Linear lower bound for the raw smooth correction pool

Fix natural parameters $W,K$ and a real $c>0$. Let $h_n$ be the canonical upper-tail length and $P_{W,n,h_n,K}$ the raw head-free smooth base pool. With $d_W$ the rough-head density and $r_*$ the canonical Dickman pool floor, eventually

The quantifier is over all sufficiently large natural $n$.

This supplies positive linear capacity for label one, which is excluded from the nonsmooth active-row estimate.