If the Fukaya category is defined over $\mathbb{Z}$, then all the weighting factors to the various universal families are all integers, and $\mathcal{C}$ is naturally an integral current. If we use Fukaya categories over $\mathbb{Q}$ or $\mathbb{R}$ instead, then $\mathcal{C}$ is only guaranteed to be a finite $\mathbb{Q}$ (resp. $\mathbb{R}$) linear combination of integral currents.