Moreira's conjecture on sums and products in positive-density sets

Let $A\subseteq\mathbb{N}$ have positive density, where its density is

$$d(A)=\lim_{N\to\infty}\frac{|A\cap\{1,\ldots,N\}|}{N}$$

whenever this limit exists. Moreira's conjecture. There exist $x,y\in\mathbb{N}\backslash\{1\}$ such that

$$\{x+y-1,xy\}\subseteq A.$$

This is a positive-density sum-product problem in the integers, motivated by analogous results over fields; the supplied text does not state whether the conjecture has been resolved.