For a parameter $\nu$ with $1\ll\nu<\epsilon_{0}A^{3/4}$, define the subregion of $M^{-}$

$$M^{-}_{\nu}=\{A^{-1/4}\varrho<e^{\nu}\}\subset M^{-}.$$

Its base is $\mathcal{B}^{-}_{\nu}=\{A^{-1/4}\varrho<e^{\nu}\}\subset(\mathbb{C}^{*})^{2}_{\eta_{1},\eta_{2}}\times\mathbb{R}_{\mu}$.