In distributed collaborative systems, participants maintain a replicated copy of shared documents. They edit their own copy and then share their modifications without any coordination. Copies follow successions of divergence and convergence. Convergence is a liveness property of collaborative systems. Some malicious participants may find an advantage to make the collaboration fail. To that end, they can preclude convergence of the copies. To protect convergence of copies, participants can exploit an authenticated log of modifications. New participants have to retrieve the entire log in order to contribute. Unfortunately, the cost of joining a collaboration increases with the size of this log. Causal Stability allows to prune authenticated logs in a static collaborative group without any malicious participants. In this paper, we first tailor Causal Stability to dynamic groups in presence of malicious participants. We then propose a mechanism to verify the consistency of a pruned log and a mechanism to authenticate a snapshot from a pruned log.