Sharp fixed-head shift budget at the canonical row scale

Write $L=\log n$, $Y_n=\lfloor n^{2/9}\rfloor$, $h=\lceil cn/\log n\rceil$, and $K=K_0+1$. Fix natural W and $K_0$, real $\beta$, and $c>0$. Suppose $n,y\ge2$, $L\ge1$, $\log y\ge L/5$, $h\le2cn/L$, and $Kh\le n$. Let row be any canonical complete rough row of the raw candidate set at cutoff y whose label $r\le n$. The source all-row sharp fixed-head shift budget $\mathcal H$, evaluated with the head-balanced alpha and beta, satisfies

The row definition ensures $r>0$, and $C_{\rm head}$ is the explicit sharp head-row scale constant.

This controls fixed-head shifts uniformly over all eligible canonical rows, including the divisor contributions.