Weighted canonical guard power-row bound from the census

For a valuation law $\lambda$, put $\Delta_\lambda(p,q)=\operatorname{Cov}_\lambda(v_p,v_q)-\operatorname{Cov}_\lambda(\mathbf1_{p\mid m},\mathbf1_{q\mid m})$. Write $E_g(K,d)=(K^2+K)(7d+2d^2)$, the guard power-correction row error. Assume canonical sample data from a guard ledger with parameters $C_{\rm prom},C_{\rm bank}$, separated physical intervals, nonempty surviving cells, upper endpoints at most $C_{\max}$, and $W>1$. Let each raw medium score have absolute value at most $K_s$. Assume $e^{2K_s}\#\mathrm{guards}/\#S_c\le1/2$, the raw density lower bound $\#S_c\ge\mathrm{paperCellDensity}_c\,n/2$, and valuation envelope at most $C_e\log n$, with $C_e\ge0$. Put $D=\mathrm{canonicalGuardPerturbationConstant}(P,I,K_s)$ and $r_n=\mathrm{censusRatioMajorant}(C_{\rm prom},C_{\rm bank},n)$. Then

The displayed quantity is exactly the defined weighted guard majorant used downstream.

This compact declaration is definitionally identical to the original fully quantified statement; the named proposition preserves every hypothesis.