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I am not well versed with mathematics publishing, but has this proof been already been peer reviewed by other mathematicians, or is it still awaiting confirmation/proof replication?

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This is just a preprint, so no peer review or anything yet. Putting out a preprint on the Arxiv like this is generally the first step of the author sharing their work for other mathematicians to take a look at, before it gets submitted for peer review and publication

Just a quick well, actually. It's common at least in my corner of mathematics to put something on arxiv simultaneously with submission to a journal or conference. If I wanted feedback on a paper before submitting I would definitely do that privately. But everyone is different.

You'd think most people who put stuff on arXiv would already be reasonably confident it is correct, at least through correspondence with their peers. However...

That said, I've no reason to doubt this proof (it is not within my wheelhouse).

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