As you know, the term natural born citizen do not exist in any US statute (including 1401).
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Does ‘citizen at birth’ mean ‘natural born citizen?’ That is something I think the SCOTUS must decide. I’m not sure if they have the guts to take this on.
If considering the 14th A, citizen at birth would not mean natural born citizen. The emancipation was aimed at making legal citizens of all those previously ‘held as slaves’ born on American soil or brought to American soil. Such a ‘statutized / naturalized’ citizen would not have citizen parents at their birth point but their children born here would absolutely be natural born citizens.
Not necessarily. Otherwise they would have adopted Hamilton's version.
Which as Leo points out, came first...preceding Jay's letter to Washington.
Not in the sense that "citizen at birth" is defined under a naturalization statute, passed pursuent to the Congress' power to define a uniform rule of naturalization, while "natural born citizen" is a Constitutional term. It means whatever it meant in 1787. It cannot be changed by statute, any more than the meaning of "solider" or "house" could be in regards to the meaning of the third amendment.