Frozen-top initial realization gives the selector mass estimate

Write $L=\log n$, $N=n/L$, $Y=\lfloor n^{2/9}\rfloor$, $h=\mathrm{upperTailLength}(c,n)$, $Q_W=\mathrm{roughHeadModulus}(W)$, and $d_W=\mathrm{roughHeadDensity}(W)$. Fix $d,W,K_0$ and an auxiliary natural pool parameter. Assume $c>0$ and $0<\delta_*<1$. Let finite-set families $F_n,B_n,C_n$ and selector $s_n$ have, eventually, the exact canonical top-frozen balanced initial realization at these parameters and coefficient $\beta$. Then

The analytic mass estimate is discharged from exact finite realization witnesses.