The general integral surgery formula conjecture

Suppose $\hat{\mu}=q\mu+p\lambda$ with $q>0$, and suppose $\hat{\lambda}=q_0\mu+p_0\lambda$ is chosen as in the setup. For $m\in\mathbb{Z}$ such that $\hat{\lambda}-m\hat{\mu}$ is not the Seifert longitude $\lambda$, let $A(s)$ and $B^\pm(s)$ be the bent complexes and associated complexes defined before the conjecture, with maps $\pi^\pm$ induced by the maps on their summands. The general integral surgery formula conjecture. There exists an isomorphism

$$\Xi_m:\bigoplus_{s\in\mathbb{Z}}H(B^+(s))\xrightarrow{\cong}\bigoplus_{s\in\mathbb{Z}}H(B^-(s+mq-q_0))$$

such that $I^\sharp(-\widehat{Y}_{\hat{\lambda}-m\hat{\mu}})$ is isomorphic to the homology of the mapping cone of

$$\pi^-+\Xi_m\circ\pi^+:\bigoplus_{s\in\mathbb{Z}}H(A(s))\longrightarrow\bigoplus_{s\in\mathbb{Z}}H(B^-(s)).$$

This is the general integral surgery formula in the stated setup. The source provides no resolution status, so the conjecture is recorded as open.