Rectifiability conjecture for the boundary of non-collapsed RCD spaces

Let $(X,\mathsf d,\mathcal{H}^{N})$ be a non-collapsed $\mathsf{RCD}(K,N)$ space. Let $\boldsymbol\partial^{*}X$ denote its reduced boundary. Boundary rectifiability conjecture. The boundary $\boldsymbol\partial X$, equivalently $\boldsymbol\partial^{*}X$ in view of the cited lemma, is $\mathcal{H}^{N-1}$-rectifiable. This is inspired by the theory of finite-perimeter sets and De Giorgi's theorem; the claim concerns the geometric regularity of the boundary in the non-collapsed RCD setting.