Canonical guard comparison for the medium power row

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. Let the bridge sample data equal the canonical constructor for a head family, physical intervals, and a guard ledger, with separated physical intervals and nonempty surviving cells. Assume the physical upper endpoints are at most $C_{\max}$, $W>1$, $K,d\ge0$, and all raw-cell valuation envelopes are at most $K$. Under each raw medium-score tilt, suppose guard mass is less than one and its exact guard perturbation is at most $d$. Then

This is the precise finite guard step linking abstract bridge data to the raw reference law.

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