True. The issues of citizenship that fell within the authority of Congress...nothing more. Making a 'uniform rule of naturalization' is NOT the same thing as determining every aspect of every type of citizenship
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That the founders were familiar with a French guy, named Vattel, does not mean that all of his views were controlling on every issue.
Having given you this general idea and description of the law of nations; need I expatiate on its dignity and importance? The law of nations is the law of sovereigns. In free states, such as ours, the sovereign or supreme power resides in the people. In free states, therefore, such as ours, the law of nations is the law of the people. Let us again beware of being misled by an ambiguity, sometimes, such is the structure of language, unavoidable. When I say that, in free states, the law of nations is the law of the people; I mean not that it is a law made by the people, or by virtue of their delegated authority; as, in free states, all municipal laws are. But when I say that, in free states, the law of nations is the law of the people; I mean that, as the law of nature, in other words, as the will of nature's God, it is indispensably binding upon the people, in whom the sovereign power resides; and who are, consequently, under the most sacred obligations to exercise that power, or to delegate it to such as will exercise it, in a manner agreeable to those rules and maxims, which the law of nature prescribes to every state, for the happiness of each, and for the happiness of all.
Of the Law of Nations, James Wilson, Lectures on Law
.... and certainty, an amendatory article was proposed, adopted, and ratified; whereby it is expressly declared, that, “the powers not delegated to the United States by the constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.” This article is, indeed, nothing more than an express recognition of the law of nations; for Vattel informs us, “that several sovereign, and independent states may unite themselves together by a perpetual confederacy, without each in particular ceasing to be a perfect state. They will form together a federal republic: the deliberations in common will offer no violence to the sovereignty of each member, though they may in certain respects put some constraint on the exercise of it, in virtue of voluntary engagements.
View of the Constitution of the United States George Tucker
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The Founders were familiar with Vattel, but they incorporated ENGLISH COMMON LAW which is entirely different from the Frenchman's ideas.
You might consider reading this part of Tucker;
Of the Unwritten, or Common Law of England; And Its Introduction into, and Authority Within the United American States
Fifthly. … That neither the articles of confederation and perpetual union, nor, the present constitution of the United States, ever did, or do, authorize the federal government, or any department thereof, to declare the common law or statutes of England, or of any other nation, to be the law of the land in the United States, generally, as one nation; nor to legislate upon, or exercise jurisdiction in, any case of municipal law, not delegated to the United States by the constitution.
View of the Constitution of the United States
[all emphasis mine]
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This merry-go-round has been loads of fun.
Shall we go 'round again?
Congress has passed legislation, several times, making and changing the rules for Birthright Citizenship.
Congress has full power to do so, and such power of Congress has never been challenged by any Court.