The metric deviation estimate and the volume form error estimate require $A^{1/4}|\vec{\mu}|_{a}\gtrsim 1$. Heuristically we may think of the discriminant locus $\mathfrak{D}$ as the source of gravitating force, and for $A^{1/4}|\vec{\mu}|\lesssim 1$ the mutual interactions of $\mathfrak{D}_{1},\mathfrak{D}_{2},\mathfrak{D}_{3}$ become too strong, so the perturbative description breaks down.