More than two years ago, the I.P.C. informed Hernandez, a gold medalist at the 2018 Paralympics in Pyeongchang, South Korea, that she and Huckaby, a 2018 gold medal winner from Baton Rouge, La., could not compete at the Beijing Games.

No one accused them of doing anything wrong. Their misfortune was to be entered in races that would be canceled for lack of other snowboarders.

Both Hernandez, 47, and Huckaby, 26, are classified as SB-LL1. An SB-LL1 racer has significant impairment in one leg, like an above-the-knee amputation, or significant combined impairments in two legs. But there were not enough qualified LL1 snowboarders to make the race viable, and the I.P.C. shut it down.

So Huckaby asked instead to be placed in the men’s LL1 race or in the women’s LL2, both ostensibly more challenging categories for her. An LL2 racer has an impairment in one or both legs, with less activity limitation than an LL1 competitor. In all para sports, classification is determined by doctors observing the athletes.

The I.P.C. declined her request, even though the racers were moving up in class. The I.P.C. is opposed to athletes of one classification moving into events of another. It could affect the integrity of the competition if athletes were allowed to race in whatever classification they chose.

Huckaby and Hernandez hired Christof Wieschemann, a German lawyer, to handle the case because, with the I.P.C. based in Bonn, German courts had jurisdiction.

Wieschemann first won a temporary injunction for Huckaby on Jan. 27, arguing that classification systems of any kind in all sports are designed to “protect the weak against the strong,” not the other way around.