RIO DE JANEIRO—The single most difficult and dangerous skill in all of women’s gymnastics—and maybe the most daring maneuver of the entire Olympic Games—won’t be attempted by anyone on the world-beating Team USA. It’s such a treacherous move that the Americans shudder when they think about it and clam up when they talk about it. The great U.S. gymnast Simone Biles equates the vault with death. Even its name sounds vaguely terrifying: “the Produnova.” The Produnova vault is technically a front-handspring to double-somersault. To translate gymnasticsese into plain English, though, the Produnova is what happens when you sprint at the horse and catapult high enough to flip twice in the air—at least in theory. This is what it looks like, and why no American is stupid enough to attempt it: Dipa Karmakar, the first female Indian gymnast to qualify for the Olympics, will be performing one of the sport’s most dangerous and difficult moves in Brazil in August. Photo: Karan Deep Singh/The Wall Street Journal But the obvious injury risks associated with tempting gravity make the Produnova a high-risk, high-reward move performed only by gymnasts with outside chances of medaling. On Sunday, Indian Dipa Karmakar, 22 years old, reeled off the rotations and landed essentially sitting on the mat. That’s not preferred gymnastics style, but she walked away to vault again, with her Produnova score of 15.1 putting her in contention for a spot in the event final a week from now. She is the first female gymnast to represent India at the Games.