Assumption: Conditional fixed-sample validation

Conditional on a declared training, selection, and calibration record $\mathcal{Z}$:

1. $n_{Aj}\ge 1$ is fixed before validation scores are observed;

2. scores $Z_{Aji}\in [-1,1]$ within each pair $A,j$ are independent and have a common mean $m_{Aj}$;

3. all three settings test the same CPTP logical channel ${\Lambda }_{0,A}$;

4. on a joint event $G$, with $\mathrm{Pr}(G^c)\le \beta$,

   $$\left|F_{\mathrm{obs},A}-F({\Lambda }_{0,A})\right|\le b_{\mathrm{cal},A},F_{\mathrm{obs},A}=\frac{1+m_{Ax}-m_{Ay}+m_{Az}}{4},$$

   and

   $$d_{\diamond }({\Lambda }_{\star ,A},{\Lambda }_{0,A})\le b_A.$$

All allowances are nonnegative, and ${\alpha }_{\mathrm{s}}+\beta <1$.