Todd's dimension conjecture for positive-characteristic multiple zeta values

Let $q$ be the cardinality of the constant field, let $k$ be the coefficient field, and for each positive integer $w$ let $\mathcal{Z}_w$ be the $k$-vector space spanned by all multiple zeta values of weight $w$. Define

$$d'_w=\begin{cases}2^{w-1}&\text{if }1\leq w<q,\\2^{q-1}-1&\text{if }w=q,\sum_{i=1}^{q}d'_{w-i}&\text{if }w>q.\end{cases}$$

Todd's dimension conjecture. For every positive integer $w$,

$$\dim_k\mathcal{Z}_w=d'_w.$$

This is the positive-characteristic analogue of Zagier's dimension conjecture, motivated by numerical computation. The source presents it as open, while the paper proves a related basis conjecture and derives the dimension formula.