For citizenship? Yes.
For Constitutional natural born citizen, the only SCOTUS definition is Minor v. Happersett: born in the US to US citizen parents.
The "natural born" crowd makes themselves look very foolish with this claim, as they rely on a quote by the justice in Minor, who said the case was not going to address the doubts. This claim is a composition fallacy as well, since the Chief Justice mentioned who were undoubtedly natural born citizens, but never specified that others were not.
WKA addressed this more directly, (although still not as directly as many of us could wish). A few quotes from WKA to start you off
In United States v. Rhodes (1866), Mr. Justice Swayne, sitting in the Circuit Court, said: "All persons born in the allegiance of the King are natural-born subjects, and all persons born in the allegiance of the United States are natural-born citizens. Birth and allegiance go together. Such is the rule of the common law, and it is the common law of this country, as well as of Englandand quoting Chancellor Kent
"And if, at common law, all human beings born within the ligeance of the King, and under the King's obedience, were natural-born subjects, and not aliens, I do not perceive why this doctrine does not apply to these United States, in all cases in which there is no express constitutional or statute declaration to the contraryand
So far as we are informed, there is no authority, legislative, executive or judicial, in England or America, which maintains or intimates that the statutes (whether considered as declaratory or as merely prospective) conferring citizenship on foreign-born children of citizens have superseded or restricted, in any respect, the established rule of citizenship by birth within the dominion. Even those authorities in this country, which have gone the farthest towards holding such statutes to be but declaratory of the common law have distinctly recognized and emphatically asserted the citizenship of native-born children of foreign parents.. And now, off to work.