Post-height seed replacement has the sharp medium-prime valuation rate

Write $L_n=\log n$, $s_n=n/\log n$, $y_n=\lfloor n^{2/9}\rfloor$, and $\mathcal P_{n,W}=\{p\text{ prime}:W<p\le y_n\}$. Fix head patterns and physical intervals, a guard ledger, $W>1$ containing all head primes, natural $K_0,d$, $c>0$, a real active coefficient $\beta_a$, and $A_z\ge0$. Consider any later bridge $B$ at cutoff $W$ with exactly the canonical guarded sample, bank realization, and guarded anchor certificate. Require the structured active values to lie in the guarded smooth row, $\delta_*\le1$, a nonempty guarded broad smooth pool, and exact synchronization of $\widetilde q$ with the guarded smooth-base mass. For each prime under consideration assume both zero-head-cell valuation means are at most $A_z/p$. Fix also $C_d\ge0$. Let the source target be arbitrary, and let a valid post-height baseline-target input have initial mass $q_0$ synchronized with the literal top-frozen rounded source mass. Require all active values to lie in the broad lower block and $|d_{\rm height}|\le C_ds_n/L_n$. Then there exist $C_{\rm place}>0,N_0$, fixed before the bridge, bank, targets, and prime, such that for $n\ge N_0$,

The moment is that of the literal structured additive placement replacing the rounded source seed by the post-height active seed. No separate valuation estimate on the replacement target is assumed.