Krachun–Petrov conjecture on sums of algebraic dilates

Let $\lambda$ be an algebraic number. For its minimal polynomial $f(x)\in\mathbb{Z}[x]$ with coprime coefficients, write

$$f(x)=\prod_{i=1}^d(a_i x+b_i)$$

for a full complex factorisation, and define

$$H(\lambda):=\prod_{i=1}^d(|a_i|+|b_i|).$$

Krachun–Petrov conjecture. For every finite subset $A\subset\mathbb{C}$,

$$|A+\lambda\cdot A|\geq H(\lambda)|A|-o(|A|).$$

This conjecture seeks the sharp asymptotic lower bound for sumsets formed from an algebraic dilate. It was posed by Krachun and Petrov after earlier work on algebraic dilates; the supplied text does not state whether it has been resolved.