Huang's rational-point upper-bound conjecture for nondegenerate submanifolds

Let $\mathcal M$ be a bounded immersed submanifold of $\mathbb{R}^{M}$ with boundary, of dimension $n$ and codimension $R$. Suppose that $\mathcal M$ is $l$-nondegenerate everywhere with $lleq R+1$. Let $N_{\mathcal M}(Q,\delta)$ denote the number of rational points of denominator at most $Q$ lying within the specified $\delta$-neighborhood of $\mathcal M$. Huang's conjecture. There exists a constant $c_{\mathcal M}>0$ depending only on $\mathcal M$ such that

$$N_{\mathcal M}(Q, \delta)\leq c_{\mathcal M}\delta^R Q^{n+1},$$

when $deltageq Q^{-\frac{1}{R}+\epsilon}$ for some $\epsilon>0$ and $Qtoinfty$. This is a sharp conjectural upper bound in the natural range for nondegenerate manifolds; the cited prior work proves related lower bounds, while the source presents this upper bound as conjectural.