I am a math postdoc, currently working on some conjecture. To avoid going into details, let's formulate it as follows: "every runcible doohickey is cromulent". A senior colleague told me last year that if I proved it, it would make for a "really nice paper" (that's her words).
Eight months ago, I found a partial proof: something like
Theorem 1: Every runcible doohickey is cromulent, unless it is in one of the families A_n, D_{2n+1} or E_6 (informally, this accounts for "less than half" of all possible families) and is larger than some minimum size.
(if you want details, the paper is here: https://arxiv.org/abs/1605.03833). I wrote it up and submitted it, to Journal A (a good but not top journal). It is currently still under review.
A few days ago, I finally completed the proof of
Theorem 2: Every runcible doohickey is cromulent.
(the paper is here: https://arxiv.org/abs/1612.08942). Following the suggestion of my colleague, I would like to try my chance and send it to Journal B (a top journal).
The problem is that the proof of Theorem 2 is really similar to the proof of Theorem 1; a lot of passages in the former are almost verbatim copies from the latter. (Of course I always disclose when it happens). There are still some significant differences:
- the definition of the central object of the paper had to be changed, adding a significant layer of complexity;
- a lot of intermediate proofs and definitions no longer worked, and had to be either considerably expanded or completely rewritten;
- paper 2 is generally cleaner and better-organized than paper 1 (despite the additional complexity);
- in paper 2, I proved an intermediate result that was not present in paper 1, and that maybe has some value on its own (though a colleague told me that in her opinion, it was just a trivial consequence of some results proved by our PhD advisor).
The issue becomes even more serious if you look at it backwards. Should paper 2 somehow get published before paper 1 (which is not completely ruled out given the vagaries of peer review in math), it would make paper 1 totally worthless, as almost every statement from paper 1 can be obtained as a particular case of a corresponding statement from paper 2.
(My feeling is that in an ideal world, paper 1 should have never been published. However I was in a rush to get published in time for job interviews, and I had no idea how long it would take me to get to Theorem 2.)
A few questions:
- Do you think there is any chance that, if the reviewer of paper 1 learns about Theorem 2, they will reject it, saying "this paper is not interesting, as it is just a particular case of Theorem 2"?
- Do you think it is likely that the presence of paper 1 will prevent paper 2 from being accepted by Journal B (which has high standards)?
- Should I go as far as to retract paper 1 before submitting paper 2? (However the reviewers of paper 1 probably wouldn't be too happy about this!)
I am also considering the following course of action: submit paper 2 to journal B, and suggest that they talk to the editors of journal A and that they assign to paper 2 the same reviewers as for paper 1 (if they are so inclined). Is it acceptable to do such a thing? I see two reasons for doing so:
- The altruistic reason is to avoid wasting the reviewers' time. Both papers are quite long (73 pages for paper A and 89 pages for paper B), and someone who has already read A would have a MUCH easier time understanding B.
- The selfish reason is that it could speed up the review process (and help the paper get published in time for job deadlines).
Any other advice about what to do in this situation is welcome! My main preoccupation is to maximize my chances for getting a job; the relevant deadlines for publication acceptance are roughly March 2017 and March 2018. So far I have only two publications, both in medium to good (but not top) journals. I would especially appreciate answers from mathematicians, as I have the impression that standard practices differ significantly from field to field.
EDIT: my judgments about journal rankings were initially maybe too harsh (see comments below Pete C. Clark's answer). I did this mostly out of modesty, as I looked at it from my perspective and from the perspective of my potential employers; however I forgot to consider the perspective of the editors or reviewers of the journals themselves. I apologize for this little blunder; I corrected it.