The dimension conjecture for finite multiple zeta values

Let $w\in\mathbb{N}$, and let $d_w$ be the dimension of the $\mathbb{Q}$-vector space generated by finite multiple zeta values (FMZVs) of weight $w$.

Dimension conjecture. The sequence $(d_w)_{w=0}^{\infty}$ satisfies

$$\nd_w=\begin{cases}0 & (w\in\{1,2\}),\\1 & (w\in\{0,3\}),\d_{w-2}+d_{w-3} & (w>3).\end{cases}$$

Finite multiple zeta values are finite analogues of multiple zeta values, and the conjecture predicts the dimensions of the spaces they generate at each weight. The source presents it as a principal conjecture in the study of the non-triviality and structure of finite multiple zeta values.