The raw smooth base pool inherits the moving-prefix 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 $K$, and $c>0$. There are $C_v>0,N_0$ such that for every $n\ge N_0$ and $p\in\mathcal P_{n,W}$, the canonical raw smooth-base pool $S$ for width $W$, multiplicity $K$, and upper-tail length associated to $c$ is nonempty and

This is the label-one, head-free broad pool used by the smooth source construction.