A finite-sample certificate

This is the attempted-run Hoeffding certificate Hoeffding1963; the separation between scalar scores and complete records is also part of the En03-A interface CheungEn03A. Using the same sample to select the best decoder or time interval requires an additional selection correction or a separate validation sample.

For a complete finite record alphabet of size $K$, coordinatewise Hoeffding and a union bound imply, with probability at least $1-\zeta$,

Dependence among records within an attempt does not increase $n$.