What survives closing a terminal
A detached tmux session on a running server can continue when a laptop sleeps, a phone loses power or an SSH client disconnects. The process runs on the server. If the process was on the laptop, turning off that laptop stops it. tmux alone does not survive a server reboot or guarantee that every application buffer has reached durable storage. Host policy can also end a process on logout or under memory pressure.
Reconnect to a run, do not create a duplicate
Keep the root task ID, child job IDs and the last event number (the event cursor). Reconnect should read those records and existing artifacts before starting more work. The same submission key must return the same task, and conflicting submissions must be rejected. The ledger belongs to the lifetime of the root task; reconnecting must not restore the original spending allowance.
There are two different failures: the client cannot reach Tvijo, or the worker cannot reach its model provider. The first may leave work running; the second may leave a billable outcome uncertain. Record each boundary and show the last confirmed event. Never label an uncertain model call free merely because the browser saw no answer.
Resources and recovery are explicit
A context window, RAM, disk quota and subscription quota are separate limits. Moving execution to your server needs an installed worker, authorization, enough resources and an explicit host selection. It is not an automatic way to bypass a provider context limit. A recovery plan includes persisted artifacts, backup verification and a controlled restart, not only a terminal session.