Note rejected from arXiv: what to do next? Short version: A note of mine was rejected by the arXiv moderation (something I didn't even know was possible) on account of being “unrefereeable”.  The moderation process provides absolutely no feedback as to why and does not answer questions.  I can think of various reasons but I don't know which are actually relevant, and I'm afraid that trying to resubmit the note, even with substantial changes, might get me banned permanently.  So I'm looking for advice from people with more experience either in the subject or in dealing with the arXiv, on what to do next (e.g., “forget it, it's crap”, “try to improve it”, “upload it somewhere else”, “do <this-or-that> to establish dialogue with the arXiv moderators”, something of the sort), or simply for insight.
[Meta-question here as to whether this question was appropriate for MO.]
The detailed story (this is long, but I thought important to get all the specifics clear; actual questions follow):
A little over a week ago, I asked a question on MO on a delay-differential equation modeling a variant of the classical SIR epidemiological model where individuals recover in constant time instead of an exponential distribution.  A little later, I found that I was able to answer my own question by finding an exact closed-form solution to this model: I wrote a short answer here and, since the answer garnered some interest, a longer discussion on the comparison of both models in a blog post (in French).  A number of people then encouraged me to try to give this a little more publicity than a blog post.  (My main conclusion is that constant-time recovery, which seems a little less unrealistic than exponential-process recovery, gives a faster initial growth, and a sharper and more pronounced epidemiological peak even assuming a given reproduction number, contagiousness and expected recovery time, while still having the same attack rate: in a world where a lot of modeling is done using SIR, I think this is worth pointing out.)
So I wrote a note on the subject, expanding a little more what I could say about the comparison between this constant-time-recovery variant and classical SIR, adding some illustrative graphs and remarks on random oriented graphs.  After getting the required endorsements, I submitted this note to the arXiv (on 2020-04-06) in the math.CA (“Classical Analysis and ODEs”) category.  The submission simply vanished without a trace, so I inquired and the arXiv help desk told me that the submission had been rejected by the moderators with the following comment:

Our moderators have determined that your submission is not of sufficient interest for inclusion within arXiv.  This decision was reached after examining your submission.  The moderators have rejected your submission as "unrefereeable": your article does not contain sufficient original or substantive scholarly research.
As a result, we have removed your submission.
Please note that our moderators are not referees and provide no reviews with such decisions.  For in-depth reviews of your work, please seek feedback from another forum.
Please do not resubmit this paper without contacting arXiv moderation and obtaining a positive response.  Resubmission of removed papers may result in the loss of your submission privileges.

I must admit I didn't know there was even such a thing as arXiv moderation (since there is already the endorsement hurdle to cross) or, if there was, I thought it was limited to removing completely off-topic material and obviously off-topic stuff like proofs that Einstein was wrong.  And I certainly disagree about the assessment that my note is “unrefereeable” (it would probably not get past the refereeing process in any moderately prestigious journal, but I find it hard to believe that no journal would even consider sending it to a referee).  I made an honest effort to try to ascertain whether the exact-form solution I wrote down had been previously known, and could come up with nothing: but of course, this sort of things is very hard to make sure and I can have missed some general theory which would imply it trivially.  I also believe the remarks I make near the end of the note concerning the link between extinction probabilities and attack rates of epidemics, extinction probabilities of Galton-Watson processes, and reachable nodes in random oriented graphs, are of interest.
The problem wouldn't be so bad if I could at least have some kind of dialogue with the arXiv moderators, e.g., inquire into how this judgment was made, and what kind of changes would get it reconsidered.  But I wrote to moderation at arxiv.org to ask for clarification and got no answer whatsoever.  So I'm taking their advice and trying to “seek feedback from another forum”.
Clearly it was a mistake of mine to submit a note with so few references and I should probably have framed the main result as a precise theorem.  Hindsight is always 20/20.  Now I don't know whether this can be fixed or whether this would be enough: I have now heard chilling stories about how the arXiv is capricious in banning people silently and permanently for trying to upload something which they don't like, which makes me wish to be careful before I try anything like re-uploading.  Also, it may have been a mistake of mine to create my arXiv account using a personal rather than institutional email address, I don't know.
It is also possible that the arXiv is currently overwhelmed by papers on the pandemic and have taken a hard line against anything remotely related to epidemiology or Covid-19.
I thought it best not to upload the note to viXra, which would probably classify it in everyone's eyes as crackpotology, so the best I could come up with (beyond self-hosting) was to place it on “HAL Archives Ouvertes”, a web site created by some French institutions which, however, does not have the same goals as the arXiv (it's more about storing than dissemination) and does not seem to provide a way to publish the source files.
Questions:


*

*Can somebody provide insight as to how the arXiv moderation process works and how they form their decisions, or why my note might have been rejected?

*Is there some way to communicate with the arXiv moderators?  Is there any way I could ask for a second opinion after improving my note (e.g., to add many references) and without risking a ban?

*Is there anything else I might try to do with that note apart from just giving up?  (Various people have suggested bioRxiv or even PLOS One, but I wouldn't want to risk being blacklisted by every scientific preprint site in existence in the attempt to make one result public.)
 A: Q1: The arXiv moderation procedure is described here; as you can read, "unrefereeable content" is a placeholder for a paper "in need of significant review and revision". Unlike refereeing, which has a relaxed time schedule, moderation is done in the 6 hour time frame between the closure of the submission window and the announcement of the new submissions. A typical moderator may find themselves deciding on a dozen submissions, so this is very much a rapid decision, and first impressions can make a big difference. A submission from a personal rather than institutional email address, formatted in a somewhat unusual way, with minimal references to the literature, on a topic where everyone and their dog seems to have an opinion, may very well trigger an unjustified negative decision.
Q2: The mathematics moderators are listed here, but it is considered inappropriate to contact a moderator directly. The appeals process, described here, outlines the steps to take, and also points out that it may be a lengthy process.
Q3: It is worth to appeal, because that will allow the moderators to take the time they would not have in their ordinary work flow. A careful look at your note should convince them this is substantial research.
A: Speaking from personal experience I would say the main 'indicators' which a moderator might use to reject an ArXiv submission are: very few references in the bibliography, poor presentation, rushed appearance or appearance of being cobbled together, short paper which does not appear to contain much content. 
A: I think of "refereeable" as meaning "a reasonable editor at some non-predatory journal somewhere could consider this paper worth sending out to a referee".
With your paper, the obvious red flag for me is that it only cites one reference - it makes no real attempt at all to connect your work to existing literature.  On that basis alone, any journal would desk-reject the paper without sending to a referee; it would be a waste of a referee's time to review a paper in that form.  So I think the arXiv moderators are literally correct in calling it "unrefereeable" and in rejecting it.  (And of course, it can't help that there is undoubtedly an uptick in crank papers on epidemic modeling right now.)
It's unclear at first glance whether you are giving a new exposition of existing results, or discussing new interpretations / consequences / applications, or whether you are presenting genuinely new results.  Any of those things would be acceptable for arXiv (the first a little bit borderline but still usually okay), but you need to make clear what's what.
So that's the obvious first way to improve the paper: include a proper literature review, and put your work in context.
Other than that, the paper certainly appears to be real mathematics (though  I'm no expert in that area).  You might be able to have someone in the field (maybe one of your endorsers?) look at the paper on the same basis: if they were a journal editor, would they send this paper to a referee?
When you get it to that point, I think it would be completely reasonable to resubmit to arXiv.  It sounds like you ought to contact the moderation team first, probably with some acknowledgement that the initial version was unacceptable but that you have improved it now.   It's possible that it will be rejected again, but if so it would be reasonable to appeal at that time.  
Also, I note that you don't include any contact info in the paper (at least not in the HAL version), nor mention any affiliation.  Contact info such as an email address is generally important.  And if you have an affiliation with an academic institution, company, or other known organization, it would not hurt to mention it (get your employer's consent if you need it, of course).  Ideally your affiliation should not be a consideration in the preprint's acceptance, but it is something that people will notice.
A: Let me give some observations with respect to your article:

*

*Your recollections about classical SIR are possibly too detailed. A short summary of the most important findings might suffice (without extensive proofs like that of Proposition 1.5).


*You could cite e.g. a paper like Hethcote's The Mathematics of Infectious Diseases which summarizes many classical results.


*Your Hypothesis 1.6 isn't a hypothesis but an assumption.


*Your emphasis on the behaviour for $t \rightarrow -\infty$ seems a bit too strong to me. Interesting things happen (only?) for $t \rightarrow +\infty$. I missed a discussion of initial conditions, instead.


*With respect to readability I would suggest to use the variable name $s_{\infty}$ instead of $\Gamma$ (which is the classical name of another transcendental function – next to Lambert's $W$) and to stick to the standard symbol $R_0$ instead of $\kappa$.


*Personally I would have been interested why $s_{\infty} = W(r\cdot e^{r})/r$ is the unique solution of $x = e^{r(1-x)}$ with $r = -R_0$. (I had to find out that this is a classical result.)
Hope this helps.
A: My own publications have all been in one tiny specialty in nuclear physics, with only one exception, which was "multidisciplinary" in the sense on touching multiple areas within physics. I found the experience of writing that paper somewhat unnerving, because it was difficult to tell whether what I was doing met the standard for being interesting, original, or even correct. When you're working within your own tidy little area, no matter how small, boring, and inconsequential, it's much easier to judge whether your peers would consider it to be good work.
Arxiv has performed a valuable service for you, and they've done it free of charge and without any ulterior motives. They've told you that this paper has problems, and in my opinion, it does. Others have pointed out that it only has one reference. This is not really the issue per se. Rather, the issue is that your paper doesn't make the case for itself as being important. One of the functions of references is to establish that, for example, people have already posed this problem and worked on it, or that it fills a need that has already been identified.
Regardless of whether your paper has many references or few, it needs to make the case that it is important, original, and of interest to someone in some field. The first step in making that case is simply to assert that. Can you assert that this work is of interest to mathematicians? To epidemiologists? If so, then assert that, possibly as the first sentence of the abstract. Of course, being able to assert this implies being able to back it up with an argument. That argument should be either explicit or implicit in your paper and its references.
