Sync conversation history per repository, across machines

I work on one project from three computers — home and two offices — with the same git repo cloned on each.

Every time I switch machines, Claude starts blank: it knows nothing about what we discussed or decided on the other computer. My workaround is a decisions file committed to the repo, and starting every session with "read the devlog."

Remote Control isn't the answer — that controls one specific machine from another device. Cloud sessions aren't either — they can't reach my local database and local toolchain.

What I'd like: conversation history tied to the repository (by git remote URL) and synced through my account. Sit down at any of my machines, and the project conversation is already there.

No files, tests, or entry points are named. Start by tracing how the CLI identifies a repository and stores conversation history, then compare that with the existing Remote Control and cloud-session boundaries described in the issue. Done means history is linked to a git remote URL and available on another machine without requiring remote control or cloud access to the local toolchain.

Written by the indexing model from the issue text.