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Let me tell you the story. I am a researcher in Mathematics and I have been the past months developing an idea that seems simple but potentially fruitful. The idea is so simple and straightforward from the current literature (at least for me) that I was even concerned that something like that was already (and) better studied. However, I was checking during some weeks and I am sure that nobody developed that idea so I began to write a paper that is now a long paper and it is in its 3rd week of preparation. I did already a lot of work.

I was in that situation when some days ago I entered in a very famous forum for math discussions (not in Stack Exchange) and saw an image (not even a TeX document, it was a mere drawing) just an image and a post of someone describing something very similar to what I am currently studying. It is not exactly the same, though, but you can consider that my construction is some kind of particularization (the object is introduced in the post is so general that without particularize you can say very few things and I also use this in connection with other branch of mathematics in a way that seems original and novel and it is of course not mentioned in that post).

The problem came when I was checking more on the person publishing that idea (as I said just one post with a text of a few paragraphs, less than half a page) and this person seems like a bit of a crackpot in the sense that the only thing that seems to do is to stake territory out by publishing some unpolished and partial ideas in his/her blog (always really short underdeveloped ideas, never -not just one- long citable papers with actual developments and content). It is reasonable to think that if you begin to write ideas randomly at this rate at some point you will touch something interesting by mere casualty, and this is what happened, though the touch is just tangential.

Do not get me wrong: I want to cite this person as I consider that there is some value in the fact that he/she saw this and introduced it although very rudimentarily and not rigorously; the problem that I face is that I am not sure how could affect to my reputation or the acceptance of my paper to cite a crackpot-like person who could (although it is clearly not true) use this against me maybe saying that I stole his/her idea. I want to be morally okay and recognize to this person his/her novelty in that generalization, but I got there independently and actually working though the idea also and I would not like that this person could make a nasty statement about my integrity when I am really trying to be fully integral and actually recognize his/her part (tangential as I did not get ideas from the post because I reached my idea independently and hard-worked on it) in the novelty of the general case. How would you manage such a situation?

I am also thinking that citing such a source could not be well-seen by a potential journal and could lead to automatic rejection of legitimate work. I am thinking in some names of crackpots that got cited in legitimate work and then some undesirable things happened (I cannot write particular examples here because it could damage some -already damaged- reputations, but we can all think in some of the kings of viXra or GM in arXiv to fit into this non-hypothetical situation).

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In the strictest sense, a citation is exactly that: A citation, not an endorsement. As a consequence, I would find it unlikely that someone would consider your paper any less just because you cite something or someone.

But then you also always have the opportunity to qualify citations. For example, you can say something like the following, which is a pretty strong endorsement of the work you are citing:

In [13], Bayer and Schmidt have previously considered this exact problem and produced an excellent algorithm to solve it. That said, while we know from their work that the algorithm has optimal complexity on average, there are also known cases where it runs for far longer than in the optimal case. This paper addresses this flaw.

Compare this with the following citation:

In preparing this work, we have spent a substantial amount of time on trying to find literature that considers the problem we address here. Very little can be found, with the possible exception of the blog post [42] that presents some ideas -- but few details and no worked out solutions -- of what we do here.

Such a statement makes it clear that you think it is related, but it's not an endorsement because you also make clear that whatever is presented there is not a full solution of the problem. This seems unobjectionable to me: Nobody can be mad at you for citing prior work this way, as you make it clear that whoever goes to that blog post will not find prior art, just ideas.

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Just cite them.

You write, I consider that there is some value in the fact that he/she saw this and introduced it although very rudimentarily and not rigorously, so mention that. You also write, I am not sure how could affect to my reputation or the acceptance of my paper to cite a crackpot-like person. Why would citing a crackpot-like person matter? You say they introduced the idea, that's what you're citing. Not citing, as you go on to write, would result in allegations that I stole his/her idea.

You could perhaps place your citation in the following context: Independently of this work, the underlying idea appears to have been first recognised by X. This work goes beyond that presentation to ABC.

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    From some collegues I know (myself probably included), if something sketchy is cited, this makes a negative impression (probably subconsiously). I don't have a better solution as you, but I see why "citing a crackpot-like person" could matter. – user111388 Sep 4 at 11:29
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    @user111388 That's a problem for your colleagues. Academia demands prior work be cited. Somewhat related: Citing prior work by Nazis. – user2768 Sep 4 at 11:32
  • I know that prior work must be cited and that there is no better solution. I wanted to remark that "citing a crackpot-like person" is, unfortunately, a problem and not as easy as "why would citing a crackpot-like person matter", unfortunately. – user111388 Sep 4 at 13:33
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    I think using the right context is key in this. I'd even go so far and formulate something like: "While preparing this manuscript, the author has been made aware that a similar approach has been independently proposed in online discussions before [citation], but no attempt has been made to carry this idea out to completion." Or even explain why this idea alone is insufficient. The main point of course is to immediately convey that your paper is completely independent, i.e. as you explain in your story, you would have come up with the same paper even if there never had been a crackpot. – mlk Sep 4 at 14:17
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Obviously, as you say yourself, you have to cite it. And I see your problem - your paper will be reviwed and read by humans, who may have their biases. One of them could be "OP cites a paper from this nationwide-known crackpot, so the paper cannot be serious". I've unfortunately encountered biases among academics in many ways (eg that people from certain nations do not produce valueable research) and I don't think anybody is completely free from them (which may sometimes good - otherwise people would have to read many useless crackpot papers which proved major theorems).

In your case, I have only two advices:

(1) Write your paper as professional as possibly be. Sometimes people are sloppy with proofs and this is widely accepted (although I read yesterday on Stack Exchange the opinion "one small typo should imply paper rejected" ) - here you should not be sloppy with proofs, layout, grammar etc. The people who read this should get the impression that it is really professional and that you are not a crackpot. Ask your collegues for their opinion. Prove in your paper that ehat the crackpot says really makes sense.

(1b) If at all possible, cite many "serious" papers. Of course, not irrelevant ones. But if you have thw choice between "putting some more results to the paper and thereby citing serious papers" or "keeping those results for a follow-up paper", choose the first option. I repeat: You should not cite papers just to cite them, but because you need them. And of course, you should not make the paper far too long just to cite and include results...I think you get my idea.

(2) Talk to other people. My impression is that "unexpected" things like "I found gold in some crackpot's work" are often better told orally than in paper. If you go to conferences and give a talk, mention the funny story that you found this result in some unexpected place. If you have dinner with collegues, tell them this funny story. Maybe this will make them look together at the result with you (if it is interesting for them), maybe they will also cite it if they need it. Anyway, when the community sees the paper, chances are good that people already know about this results and will not be surprised and possibly even checked the crackpot paper because they found this story so interesting.

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