They cannot produce affidavits that Both of their parents were citizens at the time of their birth. That is the more important criteria as it is possible a child would assume the loyalties of the non- citizen parent.
It’s admirable you have defined a term that was not defined, specifically and completely, at the time the document was ratified. But, SCOTUS won’t recognize your definition or any definition of the term because they have decided it was not meant to be defined. SCOTUS has repeatedly opined Congress is discharged with the duty of developing a uniform rule of immigration and naturalization, but it is unconstitutional for Congress to define or legislate as to the status of a citizen. Once you become a citizen, you’re a citizen and that’s it with one exception. The exception is that only a natural born citizen can be POTUS.
Consequently, the only way to determine who is eligible for POTUS is to eliminate those who are not eligible. Non-citizens are not eligible. Citizens who achieved their citizenship status by completing the naturalization process are not eligible. SCOTUS has not opined on whether or not a statutory citizen is eligible, but a good argument can be made they are not eligible because their Certificates of Citizenship are revocable.
Instead of examining a candidates birth certificate, we should examine a candidate’s immigration file to determine if they are eligible.