Dimension bound for genuine boundary singularities of mass-minimizing currents

Let $T$, $\Sigma$, and $\Gamma$ be as in the main assumptions, where $T$ is an area-minimizing integral current with boundary $\Gamma$ in the ambient setting of the paper. Genuine boundary singularities are boundary singular points that are not of crossing type.

Dimension conjecture. The Hausdorff dimension of the set of genuine boundary singularities is at most $m-2$.

This is the most daring improvement suggested by the examples known in the paper; it remains open.