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In the context of preparing a CV for a math academic job search
Is it advisable to list preprints which are not yet accessible to the wide public in the CV?
If so, should it be in a rubric of its own (i.e. separate from "research publications"), or can I put it in the same rubric but write something like "(draft, available upon request)" or "(in preparation)", depending on its actual status, to its side?
If the paper has been submitted, then of course you can list it as "submitted", whether it's public or not.
Otherwise, I think that about all you can do is to say "in preparation", but this won't really have much impact. My impression is that "in preparation" means about as much to a search committee as "I had this idea for a paper", i.e. practically nothing. They aren't really likely to believe a candidate's estimate that the paper is "99% done", since it's obviously self-serving. And anyway, the last 1% is often where you discover a critical gap that takes months to fix, or can't be fixed at all.
If the paper really is done or nearly done, your best bet is to work hard and try to get it submitted or posted publicly (preferably both) before you send in your job applications.
If you can't get to that point, then the next best thing is to make sure that at least one of your recommendation writers is familiar with the project. (If you have co-authors, ask one of them to write you a letter.) They can write about how awesome it is and assure the committee that it really is practically done. In this case you still say "in preparation" on the CV, but you have some third-party backup.
I second Nate Eldridge’s excellent answer, and in particular the opinion that “in preparation” means nothing and will be ignored.
“Submitted” is okay to write if true, but also doesn’t mean much if the paper can’t be viewed by the person reading your CV.
“Available upon request” is marginally better than “in preparation”, as it suggests you are willing to at least consider sharing the draft on the off-chance that someone will ask for it, but given that you’re putting the burden on people to contact you to ask for the paper when they may not feel comfortable doing that (or don’t have the time to start running after job candidates to ask them for materials that most other job candidates have already provided), is also not particularly helpful.
The best and most credible way, and one might say the only credible way, to claim a private preprint would be to include in the CV a private link (google docs, Dropbox, personal web site etc) to download the paper. Personally I would heavily discount any mention of a draft that doesn’t allow me some easy mechanism to view it. It’s nothing personal against you - just cumulative life experience that taught me that such claims often amount to nothing more than hot air.
Good luck with the job search!
You are a mathematician. Maybe I am overstating this a bit, but you should have no preprints that are not publicly available.
The side benefit of this approach is that accepted papers are also available on the arXiv for anyone. And you can reference your submitted but not-yet-accepted papers in your next work immediately.
In most cases, you are allowed to update the arXiv version to the post-review revision state. You are not allowed to publish the final journal PDF on the arXiv, but who cares. For this, you need to check with the journal. Even if not revised, the initial state of the paper is available to everyone, which increases visibility.
