The four statuses
Completed means every phase succeeded. The analysis is whole.
Partial means some phases succeeded and the rest are shown as calm per-phase notices rather than hidden. A partial analysis is still readable: the phases that could not be completed appear as quiet “could not be completed” notes in place, not as a wall of error, so you keep everything that did work.
Failed means nothing usable was produced. When that happens, the simplest next step is usually to run the question again.
Cancelled means you deliberately stopped the run, which you can do while it is in progress.
Interrupted runs are marked honestly
If a run is interrupted by an infrastructure problem rather than by you, a background process detects it and marks it honestly rather than leaving it appearing active forever. You will never be left watching a run that has quietly died, and a run will never sit pretending to work when it has actually stopped.
Where you see the status
Each analysis in your Research Library carries its status as a small pill, so you can tell at a glance which runs completed, which are partial or cancelled, and which failed. Opening an analysis shows the same status, with any per-phase notices in place inside the reasoning.