Is it against the "code of honor" to ask a question concerning the correctness of a mathematical argument in one's doctoral thesis?
I'm unsure about one argument in my thesis and I would like to discuss it. Would it be considered inappropriate? In which circumstances is it appropriate to talk about one's own work on the internet, i.e., when to be mindful of it?
Definitely appropriate.
A thesis is not a homework submission. You need to be the one writing the thesis (i.e., no ghostwriting or copypasting), but there is no requirement to work entirely on your own, as long as you cite the contributions of others.
A thesis may even contain no new results or ideas whatsoever, but just be a textbook-like treatise of a subject. In most cases (i.e., unless the treatise is really a lot more readable than existing literature and thus forwards science by making the subject significantly more accessible), such a thesis will probably be declined for lack of novelty if it's a PhD thesis (for a master's thesis, it's fine), but it does not constitute research misconduct.
