Nöbeling-space model conjecture for ending lamination spaces

Let $S$ be a $p$-punctured surface of genus $g$, and set $n=3g+p-4$. Define $k$ by $k=0$ if $g=0$, $k=g-1$ if both $p\neq 0$ and $g\neq 0$, and $k=g-2$ if $p=0$. Let $\mathbb{R}^{2n+1}_{n+k}$ denote the space of points in $\mathbb{R}^{2n+1}$ with at most $n+k$ rational coordinates. Nöbeling-space model conjecture. The ending lamination space $\mathcal{E} \mathcal{L} (S)$ is homeomorphic to $\mathbb{R}^{2n+1}_{n+k}$. This speculative conjecture extends the known genus-zero cases and predicts the precise Nöbeling parameter from the topology of $S$; the source provides no proof in the general case.