Feature request: save session summaries from /compact

First, let me just gush over how awesome Claude Code is. You guys are brilliant in building the ecosystem around the best coding model. The overall value is more than the sum of the parts.

I have spent significant time (and API fees!) in the last few days with Claude Code and have decided it is my preferred way to work. The /compact feature is awesome. I might use it two or three times per hour. The summary it produces is valuable history. Please provide a way to automatically save it as Markdown files with timestamps in the file name so that the chronological order is preserved when sorting alphabetically. Given that the files will have their own timestamp metadata, it may not be necessary to include the timestamp in the filename, but I think it will be useful anyway. Perhaps this preference should be configurable.