The $C^{1,b1}$-rectifiability conjecture for the singular set

Let $\Sigma$ be the singular set of the anisotropic obstacle problem, and let $A$ be the coefficient matrix with ellipticity constants. $C^{1,\alpha}$-rectifiability conjecture. The singular set $\Sigma$ is $(n-1)$-rectifiable of class $C^{1,\alpha}$ for some $\alpha > 0$ depending only on $n$ and the ellipticity constants of $A$. This strengthens the preceding rectifiability result by asserting uniform $C^{1,\alpha}$ regularity of the singular set; the stated context notes that the qualitative structure is stable under small perturbations of the anisotropy, while the limiting behavior for degenerate anisotropies remains open.