Uniform Proposition 8.7 data can be selected before the final mesh

Fix physical intervals $I$ and a guard-ledger family. If all lower endpoints are at least one and all upper endpoints are at most two, then there are a positive mesh tolerance $\tau$ and a width cutoff $W_0$. For every $W\ge W_0$, every mass family $q_n$ eventually at least one, and head patterns whose prime support is exactly the primes at most $W$, fix any construction parameters, nonnegative protected coefficient and mass bound, positive cell density and post-target margin, and nonnegative initial-deficit constant. There then exist a positive effective radius and $C_{87}\ge0$, chosen before the mesh, such that

for every permitted regular relative mesh of positive width. The callback applies Proposition 8.7 to the canonical fresh bridge with its synchronized varying active mass, target, marked deficits, and frozen/active weight ledgers.