Preselected callbacks give synchronized post-Hfit input

Fix a regular mesh $M$ with $\delta>0$ and a public bridge family $B_n$. Supply the eventual coherent bridge-source obligation, a placed-selector callback uniform in every later mesh, and the corresponding single-mesh local Proposition 8.7 callback. All use the same guard ledger, depth, cutoff, source mass families, margins, and preselected constants $C_{\rm initial}$, radius, and $C_{P87}$. Assume $c>0$, $W\ge2$ above the canonical moment cutoff, $\delta_*>0$, $\beta_{\rm prot}\ge0$, $\beta_{\rm act}>0$, $\beta_{\rm prot}+\beta_{\rm act}\le c/d_W$, $K_0+1\ge1/d_W$, $C_{\rm mass}\ge0$, positive density and $\sigma$, and $\sigma\le\beta_{\rm prot}$. Also assume $C_{\rm initial},C_{P87}\ge0$ and positive radius. Then

No new analytic constant is selected after the final mesh; the preselected Proposition 8.7 constant is used unchanged.