The Supreme Court ruled in 1874 that the term Natural Born Citizen goes undefined in the Constitution. (Minor v Happersett).
You mean they didn’t take the opportunity in 1874 to cite Vattel and Common Law?
Yes they did, and they were referring in particular to the 14th amendment. I'm glad you acknowledged this, because the 14th amendment definitely defines "citizen". That the supreme court specifically notes it doesn't define "natural born citizen" means the 14th amendment definition of "citizen" isn't the same thing. That it is explicitly different from "natural born citizen."
Why yes, yes it is. It's what we've been saying all along, and now you have unknowingly agreed with the point.