The codimension-one bound for singular sets of stationary integral varifolds

Theorem 1.1: for every stationary integral $m$-varifold $V$ in an open $U\subset\mathbb R^{m+n}$, $m,n\ge1$, $\dim_{\mathcal H}\mathrm{Sing}\,V\le m-1$, with no stability, minimizing, orientability, density or codimension hypothesis; crossing planes show it is sharp. This implies $\mathcal H^m(\mathrm{Sing}\,V)=0$. The proof combines the companion paper's signed-excess estimates with a fitting and frequency analysis around a smooth center and a measure-valued blow-up at higher-multiplicity planar tangents. It does not prove rectifiability or finer structure of the singular set, and does not cover Riemannian ambient metrics.

Theorem 1.1: for every stationary integral $m$-varifold $V$ in an open $U\subset\mathbb R^{m+n}$, $m,n\ge1$, $\dim_{\mathcal H}\mathrm{Sing}\,V\le m-1$, with no stability, minimizing, orientability, density or codimension hypothesis; crossing planes show it is sharp. This implies $\mathcal H^m(\mathrm{Sing}\,V)=0$. The proof combines the companion paper's signed-excess estimates with a fitting and frequency analysis around a smooth center and a measure-valued blow-up at higher-multiplicity planar tangents. It does not prove rectifiability or finer structure of the singular set, and does not cover Riemannian ambient metrics.