Assumption: Conditional validation model

Conditional on $\mathcal{Z}$, each setting has a predeclared positive sample count $n_j$. Its scores $Z_{j1},\dots ,Z_{j{n}_j}$ are independent, in $[-1,1]$, and have common mean $m_j$. The same logical channel is tested in all settings. The calibration bias and transfer bounds hold on $G$.

Independence between settings is not required for the union bound. No fixed-sample theorem is used after an unaccounted adaptive stopping rule.