Structural cutoff for the canonical full quotient covariance gap

Write $L_n=\log n$, $y_n=n^{2/9}$, $Y_n=\lfloor y_n\rfloor$, and $\mathcal P_{n,W}=\{p\text{ prime}:W<p\le Y_n\}$. There exist $\kappa>0$ and $W_0$ chosen before all subsequent data. For any $W\ge W_0$, choose a regular relative mesh $M$ with $\delta>0$ and a nonempty anchor-cell set whose lower endpoints exceed $1/8$, upper endpoints are at most $7/8$, and half the sum of widths is at least $1/8$. Choose a finite nonempty head family whose prime support is exactly all primes at most $W$, physical intervals between $1$ and $U\ge1$, guard ledgers, an effective radius $a\ge0$, and a positive cell-mass margin floor. For all sufficiently large $n$, consider any canonical guard-deleted bridge with these data, separated intervals, nonempty remaining cells, the canonical mesh partition, and a barycentric target having at least that margin and giving the bridge baseline. For every $\|z\|\le a$, every band coefficient vector $b$, and every real $\mu$,

The residual, band norm, and nuisance regression are those of the bridge partition; nuisance regression uses the canonical positive gap at radius $3a$.

This gives a structural coercivity constant on the full arithmetic quotient, uniformly in the scalar residual parameter.