Uniform omitted-tilt divisor law with two harmonic margins

Write $L=\log n$, $y=n^{2/9}$, $Y=\lfloor y\rfloor$, $U=9/2$, and $v_d=U-\log d/\log y$. Let $\rho$ denote the Dickman function. Fix a head pattern $H$, $0<A<C$, $B\ge0$, and integer $W>1$. There exist $K\ge0$, $c>0$, a nonnegative sequence $\epsilon$ equal to the explicit function $\mathrm{omittedTiltRemainder}(K,B,C,c,W)$, and $N_0$. Explicitly, with $M_n=\mathrm{omittedTiltMajorant}(B,C,c,W,n)$,

Uniformly for $n\ge N_0$, positive $Y$-smooth $D\le Y^4$ coprime to the head modulus, prime subsets $P\subseteq(W,Y]$ coprime to $D$, and coefficients $|\eta_p|\le B$ on $P$, the structured cell $S$ with physical endpoints $\lfloor An\rfloor,\lfloor Cn\rfloor$ is nonempty. Tilt its uniform law by $L^{-1}\sum_{p\in P}\eta_p v_p(m)$. Then

The explicit common remainder can be carried through later harmonic row sums without losing its uniformity.