Suppose a person was claiming US citizenship by virtue of being born in the US, but had some difficulty proving that they were born in the US. What would be the legal standard of proof needed to prove citizenship? Let's say they were trying to obtain a passport or avoid deportation and the matter went to court.
To make the question more concrete, suppose, for example, that a child was born on a ship or aircraft that was heading to the US and the timing of the birth corresponded approximately to the point where they crossed the 12-mile territorial limit of US waters. Now there is some real uncertainty as to whether or not the birth occurred in the US. The line is not marked and everyone was too busy to keep track of the exact time and location of the birth. Obviously, different pieces of evidence could be provided. Perhaps some witnesses recall seeing land already before the child was born or noted that the aircraft was already descending.
This (extreme) example would be a situation where the facts cannot be established with certainty. If only a preponderance of the evidence can be established, would the person be treated as a citizen?