The codimension-one conjecture for stationary integer rectifiable varifolds

Let $V$ be a stationary integer rectifiable $m$-dimensional varifold, and let its interior singular set consist of the points of ${\rm spt}(V)$ that are not regular. The codimension-one conjecture. The interior singular set has codimension not smaller than $1$. This is presented as a well-known conjecture, motivated by the absence of examples whose singular set has dimension bigger than $m-1$ and by partial regularity results.