How can I seek help in preparing a very long research article for publication? Some background first.
I recently graduated with a master's degree in applied mathematics. During graduate school I began working on a paper, which I continued to work on post-graduation. A complete working copy of the paper is done and I have posted it on the arXiv here. The work contained in the paper is completely original and solves an open problem.
It was of my opinion that the paper contained publishable material. To verify, I emailed a professor at my alma mater with a copy of the current draft (current as of approximately six months ago). The professor did reply stating that the work was publishable and even suggested some Q1/Q2 journals that might accept this type of work. While this was useful feedback, I received the reply in just a few days, so I doubt the professor in question had the ability to read my paper in depth.
The problem:
I have published a couple of papers before and thus have some experience in the world of academic publishing. That said, the scale and complexity of this paper is something I have never dealt with before so I am not comfortable with proceeding to publish it without help/guidance, i.e. on my own. In particular, I suspect I am going to have to divide the work into small portions and publish a few separate papers, but I don't know how best to do this and do not want to sink a lot of additional time into this without any direction. Also, the paper is very dense and I am concerned that its readability is not optimal. Given that I do not have a ton of experience with large papers like this and am essentially working in a vacuum, I also really desire to get feedback on the quality of my proofs, which I suspect are not as concise as they could be. My situation seems a little unusual and I suspect that the feedback I am looking for would typically be provided by an adviser in a Ph.D. program.
Given that I do not have an adviser that can provide detailed feedback, what should I do?
I have tried reaching out to researchers/experts with relevant backgrounds and offering authorship in exchange for the help I need. Since what I'm seeking entails a significant amount of work, this proposition seemed reasonable; however, my efforts have not lead to much fruit.
As mathematicians in academia, how are these types of requests viewed and how might I go about reaching out for help?  I do not have funding and so I considered the offering of authorship as a a reasonable incentive to get the help I need.  Is this practice frowned upon and is there anything else I can do to increase my chances of getting a researchers attention?
 A: You could  also just send jour work to a journal, for instance one of those suggested  six months ago by your professor. Hopefully, even if they reject it, a referee will tell you what to do in order to improve your work and make it ready for publication, including  breaking into more parts. It it true that editing is a very long process. But you would be now 6 months ahead in it, had you followed your advisor's advices.
A: First of all, I would consider it against the ethics of scientific publishing to accept an offer as a co-author when you were not involved in the research. So I don't think that is viable route.
What you have achieved is quite unusual, you have on your own identified and developed a research direction and produced a set of results that advance the state of the art. Isn't that what a Ph.D. is all about? Rather than seeking a co-author, I would seek a Ph.D. advisor. Contacting an expert in the field, asking for a chance to present your results – with the objective to expand this into a Ph.D. thesis – might very well succeed.
Preparing a seminar in which you present your work would also help you to focus on the essential innovation, which is difficult to extract from the arXiv paper. You might even find that this seminar can be converted into a paper that would be more suitable for publication. In the mean time, by posting your work on arXiv you have established your priority, so a journal publication is not at all urgent.
A: I usually solve this problem by publishing research announcements. I highlight the main results, write them down (without proofs, but with the reference to the original article in arxiv.org) in some small article and send it to a journal where they publish this (there are some Russian and French journals where mathematicians can publish texts like this).
But this is fatally important only if your employer requires you to publish regularly. If this is not necessary, you can simply send your big article to a journal which publish big texts, and if all is well, they will publish it (there are several journals for this, in particular, Journal of Mathematical Sciences). Of course, you will have to wait, most likely several years, but in any case, long articles are published with long delays. And of cource, no one bothers you to simultaneously publish a research announcement, as I wrote above.
Offering co-authorship to an outsider is an absurd idea.
