In Louisiana white reserve seat law was challenged by a black man. Plessy vs fergurson " separate but equal" case. Jim crow statute that requires racially segregated seats on train and interstate commerce in the state of Louisiana had a big debate in the supreme court when black man named Phlessy who has same status as Obama claimed that he is only one-eight negro. Means he has more white blood than other Negroes. The U.S supreme court accepted his contention and allowed him to ride the train as white man. They made that decision as "judicial notice". That means they did not defined who is negro and who is not negro.
The funny thing is to me even the word negro was not agreed upon the United states supreme court.
----------------------------------------------------------------------------------------------------------------------------------------------------------------Remember U.S population before 1820's, there were 1.2 million African people who never claimed as black people because they were mixed with Indian or whites.