One way of noticing the Son-of-CDT issue dxu mentioned is thinking of CDT as not just being unable to control the events outside the future lightcone, but as not caring about the events outside the future lightcone. So even if it self-modifies, it’s not going to accept tradeoffs between the future and not-the-future of the self-modification event, as that would involve changing its preference (and somehow reinventing preference for the events it didn’t care about just before the self-modification event).
With time, CDT continually becomes numb to events outside its future, loses parts of its values. Self-modifying to Son-of-CDT stops further loss, but doesn’t reverse past loss.
One way of noticing the Son-of-CDT issue dxu mentioned is thinking of CDT as not just being unable to control the events outside the future lightcone, but as not caring about the events outside the future lightcone. So even if it self-modifies, it’s not going to accept tradeoffs between the future and not-the-future of the self-modification event, as that would involve changing its preference (and somehow reinventing preference for the events it didn’t care about just before the self-modification event).
With time, CDT continually becomes numb to events outside its future, loses parts of its values. Self-modifying to Son-of-CDT stops further loss, but doesn’t reverse past loss.