Fringe social networks, e.g., 4chan or Truth, position themselves as "free speech" alternatives to their mainstream counterparts like Facebook or X (formerly Twitter). Due to their very lax moderation policies, they however tend to become a hotbed for misinformation or otherwise malicious content, which then tends to spread towards the general public. In order to effectively counter such a process, it is important to properly understand and model how content appears and spreads over fringe social networks. Accordingly, in this study we focus on the now-defunct Parler social network, and conduct a statistical analysis over 183 million posts dating from August 2018 to January 2021. The primary objective is to comprehensively analyze hashtag cascades related to the first impeachment of U.S. President Donald Trump. Our aim is to (i) uncover how external actors inject malicious and hateful tendencies into the network and (ii) quantify the levels of attention within these communities. We find that the hashtag cascade can be effectively modeled using the Hawkes process framework, specifically, employing an exponential decay kernel. Rigorous parameter estimation and statistical tools are applied to substantiate this assertion and evaluate the model's goodness of fit. Importantly, the analysis reveals correlations between levels of hate, the dissemination of misleading information, and the attention garnered within these fringe social communities. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
