I think it’s trained into them so they emit a stop token with enough window left to generate a compaction summary

I would assume it's the harness sending the model a notification toward the end. At least Claude Code is designed to attach reminders with tool call output as a way for the harness itself to steer the model slightly.

Any idea what the ~rule is or how it's meant to work? I assume it'd work better if I can wire up my harness to handle it, but no idea. It didn't seem to know itself, from it's training. I didn't search too much yet though.