how did Ananda prove his "arahant" state at the First Buddhist Council?

similarly, how did all the other present arahants prove that they were indeed arahants? Was this rank assigned administratively by a commission?

According to Buddhist legend, he proved that he was an arahant by floating through the air and taking the empty seat at the council.

Less legendary, he was Buddha’s personal attendant, and closer to him than anyone else, and had a close to photographic memory, and was therefore a walking library of the Buddha’s teachings. It’s pretty much inevitable he’d be considered an arahant.