Stroppel's intrinsic formality conjecture for extended Khovanov arc algebras

Let ${\mathrm{K}}_m^n$ be the extended Khovanov arc algebra indexed by $m$ and $n$, and let $\operatorname{HH}^2_{i-2}({\mathrm{K}}_m^n,${\mathrm{K}}_m^n)$denote its Hochschild cohomology in Hochschild degree$2$and internal degree$i-2$. Stroppel's conjecture.

\operatorname{HH}^2_{i-2}({\mathrm{K}}_m^n,${\mathrm{K}}_m^n)=0 \quad\text{if } i\neq 0.

This vanishing would imply that the algebras ${\mathrm{K}}_m^n$ admit no nontrivial $A_\infty$ deformations and are intrinsically formal. The conjecture is attributed to Stroppel's ICM 2010 address; its resolution is not specified in the supplied text.