The RCD characterization by the five gradients inequality

Let $(X,d,\mu)$ be an infinitesimally Hilbertian Polish metric space, and let $K$ be the Ricci-curvature lower-bound parameter in the $RCD(K,\infty)$ condition.

RCD characterization conjecture. The metric-measure space $(X,d,\mu)$ is $RCD(K,\infty)$ if and only if the five gradients inequality holds.

This proposes an equivalence between the five gradients inequality and the synthetic Ricci-curvature condition in infinitesimally Hilbertian metric spaces. The source presents it as a conjecture; the corresponding general equivalence remains open.