  The main results of this paper provide VMO-type estimates for the quadratic
tilt-excess on varifolds with critical generalized mean curvature. These
estimates apply to varifolds with "almost-integral" density which are close to
a multiplicity one $m$-disc in a ball in the usual senses. The class of
almost-integral varifolds allows for varifolds with non-perpendicular mean
curvature. Moreover, the estimates hold \emph{uniformly for every point} in a
relatively open set in $\text{spt}||V||$ and naturally imply a Reifenberg-type
parametrization. The proof relies upon generalizing the $Q$-valued Lipschitz
approximation and Sobolev-Poincar\'e estimates of arXiv:0808.3660 to
almost-integral rectifiable varifolds.
