New paper which is very similar, but subtly different, from previous paper

Question

I wrote a paper that contains a fairly long and intricate proof. Now I have a new paper I am working on that extends this proof to a slightly different setting. Even though the overall setting is only slightly different, in my opinion this small difference is still quite noteworthy. For example, there are a number of other papers which use the result from the previous paper, and one can almost automatically get improved parameters for these applications.

The overall outline of the new proof is almost identical to the previous one --- it consists of about 5-6 pages with ~10 definitions/propositions, which occur in the exact same order in the two papers.

However, the proofs are subtly different --- I would say that the difference are far too subtle to merely hand-wave away with something like "We can show using a similar proof that ...." These differences are not confined to a single proposition either, they are spread out across the entire proof.

So, I am faced with a few options which seem less than appealing:

1. Copy the old paper nearly verbatim, with new proofs in the appropriate places. This has the advantage that the new paper will be mostly self-contained and readable. But the downside is that the is massive (self) plagiarism --- I am forced to copy pages of text without block quotes or specific attribution. (I of course state in my new paper that I am heavily copying from my old one, so there is some attribution)

2. Try to rewrite the old proof in a basically different way. This avoids the plagiarism problem. However, this will definitely not help the reader trying to compare the new result with the old one. It also seems perverse that a proof which was carefully laid out and understandable has to be restructured for no good reason.

3. Just mention the differences between the new paper and the old paper. But this will be almost unreadable unless the reader has a copy of the old paper and compares the two papers line by line. I would be forced to say something like "as was shown in Proposition 6.13 of [old paper], we have the following.... We then apply Proposition 6.14 of [old paper] and ...."

I am inclined to go with option (1). (If I was not the author of the old paper, it would make me much more queasy). Are there any good guidelines or suggestions for this situation?

Answer 1

What I would do, assuming this new development is worthy of publishing (which I cannot guess without knowing the contents - and the reviewers will do anyway):

Write the paper (the new one), in a self contained manner. Your previous work is a related work, goes in the bibliographical review. Compare and position your new paper wrt the old one, in the same way you would do if it was from another author. Including using the same proofs as references ("Theorem 4 from [1]"), for the ones that do not have differences. Don't copy stuff...

There is no problem if you paper is similar to another one. Just highlight the similarities and differences. I usually like such works, because subtle differences can be derived from different interpretations of the same stuff, which can lead to very cool stuff :)

Answer 2

I agree that option 1 is the best, but I think this option is not as unappealing as you think. Specifically, it's important to stress that if you cite the previous paper and acknowledge the parts that you are copying from it, then this cannot in any sense be considered self-plagiarism. At worst, it would be a reason to reject your paper for not being novel enough (which is an "honorable" reason for rejection, as opposed to self-plagiarism which is a form of academic misconduct).

I also notice that you mention that there would not be "specific attribution"; I'm not sure what you mean by this. I don't think it's necessary to delineate precisely every line that you copy from the old paper, or to point out every place where you modify a word here and there. Simply write the theorem, then write your 5-6 pages of definitions and propositions, preceding them with a statement along the following lines:

In the remainder of this section we prove Theorem 1.3. We remark that the structure of the proof closely resembles the proof of Theorem 2.3 from [citation], and consists of a sequence of definitions and propositions (Definition 1.4 to Proposition 1.11), which are fairly exact parallels (and in places identical) to the analogous sequence of definitions and propositions in section 2 of [citation]. Note that it is necessary to include the complete proof here rather than appeal to the results of [citation] due to the difference in the settings of our Theorem 1.3 and Theorem 2.3 of that paper, which requires certain subtle modifications to be made in a few of the arguments and definitions.

After the end of the proof, you may want to add a short discussion of specific places where the subtle changes in the arguments or definitions were inserted and why they were necessary. This would preempt a possible criticism that your paper repeats too much of the content of the older paper and is therefore not novel enough, and increase the chances that the new paper would be accepted.