The Framers did NOT tie the hands of Congress or the Courts on this matter, save for the Engish Language understanding of the term, which would mean Citizen at the Moment of Birth! The could have been more specific, however --- ---- the Framers made Citizenship issues VAGUE ON PURPOSE, as they wanted Congress to settle that matter, and, during a time of slavery, too much discussion of the matter would have prevented the Union from ever forming!
The Founders disagreed very much over Citizenship issues.
Would Vattel think that J.C. Watts or his ancestors could become President?