Save Playground Conversation

A transcript to save, whole: there is no append-a-turn endpoint.

The page saves on an explicit click, with the conversation it currently shows, so the write is one row plus its turns and a resave is a new conversation rather than a mutation of the old one. That is also what keeps the ordering column honest: position is assigned here, from the list's own order, and never negotiated with a client over several requests.

A row in the history list: enough to recognize, not the transcript.