Assumption: Validation contract

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

1. the scores within each label-setting pair are independent and have common mean $m_{\lambda j}$;

2. the same logical channel ${\Lambda }_{0,\lambda }$ is tested in all three settings for that label;

3. on a joint event $G$, of failure probability at most $\beta$,

   $$|F_{\mathrm{obs},\lambda }-F({\Lambda }_{0,\lambda })|\le b_{\mathrm{cal},\lambda },F_{\mathrm{obs},\lambda }=\frac{1+m_{\lambda x}-m_{\lambda y}+m_{\lambda z}}{4},$$

   and

   $$d_{\diamond }({\Lambda }_{\star ,\lambda },{\Lambda }_{0,\lambda })\le b_{\lambda }.$$

The target ${\Lambda }_{\star ,\lambda }$ has the same finite logical input and output spaces. All allowances are nonnegative.