After four years of dating, Bradley Cooper and Irina Shayk have split, according to a report by People on Thursday night. The news comes after much speculation about the pair in the tabloids, which came to a head this week when Page Six reported that, according to an unnamed source, Cooper and Shayk’s relationship was “hanging by a thread.” (Amid the frenzy, Shayk made headlines when she was photographed without wearing an engagement ring, even though it’s never been confirmed that the couple was engaged.)

The 44-year-old actor, who had been dating the actress and model Suki Waterhouse, and the 33-year-old model, who had been dating the soccer star Cristiano Ronaldo, are thought to have begun their relationship in the spring of 2015. They’ve made a point to keep things private since—so successfully that it made headlines when Shayk Instagrammed a cropped photo of herself featuring Cooper’s disembodied shoulders in April of 2016. Their daughter, whom Shayk gave birth to the following year, is now 2.

Still, the tabloids haven’t been alone in their speculation about Cooper and Shayk; it was rampant throughout the buildup and release of A Star Is Born, which Cooper directed and starred in, as the flailing country star Jackson Maine, opposite Lady Gaga, whom he cast as Ally, his pop prodigy and love interest. After a very affectionate press tour—and Gaga’s split from her now ex-fiancé, Christian Carino—the pair performed their hit single “Shallow” at the 2019 Academy Awards in February, sending the Internet into a frenzy when they appeared to almost kiss.

Gaga later refuted that there was any real romance behind their performance: “People saw love, and guess what? That’s what we wanted you to see,” she told Jimmy Kimmel—later adding “fooled ya!”—in the days after the Oscars. “You know, I mean, this is a love song, ‘Shallow.’ The movie, A Star Is Born, it’s a love story.”

As for the Internet’s reaction, Gaga also told Kimmel—with an eye roll—that “social media, quite frankly, is the toilet of the Internet.” As if to illustrate that point, it soon turned out that the reports that Shayk had unfollowed Gaga on Instagram after the performance were false; she hadn’t even been following Gaga in the first place. (Not that that stopped even more speculation about Cooper and Shayk’s relationship when the latter walked the red carpet of the 2019 Met Gala solo.)

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Representatives for Cooper and Shayk did not respond to People’s requests for comments, and it seems doubtful that they’ll open up about their relationship any time soon. “Because my work requires me to be out there, I just decided my personal life will be quiet,” Shayk told Glamour UK, in February, of her approach to social media in particular. “That’s why it’s called personal, because it’s something for you and your family, and I feel happy with it.”

Related: Bradley Cooper Is Already Plotting an A Star Is Born Revival