Mate I really don't know how to help you but even on the examples in the pdf there are clearly n-gons. In 5 of my 10 test there were n-gons. There are always starfishes with 5 or more connected verts. If you want to nitpick on the wording go ahead but these meshes are shite.
I wasn't picking a fight or scoring points. This isn't Reddit and I'm a grown adult. I'm trying to understand what you're saying and maybe learn something in the process.
> In 5 of my 10 test there were n-gons. There are always starfishes with 5 or more connected verts.
Ok. So you are basing your definition on the number of edges that meet at a vertex. My understanding was that the important metric was "number of edges on a given face"