We consider holomorphic polygons whose boundary $\partial\Sigma$ encounters in the clockwise order intersections in $p_{N-1}\in CF^{1}(L_{N},L_{N-1}),\ldots$, $p_{1}\in CF^{1}(L_{2},L_{1})$, $p_{0}\in CF^{0}(L_{1},L_{0})$, $p_{N}\in CF^{0}(L_{0},L_{N})$, juxaposed possibly by more degree one self intersections $b_{i}$ of $L_{i}$. The notation here does not constrain the number of self intersections of $L_{i}$ that can occur on $\partial\Sigma$. The topological energy formula (66) expresses $E(u)$ in terms of the Lagrangian potentials at the intersections

By the Novikov positivity requirement of the bounding cochains $f_{L_{i}}|^{+}_{-}(b_{i})\geq 0$, and the energy of the holomorphic curve is also positive, so they are individually bounded.

More generally, the polygons may miss some of the Lagrangians in $L_{1},\ldots L_{N}$, but cannot reverse the order of the Lagrangians. This amounts to using a smaller effective value $N$, and the same argument implies the energy bound. ∎