Canonical guard deletion preserves the sharp full-valuation profile

Write $L_n=\log n$, $s_n=n/\log n$, $y_n=\lfloor n^{2/9}\rfloor$, and $\mathcal P_{n,W}=\{p\text{ prime}:W<p\le y_n\}$. For a prime $p\in\mathcal P_{n,W}$ put $k_p=\lfloor\log_p(y_n^4)\rfloor$ and $V_n(p)=\sum_{j=1}^{k_p}M_n(p^j)$, where $M_n(D)$ is the paper Dickman divisibility main term. Fix a nonempty finite family of head patterns, physical intervals, a guard ledger with fixed promotion and bank parameters, and $W>1$ containing all head primes. There are $C_v>0$ and $N_0$ such that for every $n\ge N_0$, every band prime $p$, every head/physical cell $c$, and every witness that its raw cell minus the guards is nonempty,

The statement is uniform over the finite cell family and controls the full valuation, not only prime-divisibility indicators.