(Sketch) In the region $\{R\lesssim A^{1/4}\}$ the volume form estimate follows from Proposition 4.16 and 4.18. In the region $\{R\gtrsim A^{1/4}\}$ the absolute estimate follows by combining Section 4.2, 4.3, notably the exponential decay estimate in Proposition 4.13, and the higher order estimate uses the $\Delta_{a}$-harmonicity on $w^{p\bar{q}}$. ∎