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Is there any reason to expect that it doesn't mean all four of these things, in different circumstances?
Nate, given your scrupulosity, if the paper does not exist in a form that you will be willing to share with people evaluating your CV then probably you shouldn't include it there. If you want to be specific, as a part of job application or grant application, nothing prevents you from explaining in as much detail as you like what the status is, as part of the cover letter, the research statement, or a similar document that you are submitting. I want to make it clear that this is my personal opinion based on my experience. One reason why MO is not a good place for getting information about things like that is that no matter what answers you get, even if you ask a very narrowly formulated question, the actual practices that will matter to you, perhaps critically, may differ. Also, somewhat paradoxically, the MO voting system may skew the sample (a highly voted answer may represent wishful thinking; posting accurate but unappetizing details often generates hostile reactions; people who tend to answer such questions at MO are quite outspoken but aren't necessarily representative of the majority).
I am inclined to doubt that you're going to get a better answer than Scott Morrison's.
Certainly you can assume that the amount of credit given to you by listing a paper as "in preparation" on your CV (and not saying anything else about it) is essentially infinitesimal. If you want people to count it somehow, you should do something like posting a draft version on your webpage or at least an abstract / summary of results you have proven and/or want to prove. If dealing with someone else who lists this on their CV -- if you care about it, ask for more information.
Dear Nate,
Since this thread is turning into a de facto advice thread regarding the original question, let me say that my view is somewhat different from Kevin's: I would take "in preparation'' to mean that there is an announcement, that perhaps talks have been given, but there is no preprint (otherwise the paper would be listed as a preprint). I take "preprint'' to mean that a preprint exists, and is available somewhere (on the person's web-page, or on the arxiv) --- if I couldn't find the preprint after some straightforward searching, I would regard the CV as misleading.
As far as evaluating a candidate goes, listing a paper on a topic as "in preparation'' gives a sense of what the person is currently working on, what their ambitions are (in terms of what kind of problems they are trying to solve), and so gives useful information. On the other hand, this information doesn't really help in evaluating the strength of a candidate (say when attempting to rank competing candidates), because it is too ephemeral.
On the other hand, a preprint is a more substantial thing. If the candidate is in my field, or a nearby one, I can look at the preprint myself and form my own judgement, regardless of whether it has appeared somewhere. Also, a preprint can be read by letter writers, who may well comment on it in their letters. In other words, a preprint is part of the written record, and can carry weight just like any other part; it is missing the imprimatur of a journal, but this is just one aspect of evaluating a piece of work (one's own evaluation, and the evaluation of letter writers, being two other important aspects).
(For a more senior candidate, the issue of preprints is less relevant, since presumably these are only a small fraction of their written work. But for junior candidates, given the time that it can take for a paper to go from preprint form to acceptance in a journal, I don't think that it makes sense to ignore preprints a priori; they form data points which it may well be possible to evaluate.)
In the case of a paper,it means they don't know how to prove a result they've already announced and are too embarrassed to admit publically they jumped the gun.
In the case of textbooks or treatises,real life keeps getting in the way of finishing it.
Simple.
Andrew L.
Dear Andrew L,
That is an extremely uncharitable interpretation, which seems likely to be unfounded in most cases. Papers take time to write (my most recent substantial paper took more than four years to write), while the job market is on a set schedule. If it is time to apply for jobs, but the paper is not yet written, it is completely understandable why someone would describe a paper as in preparation; they are making the best of an unfortunate piece of timing. Whether this is particularly helpful in a job application is another matter (see the various comments above for different opinions on this), but I don't think there's any reason for believing that this kind of entry on a CV is typically insincere.
Yours sincerely,
Matthew
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