We revisit the setting of Interactive Proof Systems for Distribution Testing, introduced by Chiesa and Gur (2018), showing that a simple twist on the task requirements may lead to dramatic improvements, allowing verifiers with constant sample complexity.

We define and investigate the multi-prover and zero-knowledge versions of these interactive proof systems, using as flagship example the task of farness verification — the "dual" version of closeness testing. We hope our results will inspire others to investigate and analyze the power and limitations of multiple provers for distribution verification.