Bourgain--Demeter's additive-energy conjecture for the 2-sphere

Let $\mathcal{S}_{3,1}=\{\bm{x}\in\mathbb{R}^3:x_1^2+x_2^2+x_3^2=1\}$, and let $E_{2,2}(A)$ denote the number of quadruples $(\bm{x}_1,\bm{x}_2,\bm{x}_3,\bm{x}_4)\in A^4$ satisfying $\bm{x}_1+\bm{x}_2=\bm{x}_3+\bm{x}_4$. Bourgain--Demeter's additive-energy conjecture. For every finite, non-empty subset $A\subseteq\mathcal{S}_{3,1}$,

$$E_{2,2}(A)\ll_{\epsilon}|A|^{2+\epsilon}.$$

This is the conjectured sharp spacing-independent bound for additive energies on the 2-sphere, analogous to the corresponding estimate for the truncated paraboloid. The paper does not state that it has been resolved.