Vanishing boundary-singular measure for mass-minimizing currents

Let $T$, $\Sigma$, and $\Gamma$ be as in the main assumptions, and let ${\rm Sing_b}(T)$ denote the boundary singular set.

Boundary-measure conjecture.

$$\mathcal{H}^{m-1}({\rm Sing_b}(T))=0.$$

This is a milder improvement of the paper's generic boundary regularity theorem than the dimension bound for genuine singularities. It is stated as open.