The ledger gives uniform eventual source-input and primitive-gap assembly

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 a finite prime set $P$ containing all primes at most $W$, exponent $E>0$, physical intervals with lower endpoints at least one and upper endpoints strictly below two, and a guarded tail family $F$. Assume $c,\beta_a,\mu>0$, $\beta_p\ge0$, four positive margin floors, and the Section 8 ledger for the raw and guarded smooth mass families and the prescribed $\log Y,\Lambda_0,m_f$. There are constants $C_m,\rho>0$, chosen before the mesh, such that for every regular relative mesh, eventually the following implication holds. For any source bridge at index $n$ and cutoff $W$ on the literal fiber of $F$, and any fresh inputs $J$ with the fixed exponent and coefficients, suppose its sample is the canonical guarded sample, its smooth mass is synchronized, the four margins meet their floors, its frozen and final active masses equal the scalar-family values, and its rounded-source residual inputs hold. If the combined anchor/bank divisibility and selector-charge divisibility hold, then source and primitive-gap packages exist for $J$ with

Thus neither constant depends on the later mesh or bridge choice; the eventual threshold may depend on the mesh.