What is Learnable in Valiant's Theory of the Learnable?

ArXi:2605.13840v1 Announce Type: cross Valiant's 1984 paper is widely credited with For every finite domain, including Valiant's Boolean-hypercube setting, we show that a class is learnable if and only if every realizable positive sample can be certified by a poly-size adaptive query-compression scheme. This is a new variant of sample compression where the learner certifies samples via a short interaction with the membership oracle.