(Homological uniqueness of the bordism current) Some auxiliary perturbation data goes into the construction of $\mathcal{C}$ due to the need to ensure transversality. If we fix $L,L^{\prime}$, but change the domain dependent almost complex structures, then the difference of two bordism currents $\mathcal{C}-\mathcal{C}^{\prime}$ has zero boundary in the sense of currents. Recall that Stein manifolds have the homotopy type of a CW complex of dimension $\leq n$, and thus $H_{k}(X)=0$ for $k\geq n+1$, so $\mathcal{C}-\mathcal{C}^{\prime}$ must be the boundary of an $(n+2)$-dimensional current. For an alternative viewpoint, this $(n+2)$-dimensional current can be concretely provided by parametrized families of pseudoholomorphic curves (cf. Remark 3.5).