If there are degree $-2$ self intersections of $L$, then the choice of $\gamma$ is only unique up to $m_{1}^{b}$ of some element in $CF^{-2}(L,L)$. The corresponding choice of $\mathcal{C}$ would be ambiguous by the boundary of an $(n+2)$-dimensional integration current. As a closely related issue, our conditions on $\alpha,\beta$ are merely cohomological, so in general we can adjust $\alpha$ and $\beta$ by coboundary terms, which would affect $\mathcal{C}$ also by the boundary of an $(n+2)$ dimensional current. If we impose $L,L^{\prime}$ to be almost calibrated, then there are no $CF^{-1}(L,L^{\prime})$ elements to begin with, and these phenomena do not happen.

On the other hand, $\mathcal{C}$ still depends on the choice of local systems and bounding cochains, which may contribute nontrivial holonomy factors. Gauge equivalent choices affect $\mathcal{C}$ by the boundary of an $(n+2)$-dimensional current. One may naturally ask: