Suppose we drop the positivity condition on the bordism current, but keep all the other assumptions. Then the key difference is that for holomorphic curves contributing negatively to $\partial\mathcal{C}$, we need to replace Claim 3.22 by Claim 3.29, and Claim 3.23 by Claim 3.30. Correspondingly, all appearance of $\text{Re }F(p)$ is replaced by its absolute value. Then the conclusion in Theorem 3.43 is replaced by

$$|\mathcal{S}(L)-\bar{S}(L)|\leq\frac{A(4N+2)}{\sin\epsilon}\int_{\mathcal{M}}|\text{Re }\tilde{\Omega}_{L_{0}}|.$$

(49)

The problem is that the RHS is no longer a manefestedly a priori bounded quantity.