Complete scores, conditional trials, and allowances

Independence between different settings or different labels is not needed for a union bound. Independence inside each conditional sample is needed. An unaccounted adaptive stopping rule invalidates this fixed-sample contract.

A sufficient calibration conversion is useful. If the actual common tested state ${\rho }_{\lambda }$ obeys $d_{\mathrm{tr}}({\rho }_{\lambda },J_{{\Lambda }_{0,\lambda }})\le {\delta }_{\lambda }$, and each complete score observable differs from its Pauli correlator by operator norm at most ${\eta }_{\lambda j}$, then

is valid. The Bell projector is an effect, so the state comparison costs ${\delta }_{\lambda }$; the analyzer comparisons cost the displayed norm sum.

The transfer allowance $b_{\lambda }$ is already in channel-distance units. It is not a fidelity bias.