The conjecture relating Whitney homology and hyperarboreal Lie algebras

Let $\mathcal{HA}_n$ be the poset of hyperarbres, and let $\operatorname{WH}_i(\mathcal{HA}_n)$ denote its Whitney homology groups. Define the symmetric-function generating series

$$\operatorname{WH}:=\sum_{n \geq 2} \sum_{i=0}^{n-2} \operatorname{ch}(\operatorname{WH}_i(\mathcal{HA}_n)) (-t)^i.$$

Let $\mathsf{HAL}$ denote the symmetric-function series associated with hyperarbres. Whitney-homology conjecture. One has

$$\operatorname{WH}=\mathsf{HAL}.$$

This conjecture predicts that the symmetric-group action on the Whitney homology of the hyperarboreal posets is encoded by the hyperarboreal Lie-algebra series. The supplied text gives no evidence that the relation has been proved or disproved.