I built a project achieving similar goals. You launch a web server then connect to it using either browser or Android app, then create a session to talk to Claude Code. The sessions are synchronized in real time across all devices and automatically saved to disk and continued when server restarts. Recently I've added features to schedule tasks in the future and to assemble agent teams. The project is mostly vibe-coded with Opus 4.6 with few supervision beyond trying its functionalities out.
I don’t think zero knowledge systems are practical at the moment. It will take over around 8 orders of magnitude more compute and memory to produce a ZKP proof of generic computation like compilation. Even 2 orders of magnitude is barely acceptable.
The anti-terrorism act used in this case allows detention of no more than 1 hour, or no more than 6 hours under certain conditions. Arrest involves other charges so what you described could happen, but not without turns.
Project is at http://github.com/vincent-163/claude-code-multi/. Can be installed easily with nodejs.
Please provide feedbacks and suggestions!