Nontriviality conjecture for the associahedral class in the curve complex

Let $\Sigma_g^1$ be a genus-$g$ surface with one boundary component, and let $\mathcal{C}(\Sigma_g^1)$ denote its curve complex. For the simplicial map $q$ from the boundary $\Theta$ of the dual of the $(2g-1)$-dimensional associahedron to $\mathcal{C}(\Sigma_g^1)$ described in the source, write $[q]$ for its homotopy class in reduced homology.

Nontriviality conjecture. For $g \geq 1$, the class

$$[q] \in \widetilde{\mathrm{H}}_{2g-2}(\mathcal{C}(\Sigma_g^1);\mathbb{Z})$$

is nontrivial. When $g=1$, the corresponding picture consists of $2$ pairs of parallel curves.

This proposes an explicit homologically nontrivial sphere in the curve complex, avoiding the increasingly impractical direct construction from the earlier proposition. The source gives no resolution of the claim.