Anyone else notice a math purgatory?

Looking through your recent questions, I suspect the ‘purgatory’ you’re seeing is about your style of question-writing, not the level of the mathematical content. In general, I don’t think there’s a gap between the level of material accepted on Math Stackexchange and here — at least in the fields I’m active in, there’s a decent overlap between what I see getting asked and answered on the two sites; and as Timothy Chow says, when questions are borderline here, people are usually sympathetic if there’s an explicit declaration that it’s cross-posted after not receiving answers on Math Stackexchange after a suitable wait (about a week).

However, I think MathOverflow has much higher expectations of writing quality compared to Math Stackexchange. There, questions come from students at all levels of maturity and experience, so readers (= potential answerers) accept as a baseline that untangling some bad writing is part of the answering process. Here, if a question isn’t presented clearly, people are more likely to just bounce off it and move on — and that’s what I’m seeing on your questions: not downvotes or close votes, but just not much engagement.

So I think your issue specifically is that your questions are too advanced in content for Math Stackexchange, but not well-enough presented to go over well here; it seems like your content knowledge is a bit ahead of your mathematical writing skills. Looking at your questions myself, the things I’d suggest trying to work on are:

• Make sure that the opening quickly gives readers an idea of what the question is, enough to judge whether it’s relevant to their interests. Generally a self-contained high-level summary paragraph (2 or 3 sentences) works well for this, though other ways can too.

• Organise your thoughts clearly, into a coherent exposition of the problem at hand.

• Think about how much background detail is helpful! Several of your questions have answers/comments pointing out where more background would be helpful; at the same time, in some places your questions come across as a bit of a wall of text, with more detail than is really necessary.

• Follow good formatting conventions. A couple of specifics here: mark quotations using block-quote formatting (> like this in Markdown); and include author names when referring to papers (in my experience academics usually remember papers by author names ≫ year > title ~ journal, in rough order of salience)

Especially the middle two points aren’t easy things to fix immediately — they’re just part of developing good mature mathematical writing skills, which is a big and non-trivial part of developing as a mathematician — but I think working on this is will really help you get out of the purgatory, and will also pay off in your studies in general.