Jennifer Brady serves to Yulia Putintseva during the quarterfinals of the U.S. Open on Tuesday in New York. Seth Wenig/Associated Press

NEW YORK — A curious rule of life around Naomi Osaka and an uplifting well of confidence around Jennifer Brady will intersect come Thursday in the U.S. Open semifinals, and it almost seems too bad. With sports always so persnickety about insisting somebody loses, one shining moment or the other will have to yield.

Naomi Osaka beat Shelby Rogers, of the United States, in straight sets to reach the U.S. Open semifinals. Frank Franklin II/Associated Press

The rule of Osaka goes like this: If she surpasses any Grand Slam fourth round, she wins the whole bloody tournament. That rule stayed afloat Tuesday night in her 6-3, 6-4, service master class in the quarterfinals against South Carolinian Shelby Rogers. It made the Japanese Haitian superstar 7-0 in Grand Slam quarterfinals, semifinals and finals, her eccentric record at 22 decorated with two titles and 14 departures in the fourth round or earlier, with nothing ever ending up in between.

“You can definitely see my game is improving,” she said. “And there was a mental block, I think, last year because I was always comparing results (to the past).”

The well around Brady looks like this: It’s a beacon both to American tennis fans and anyone who respects the value of struggle. Brady found her first Grand Slam semifinal at 25 on Tuesday afternoon with a 6-3, 6-2 piece of power artwork against Kazakh Yulia Putintseva, then looked back across a long vista to her outset, which included the charming back roads of college tennis and the trying back roads of the Triple-A tours.

“I know what I’m doing out there,” she said, her story proving again how humans can figure out things even when they are not sure they can.

Osaka and Brady arranged their meeting on a day when fifth-ranked Alexander Zverev became the first person to reach a second Grand Slam semifinal in this mangled 2020 season. His 1-6, 7-6 (7-5), 7-6 (7-1), 6-3 win over 32nd-ranked Borna Coric let Zverev back up his semifinal showing at the Australian Open – that event from January, allegedly also in 2020. It also gave him a meeting with the winner of the late-night match between 17th-ranked Denis Shapovalov of that fresh tennis nirvana of Canada and No. 27 Pablo Carreño Busta of Spain.

Their match began just after Osaka’s serves finished smoking the hollowed and hallowed Arthur Ashe Stadium, frequenting the mid-to-high 110s when they were not whirring more slowly into clever spots. She won 39 of 51 service points. She held at love in five of her 10 service games. She had a happy little total of unforced errors: eight. Those numbers signaled the end of a moment for Rogers, a 27-year-old ranked 93rd who steeled through two match points against Petra Kvitova in the fourth round. “I think she’s in great shape,” Rogers said of Osaka. “I think she’s very quick. I think she’s very powerful. I think a lot of other girls are, too.”

“No, I don’t feel like the favorite, weirdly enough,” Osaka said of her match with Brady. “Because there’s no fans, I don’t feel anything. I just feel like I’m going into a match with a really talented player, which is all of my previous matches anyway.”

The ninth-ranked Osaka won a U.S. Open at 20, won an Australian Open at 21 and reached No. 1 also at 21, Brady’s winding road might resonate more with the plodding among us. A Pennsylvanian who moved to Florida at 9 for non-tennis reasons and ventured to UCLA for two seasons and one team NCAA title, Brady spent much of 2015 and 2016 scrounging through the second tier, winning $444 in Waco, Texas, here, $760 in Charlottesville, Virginia, there, $1,267 in Dothan, Alabama, over there. When she up and reached the 2017 Australian Open fourth round even after having to qualify, one reporter noted she had doubled her lifetime prize money.

“Cool, thanks,” she said. “Thanks for sharing. I didn’t know that.”

So after she quelled her nerves and presented a picture of self-belief in her first Grand Slam quarterfinal, she sat at a big moment in a big year with a first tournament title and six wins against players in the current top 25 and gave a meaningful glimpse at the past.

“I mean, I was playing Challenger (Tour) events, lower Challenger events, losing in the qualifying first round, and I was thinking: ‘OK, do I have a chance to make it?'” she said. “‘Will I make it? How can I really succeed doing this? Am I meant to play this sport?’ There were a lot of doubts, a lot of questions, you know, definitely not positive thoughts during those times. But I think I’m pretty lucky to have just stuck to it and just really continue to just play and practice and compete and get better. You know, here I am today.”

Here she is now, and formidable.

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