The system of law that the American founding fathers were most familiar with was English law - not the writings of Vattel - which never were codified into law in any nation.
>> “the exact same phrase encoded into English law.” <<
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English law recognizes no citizen.
English law is the prolongation of the Monarchial lie that all Protestant Christians rejected, because they knew that Christ had no progeny.
If you were to study the important issues of why the original ‘Pilgrims’ migrated, you would not be so confused on this issue. They knew that no man could bow to any King but Christ.
They had already rejected and departed from England, and made homes in the Netherlands for that reason, and never would anything of the culture of England be acceptable.
You said: “The system of law that the American founding fathers were most familiar with was English law - not the writings of Vattel - which never were codified into law in any nation.” You must be kidding, right?
Blackstone explained that
[T]he law of nations (wherever any question arises which is properly the object of its [sic] jurisdiction) is here adopted in its [sic] full extent by the common law, and is held to be a part of the law of the land. And those acts [sic] parliament, which have from time to time been made to enforce this universal law, or to facilitate the execution of its [sic] decisions, are not to be considered as introductive of any new rule, but merely as declaratory of the old fundamental constitutions of the kingdom; without which it must cease to be a part of the civilized world.”
William Blackstone, Commentaries on the Laws of England, Book 4, Chapter 5 Of Offenses Against the Law of Nations (1765-1769). http://ebooks.adelaide.edu.au/b/blackstone/william/comment/book4.5.html .