Well, that's just not true but for the sake of debate let's pretend this birther myth is the Law of the Land. How must each and every presidential candidate prove to the Arizona Secretary of State that their parents were U.S. citizens at the time of their birth?
“How must each and every presidential candidate prove to the Arizona Secretary of State that their parents were U.S. citizens at the time of their birth?”
By whatever means they have. Maybe their birth cirtificates, or their naturalization papers. If they are dead, then their death certificates would help.