The Section 8 ledger provides a pre-mesh placed-selector deficit constant

Write $L_n=\log n$, $s_n=n/\log n$, $y_n=\lfloor n^{2/9}\rfloor$, and $\mathcal P_{n,W}=\{p\text{ prime}:W<p\le y_n\}$. Fix head patterns, physical intervals, a guard ledger, $c>0$, $W\ge2$, $W\ge2d+1$, $0<\delta_*<1/18$, $\beta_a>0$, and $\mu>0$, with all head primes at most $W$. Suppose total families $\log Y,\Lambda_0,m_f,\widetilde q$ satisfy the Section 8 ledger $q_{\rm raw}-\widetilde q=o(s_n)$ and $A_0=O(s_n)$. Then a nonnegative constant $C_{\rm init}$ exists before the final mesh such that eventually every compatible fresh canonical bridge and source package satisfies

Here compatibility means the prescribed protected and active coefficients and canonical guarded sample, exact synchronization of $\widetilde q$ with the guarded smooth-base mass, balanced and total coefficients in $[0,1]$, a nonempty broad smooth correction pool, and exact equality of the local height correction $d$ and active mass $q$ with the displayed Section 8 families. The eventual threshold is common to all meshes and such local choices.