The guarded smooth broad pool retains the sharp valuation profile

Write $L_n=\log n$, $s_n=n/\log n$, $y_n=\lfloor n^{2/9}\rfloor$, and $\mathcal P_{n,W}=\{p\text{ prime}:W<p\le y_n\}$. For a prime $p\in\mathcal P_{n,W}$ put $k_p=\lfloor\log_p(y_n^4)\rfloor$ and $V_n(p)=\sum_{j=1}^{k_p}M_n(p^j)$, where $M_n(D)$ is the paper Dickman divisibility main term. Fix $W>1$, natural multiplicity $K$ and depth $d$, and $c>0$. There exist $C_v>0$ and $N_0$ such that uniformly over every bank realization at $n\ge N_0$, its guarded central-anchor certificate at depth $d$, every real $\delta_*$, and every band prime $p$, the nonempty guarded broad correction pool of label one satisfies

The constant is independent of the bank, certificate, and $\delta_*$.