"Definitely feels solid," Williams said.
Not sure? There's plenty of evidence. No need to take her word — or her coach's — for it.
Look at the way Williams beat 47th-ranked Johanna Larsson 6-1, 6-1 on Saturday to reach the fourth round at Flushing Meadows and collect the 307th Grand Slam match victory of her career, surpassing Martina Navratilova for most by a woman in the Open era and equaling Roger Federer for most by anyone since 1968.
Williams reached 121 mph on a serve. She had a half-dozen aces, bringing her total this week to 31. She faced only one break point — her first of the tournament — and saved it. She smacked seven return winners. She compiled a 24-5 total edge in winners.
"Tennis-wise, I think it was very satisfying in all aspects. It's not perfect, of course," said her coach, Patrick Mouratoglou. "But for someone who didn't play much matches in the last two months, I think she's competitive."
Now there's an understatement.
"There is no pain. Maybe she feels a little. I don't know; I'm not in her shoulder. But I see she plays normal. She serves normal. At practice, she serves the quantity that we usually do, full power," Mouratoglou said. "So I don't see any problem. And she doesn't even talk about it. I know it's under control now."
That sounds like bad news for upcoming opponents, starting with 52nd-ranked Yaroslava Shvedova, who advanced to the round of 16 in New York for the first time by beating Zhang Shuai 6-2, 7-5.
Monday's other fourth-round women's matchups will be No. 5 Simona Halep vs. No. 11 Carla Suarez Navarro, No. 4 Agnieszka Radwanska vs. Ana Konjuh, and No. 10 Karolina Pliskova against the winner of Saturday night's match between Williams' older sister Venus and No. 26 Laura Siegemund. In that half of the draw, only the players with the last name Williams have won a Grand Slam title.
Two past men's champions, Andy Murray and Juan Martin del Potro, moved into the fourth round.
Murray, who won the 2012 US Open, had trouble in each of the first two sets, but eventually became more patient during baseline exchanges and took control for a 7-6 (4), 5-7, 6-2, 6-3 victory over Paolo Lorenzi. Murray faces No. 22 Grigor Dimitrov in the round of 16.
Del Potro's resurgence continued with a 7-6 (3), 6-2, 6-3 victory over No. 11 David Ferrer. The 2009 champion in New York missed 2 1/2 years' worth of major tournaments because of three operations on his left wrist, and he's ranked only 142nd, which is why he needed a wild-card invitation to get into the field.
But del Potro showed that he's back and about as good as ever, especially with his thunderous forehand, by beating Novak Djokovic and Rafael Nadal on the way to winning a silver medal for Argentina at the Rio de Janeiro Olympics last month.
For a spot in the quarterfinals, Del Potro will now need to get past No. 8 Dominic Thiem, who defeated Pablo Carreno Busta 1-6, 6-4, 6-4, 7-5.
Stan Wawrinka and Nick Kyrgios were among the men playing later Saturday.
Williams is 4-0 against Shvedova, taking 8 of 9 sets. Shvedova is best known for the first "golden set" in the Open era, which began in 1968: She won all 24 points of the first set of a victory over Sara Errani at Wimbledon in 2012, one match before a three-set loss to Williams there.
"She's a good player. She's dangerous," Mouratoglou said about Shvedova. "But I think Serena is even more dangerous."
Larsson would probably agree.
She was surprised by the variety Williams displayed Saturday, especially with some heavy-spin, high-bouncing strokes.
"You're out there, you're trying to find ways to win," Larsson said, "but sometimes, it's just not happening."
Mouratoglou said Williams' shoulder began bothering her a day or two after Wimbledon, where she teamed with Venus to win doubles and tied Steffi Graf's Open-era record with Grand Slam singles title No. 22.
After that, Williams played only one event before the US Open, losing in the third round of the Olympics.
This was Williams' first daytime match of the tournament, so she debuted a new outfit — a white dress accessorized with neon pink compression wraps on her arms, which she called "my 'Wonder Woman' sleeves."
"I feel this design, in particular, really is kind of like a superhero design," Williams said. "Like a really powerful, strong character that is strong, but yet isn't afraid to be soft at the same time."
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