Inverse-log-square endpoint approximation from the normal-form defect

Let $C\ge0$ and $Y_0\in\mathbb N$. Suppose the reverse normal-form defect satisfies $|D(X,y,X)|\le CX/\log^2y$ whenever $y\ge Y_0$, $y\ge2$, $y<X$ and $\log X\le5\log y$. Let $Y_*=\max(Y_0,Y_{\rm contraction})$, where the latter is the canonical reciprocal-log prime contraction threshold. Then for all natural $X>0$ and $y\ge\max(2,Y_*)$ with $\log X\le5\log y$, the Saias endpoint error satisfies

This produces the sharp endpoint envelope on all five constructed faces from the explicit defect bound.