“She wouldn’t say she’s coach although she does have the coach’s badge,” added Dart of her mother after thrashing Paquet 6-1, 6-2. “She says her role is feeding balls, and throwing me balls, but there’s much more to it than that. She’s been helping me a lot.

“She played county and vets. And a couple of pro tournaments as well, but then she went to university and had me, so that changed her plans.

“She can hit with me a little bit – she can warm me up easy – and she’s played so she understands a lot of things. I think she realises also how full-on these days are and how long it is today. It’s not like you can leave the site during the day before you go on. It’s nice to have her here.”

Canine companions

One thing the Dart family appear not to have considered is the possibility of bringing their dog on tour, perhaps because he is a cockapoo, and thus on the large side for a travelling pet.

Several other players have gone down this road, however, by using a dog to add companionship to the notoriously lonely lifestyle of a touring tennis pro.

Indeed, Kostyuk herself has been photographed in the US Open gym this week alongside what appears to be a Yorkiepoo – a Yorkshire terrier crossed with a toy poodle – called Mander.

Most of the dogs on tour are owned by female players, and most are on the smaller side, such as Coco and Brando, two poodles who belong respectively to Canada’s former US Open champion Bianca Andreescu and Italy’s Martina Trevisan. There was also a Yorkshire terrier, Rafa, who used to travel with the legendary American star Serena Williams.

While Lennie might be too substantial a dog to fit into the confines of hotel rooms and player lounges, he should provide a consoling welcome when Dart’s excellent run in America finally comes to an end.