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Pardon my curiosity, but have you been studying the natural born / naturalized citizen issue for a long time, or is your interest a recent one?
So my obvious question is...what did I get wrong this time?
If you believe We the People are Sovereign, the question should be -
Can a minor child personally sign a legally binding contract?
If the answer is 'no', then it matters not whether the contract is offered, as no legal implied or expressed acceptance of it can ever occur.
Nor would the alien/foreign parents have the standing to sign such a contract on their child's behalf, as they are among the excluded classes of the intent of the 14th Amendment.
The above, of course, should not be confused with the legitimate legal concept of derivation, where a child becomes a naturalized citizen when the parent, with knowledge and consent, has completed the naturalization process to become a citizen himself.
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IMHO, the entire legalistic perversion by the federal government of the naturalization-at-birth concept is for no other reason that to control the quality and quantity of the populace.