You get a DOI on the arXiv. You can just publish the PDF on the arXiv, but this is a sure sign you are a crackpot.

You cannot just publish the PDF, they have checks that make sure that you didn't produce your PDF with LaTeX. There are probably ways to get around that, but why? Just use zenodo instead.

https://info.arxiv.org/help/submit_pdf.html explains all the constraints on direct PDF publication.

If you disagree with their good reasons https://info.arxiv.org/help/faq/whytex.html to submit the TeX you might be granted an exception.

Or just publish on zenodo, without all that fuss. The reasons the ArXiv gives may be good from their point of view, but if you don’t care too much about that but have your own good reasons for not wanting to publish your source, then zenodo is a great and in many respects superior alternative, no questions asked.

You mean, like Grisha Perelman?

There are exceptions to every rule.

See, every rule has an exception.

Let's assume that every rule has an exception. Then this rule must have an exception as well, so there is a rule with no exception. That is a contradiction.

So most definitely, there are some rules with no exception. The ones you are sure about should be among them.

arXiv issues DOIs for submissions.

I didn't say otherwise. In fact, the "also" is meant to express exactly that.