Use of an appendix in a long paper

Question

I am writing a long paper (around 100 pages). I would consider 50 pages of it interesting in that it solves a problem of some significance in my field and contains an number of difficult ideas in the proof (I think!). The other half is basically case checking using the definitions/lemmas from the first half. The case checks are fairly straightforward but rather tedious and are appendix material.

My main concern is publishability. I'm hoping that the first half might be publishable at level X but worried the overall length would make it difficult to publish there or maybe almost anywhere.

Thus, assuming things have been done efficiently, my question is which of the following options sounds most reasonable, or if there are other options?

1. Submit the 100 page piece to the arXiv and to the journal; let the editor/referee decide to ask the 50 pages to be cut or not. (Concern is that the length leaves an immediate impression of "too long".)

2. Break the 100 pages into a main paper and an appendix. Submit two things to the arXiv and submit the main paper to the journal with a pointer to the appendix. Figure that if the main paper is acceptable the editor/referee can ask to publish the appendix, or not. If not, the appendix is arxiv only.

3. Submit the 100 page piece to the arXiv. Then submit the abridged version to the journal, pointing that full details of the case checks are in the arxiv version. (Concern is that it leaves a bad impression that the submitted version and arXiv version are drastically different.)

Thank you.

Answer 1

This is tricky, because it strikes at the tension between pressures from the publication system to keep papers short vs our collective desire to have a peer-reviewed literature with no gaps. Let's think about what's driving those tensions before we dive into what's the best course of action.

Pressures to keep papers short come from:

• Journals, because there's often a higher bar for longer papers, because they take up more space in the issue.
• Time, because referees take more time when sent a longer paper.
• Jobs, because, all things being equal, a series of short publications is looked upon more favorably than one long preprint.

On the other hand:

• Sometimes the appendix is long simply because of the nature of the proof, and cannot reasonably be shortened or split into separate papers.
• Depending on the referee, it can take the same amount of time to referee a series of papers, because referees for the later ones want to also read the earlier ones to be sure they can be relied upon.
• It's important for results to be peer reviewed and published. If you leave a chunk of the proof on the arXiv but the published part of the paper needs that work, it can raise questions from the reader. People might be unsure if the proof was fully checked, and might wonder why this chunk wasn't published.

When faced with hard questions, it's good to be guided by what's best for the reader while also thinking about what's best for your career. It's clear that, if the paper can be split into a series of short papers, that will make it easier for the reader to digest them in small chunks, and will be best for your career because it's more publications and generally shorter referee waiting times (so, I support "possibility 4" if you can do it). But let's assume the proof cannot be broken up in this way. In that case, I think it's best to publish the one long paper, where half of it is this technical appendix. That is, I support option (1). I also think the advice in the comments to communicate with the editor is good advice. Editors understand the importance of creating a body of literature that avoids relying in critical ways on unpublished proofs. Whenever possible, it's good to have the editor on your side. If you get the editor in your corner, that removes the main obstacle. Your editor can then argue on your behalf to the editorial board if anyone raises an objection about the length. If you are at a stage of your career where you need publications quickly, the editor can also lean on the referee to do their job faster. It would also be smart to aim for journals that publish long papers and aim for electronic journals where length is less of a concern.

One last comment is that sometimes junior mathematicians don't know what bits of a proof can be left to the reader. If something is straightforward, and the author carefully checked it, sometimes it's ok to leave the proof to the reader as an exercise, especially if you think that's important for the reader's success later on in the paper. These kinds of things are not "gaps in the literature." But, I can't imagine leaving 50 pages worth of exercises for the reader. In this answer, I assume the author knows which things are essential to include and which details could be left out, and has decided that all 100 pages are necessary to convincingly prove the result.