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

$$M_{\nu}^{+}=\{A^{-1/2}\varrho<e^{\nu}\}\subset M^{+}.$$

Its base is $\mathcal{B}^{+}_{\nu}=\{A^{-1/2}\varrho<e^{\nu}\}\subset\mathbb{R}^{2}_{\mu_{1},\mu_{2}}\times(S^{1}\times\mathbb{R})_{\eta}$.