A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu graph. An empirical justification is presented for the self-organization of the segment of the X social network to the edge, which unites network users who post and repost content relevant to the 2016 and 2020 United States presidential debates. The time intervals during which the network is on the edge have been established. A comparison of quantitative indicators of the criticality of real and model time intervals was used to validate the discrete-time model.