The volume form error $\tilde{E}^{(2)}$ of $(\tilde{g}^{(2)},\tilde{\omega}^{(2)},\tilde{J}^{(2)},\tilde{\Omega}^{(2)})$ is zero on $M^{+}_{\nu}\cap\{\ell>2A^{1/2}\}$ and satisfies the bound on $M^{+}_{\nu}\cap\{|\vec{\mu}|_{a}\gtrsim A^{1/2}\}$