An upper Minkowski dimension estimate for the interior singular set of area minimizing currents

We show that for an area minimizing m-dimensional integral current T of codimension at least two inside a sufficiently regular Riemannian manifold, the upper Minkowski dimension of the interior singular set is at most $m-2$. This provides a strengthening of the existing $(m-2)$-dimensional Hausdorff dimension bound due to Almgren and De Lellis & Spadaro. As a by-product of the proof, we establish an improvement on the persistence of singularities along the sequence of center manifolds taken to approximate T along blow-up scales.