Endpoint variation bound for the Saias–Dickman correction

Assume the source's compact bounded-variation translation principle. For natural $0<A\le B$, $y\ge2$, and $u(B,y)=\log B/\log y\le5$, let $E(X,y)$ denote the source's Saias–Dickman correction. Then

This turns the compact translation estimate into an interval error bound for the correction term.