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This is a bit vague because I don't want to out myself--but I got an on the spot CB last week at a job fair, but they haven't emailed me any information or indication making it "official." Does anyone have any experience dealing with this?

If it helps, I'm a 3L.

Reach out to recruiting, just saying something like "Last week on x day, I interviewed with [Attorney name], and he/she invited me for a callback. I'm very interested in your firm and was very excited to receive the callback offer. I wanted to check in regarding scheduling."