Bounded complete-record certificates

For randomized settings with known probabilities ${\omega }_s>0$, define

The outcomes include setting labels, preparation records, rejections, and sensing failures. Nuisance parameters are jointly constrained across settings.

For a predeclared $f(s,z)\in [0,1]$, set $q_h({\theta }_h)={\mathbb{E}}_{h}f$.