BO has run for, and served in, the offices of the Illinois House and the United States Senate.
Both offices require U.S. citizenship for eligibility.
What sort of proof of U.S. citizenship (if any) did BO provide when he ran for and served in the above offices?
None that I am aware of.
When it comes to President you have to be a natural born Citizen. Natural born Citizens would not have explicit citizenship paperwork. This is the meaning of being a natural born Citizen - you need no man made law and no amendment and no explicit paperwork to be or show you are a citizen.
A naturalized citizen of course would have forms and papers and documents.
The cover-up that may be bigger than the actual events of birth may very well be the cover-up of naturalization papers for Obama. Again, since at any one point-in-time a person can be a natural born citizen or a naturalized citizen any evidence of naturalization would disqualify a candidate from the office of President.