Grove formula conjecture for the bounded cube recurrence

Let $S$ be a section, let $f$ be a state, and let $(x_0,y_0,t_0)$ be a point in $\overset{\circ}{Y}\cap\mathcal{L}$ in the future of $S$. Assume that the cone $\mathcal{C}$ meets $S$ in at least one point, and let $W$ be the closure of the prescribed intersection of $S$ with the interior of $\mathcal{C}$ together with the two specified points. A grove is a grove on $W$, and $\mu(G)$ denotes its associated weight. Grove formula conjecture. There exists a constant $c$ such that the bounded cube recurrence is computed from $f|_S$ by a formula of the form

$$f(x_0,y_0,t_0)=c\cdot\sum_{G\in\text{groves on }W}\mu(G).$$

The formula is intended to express the output of the bounded cube recurrence in terms of the initial state on the section; the source refers to Carroll and Speyer for the definition of groves. The parser supplies no evidence resolving this claim, so its status remains open.