{i-1}$$

at the crossing corresponding to the last letter $\sigma_i$. Surjectivity conjecture. This saddle cobordism induces a surjection in rational Khovanov homology. Equivalently, the associated exact triangle splits into a short exact sequence. An affirmative answer would express the rational Khovanov homology of $T(n,n)$ in terms of that of torus knots $T(n'+1,n')$; the supplied text gives no resolution status.