About a year ago I asked on MO when a Newton basin fractal is continuously determined by the roots of its polynomial. I mentioned in that question that I had convinced myself that the roots of the polynomial must all be simple, and nobody in the answers or comments called that out as wrong or as obvious.
I'd like to nail down whether this result is correct, already known, interesting etc. Is it appropriate for me to post a question (suitably elaborated) like:
Is this "fact" I mentioned in my other question already known? Is it even correct?
It's basically a reference request, but it's also pretty close to a "here's my work, please give me feedback" kind of question, which makes me hesitant to post it on MO without checking meta first.