Generalized instanton surgery exact-triangle conjecture

Let $Y$ be a closed three-manifold, let $K\subset Y$ be a knot, and let $Y_n(K)$ denote the result of $n$-surgery on $K$. Let $W_n^\prime(K)$ be the cobordism defined above, and let $I^\sharp$ denote the instanton Floer homology theory. Generalized instanton surgery exact-triangle conjecture. For any integer $n$ and any positive integer $m$, there is an exact triangle

\xymatrix@R=6ex{ I^\sharp(Y_n(K))\ar[rr]&&I^\sharp(Y_{n+m}(K))\ar[dl]^{F^\prime}\\ &\bigoplus_{i=1}^m I^\sharp(Y)\ar[ul]& }

where the map $F$ is related to the cobordism $W_n^\prime(K)$. This would generalize the usual instanton surgery exact triangle; the source explains that the expected proof should adapt the standard proof with modifications, but does not establish the statement.