Teheranchi's strong Gaussian correlation conjecture for symmetric convex sets

Let $d>0$ and let $K,T\subseteq \mathbb R^d$ be origin-symmetric convex sets, and let $\gamma_d$ denote the usual Gaussian probability measure. Teheranchi's strong Gaussian correlation conjecture.

$$\gamma_d(K+T)\gamma_d(K\cap T)\ge \gamma_d(K)\gamma_d(T).$$

This geometric formulation strengthens Royen's Gaussian correlation inequality and was conjectured by Teheranchi. The paper presents it as a weaker inequality than the slab-based geometric refinement, but its general validity remains open.