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I think that this kind of question is acceptable on MO. It is absolutely the sort of question that a research mathematician would like to ask to a ready-made community of other research mathematicians, so it seems in the spirit of the site.
There is the point that it is hard to definitively answer "no" to such questions. But in this case the next best thing is to hear "no, I don't think so" from a leading expert, and MO can provide that.
Moreover, reference requests seem to be completely kosher. Isn't this a kind of reference request?
Does "without success" in this context mean you've talked to people and the theorem you've proven is not known to them? Wouldn't that be success? Anyway, it's obviously appropriate to post such a question.
Yes, this is fine.
There is a slight danger with these questions: they could potentially provide "cover" for self promotion that we'd feel uncomfortable about. Certainly if it's asked as "There's this result I need, and which I know how to prove, but I'd really prefer if I can just cite something." then it's certainly okay. I think on the whole it's safe enough to just blanket approve this genre and deal with problematic cases on their merits.
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