BEIJING — Eileen Gu needed the best jump of her life to win a gold medal. The 18-year-old from California had come to her mother’s home country hoping to win three events at the Winter Olympics while representing China.

Under the glare of a bright sun and the eyes of the international news media, Gu stood on top of the huge, modern big air jump, set in an industrial park amid concrete cooling towers. She was in third place with one jump to go.

Her mother called. Yan Gu, who grew up in Beijing, was at the bottom of the jump, trying to give her daughter advice.

Do the 1440 again, she told her, referring to a four-rotation trick that Gu had landed nearly perfectly already. Maybe it lifts you to a silver medal. Gu had other ideas.

“Mom, executive call here,” she recalled saying. “Vetoed. I am going to make the 16, and you are going to deal with it.”

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