The strongly non-degenerate manifold covering conjecture for missing digits sets

Let $n\geq 1$ be an integer, let $M\subset\mathbb{R}^n$ be a strongly non-degenerate analytic manifold, let $p>2$ be an integer, and let $D\subsetneq\{0,\dots,p-1\}^n$ be a choice of at least two digits. For $\delta>0$, let $M^\delta$ be the $\delta$-neighbourhood of $M$ in $\mathbb{R}^n$. Covering conjecture. The set $(M\cap K_{p,D})^\delta$ can be covered by

$$\ll \left(\frac{1}{\delta}\right)^{\max\{0,\dim_{\mathrm{H}} K_{p,D}-(n-\dim_{\mathrm{H}} M)\}}$$

many $\delta$-balls. Here $K_{p,D}$ is the missing digits set associated with the base $p$ and digit set $D$. Strong non-degeneracy is introduced to exclude excessive intersections with affine subspaces. The text gives no resolution; when the exponent is zero, the conjecture predicts that $M\cap K_{p,D}$ is finite.