Question: Does Claude include CLAUDE.md in its own context after compact?

When compacting, Claude creates a summary of the problems it has been working on, and uses that as initialization for the next context window.

But one thing I'm uncertain of, which has large implications for tool use in general, is whether Claude also includes its CLAUDE.md in this compaction?

If not, that would seem to indicate that we need to tell Claude to re-read his CLAUDE.md after every compact, if there are important rules in there.

So I'd love to get an answer on this from someone who knows for certain. Because it also impacts MCPs as well (for example if I have an MCP that includes context instructions, do those get included in the new context after compact as well?).