A CDT agent who is given the choice to self-modify at time t will not self-modify completely into a UDT agent. After self-modification, the agent will one-box in a Newcomb's problem where Omega made its prediction by examining the agent after time t, and will two-box in a Newcomb's problem where Omega made its prediction by examining the agent before time t, even if Omega knew that the agent would have the opportunity to self-modify.

In other words, the CDT agent can self-modify to stop updating, but it isn't motivated to un-update.