Integral surgery exact triangle for combinatorial Heegaard Floer homology

Let $Y$ be a closed, oriented $3$-manifold and let $K$ be a framed knot in $Y$. Let $\mathcal H$ be a nice bordered Heegaard diagram for the infinity-framed complement $Y\setminus\operatorname{Nbhd}(K)$, and suppose that $\mathcal H_i'\coloneqq\mathcal H\cup\mathcal H_i$ is a nice Heegaard diagram for the $3$-manifold $Y_i$ obtained from $Y$ by $i$-surgery on $K$, for $i\in\{\infty,-1,0\}$. Surgery exact-triangle conjecture. There is an exact sequence

$$\cdots\to\widetilde{\operatorname{HF}}(\mathcal H_\infty';\mathbb Z)\to\widetilde{\operatorname{HF}}(\mathcal H_{-1}';\mathbb Z)\to\widetilde{\operatorname{HF}}(\mathcal H_0';\mathbb Z)\to\cdots.$$

This is the integral analogue of the surgery exact triangle known over $\mathbb F_2$; the paper presents it as a conjectural application for the combinatorially defined theory $\widetilde{\operatorname{HF}}$ over $\mathbb Z$.