(Uniform energy bound) Under the potential clustering assumption, all holomorphic polygons $u:\Sigma\to X$ with boundary on $L$ and $L_{0}$ contributing to $\mathcal{C}$ have uniformly bounded energy independent of $L$:

$$E(u)=\int_{\Sigma}u^{*}\omega\leq A(N+1),$$

and along $\partial\Sigma$ the degree one self intersections of $L_{0},L_{1},\ldots L_{N}$ arising from the bounding cochains satisfy a uniform bound

$$\sum_{i}\sum_{b_{i}}f_{L_{i}}|^{+}_{-}(b_{i})\leq A(N+1).$$