Once on a late-night session, I had Cline!Claude spontaneously point out the time to me and suggest that I get to bed and come back fresh the next day.
I don't think it's in the system prompt, but that the harnesses time-stamp each turn in the context.
And from what I've seen, they also include the current and max context, so that the model can decide whether to continue work, suggest compaction, or prefer actions that might reduce the growth of its context.
> Once on a late-night session, I had Cline!Claude spontaneously point out the time to me and suggest that I get to bed and come back fresh the next day.
I had Claude say something "It's getting late, let's pick this up tomorrow" at like 11am.
As for context, in my experience Claude starts trying either to do maximum work with minimum tokens when it's approaching limit, or it starts deferring useful work while doing busy work. Both result in a mess and complete loss of traction after compaction.