In the region defined by (4.14) we have $|\gamma_{4}-\bar{\gamma}_{4}|\leq CA^{-1/4}$. For $i=1,2,3$, in the subset of the region (4.14) where $\text{dist}_{g_{a}^{\prime}}(\cdot,\mathfrak{D}_{i})\gtrsim A^{1/4}$ we have $|\gamma_{i}-\bar{\gamma}_{i}|\leq CA^{-1/4}$.