Integral-coefficient conjecture for higher-dimensional Heegaard Floer homology

Let $\Sigma$ be the surface appearing in the definition of the higher-dimensional Heegaard Floer algebra, let $q_i$ be the chosen points, and let $c$ denote the parameter in $HW(\sqcup_i T_{q_i}^*\Sigma)_c$. The algebra is considered over the polynomial ring $\mathbb{Z}[\hbar]$. Integral-coefficient conjecture. The algebra

$$HW(\sqcup_i T_{q_i}^*\Sigma)_c$$

is well-defined over $\mathbb{Z}[\hbar]$, and the main isomorphism theorem remains valid over $\mathbb{Z}[\hbar]$. The paper has established the corresponding result only after tensoring with $\mathbb{Z}[[\hbar]]$; the conjecture asserts that the coefficient ring can be taken to be $\mathbb{Z}[\hbar]$ itself.