A new bound for the Furstenberg--Sárközy theorem using the van der Corput property

We show that if $A\subseteq \mathbb{N}\cap[1,N]$ has no nonzero square difference, then \[ |A|\ll N\exp(-c\sqrt{\log N\log\log N}), \] improving upon a recent result of Green and Sawhney. The proof exploits a quantitative version of the van der Corput property with signed coefficients and builds o