Test-time search — best-of-N saturates at the support ceiling

samples N 12

expected quality–

in-support ceiling–

Teal = expected best-of-N quality as N grows. It smoothly saturates to the amber dashed line (the in-support ceiling) and never touches the red one (the global optimum, which the base doesn't cover). To surface a good action of density ε you need N ∼ 1/ε — that's the coverage coefficient C^★. More samples buys you precision inside the support, never a way out of it.