Uniform canonical residual-physical power-row estimate

Fix a finite nonempty head family $P$, physical intervals $I$ with lower endpoints at least one and upper endpoints at most $C_{\max}$, and a guard ledger at every $n$ with fixed census constants $C_{\rm prom},C_{\rm bank}$. For a valuation law $\lambda$, put $\Delta_\lambda(p,q)=\operatorname{Cov}_\lambda(v_p,v_q)-\operatorname{Cov}_\lambda(\mathbf1_{p\mid m},\mathbf1_{q\mid m})$. Fix $W>1$ and coefficient bounds $A_c,A_p\ge0$. Write $G=\mathrm{canonicalPhysicalPowerCorrectionConstant}(P,I,C_{\max},W,A_c)$, $e_n=A_p\log C_{\max}/\log n$, and $R_n=\mathrm{physicalPowerCorrectionRowError}(e_n,G,n,W)$. The estimates hold uniformly for every later finite band partition, bridge $B$, and tilt parameter $\xi$ at ambient $n\ge N_0$, provided its cutoff is $W$, its sample data equal the canonical constructor with separated intervals and nonempty surviving cells, every effective prime coefficient is at most $A_c$ in absolute value, and the physical coordinate has absolute value at most $A_p$.

The threshold is chosen before the later partition, bridge realization, tilt point, and marked row.