Common law provides the understanding of marriage as codified.
Common law also provides the understanding of the term natural born citizen.
Neither are ultimately statutory, but there certainly can be statutory consequences associated with either one.
Nice try, though.
What do you understand that sentence to mean?
What is it about your conception of the "common law" that makes you think that, because of the common law, the meaning of the term "natural born citizen" in our national Constitution is dependent upon the rules that some local governments employ to determine child custody and support obligations?
“In Smith v. Alabama, Mr. Justice Matthews, delivering the judgment of the court, said:
There is no common law of the United States, in the sense of a national customary law, distinct from the common law of England as adopted by the several States each for itself, applied as its local law, and subject to such alteration as may be provided by its own statutes. . . . There is, however, one clear exception to the statement that there is no national common law. The interpretation of the Constitution of the United States is necessarily influenced by the fact that its provisions are framed in the language of the English common law, and are to be read in the light of its history.”