Involution compatibility for positive-characteristic multiple zeta values

Let $\mathcal{I}$ be the set of indices, let $\mathcal{Z}_{R}$ be the $R$-algebra of multiple zeta values, and let $\iota$ be the non-trivial $R$-algebra involution on

$$\mathcal{Z}_{R}/\zeta_{A}(q-1)\mathcal{Z}_{R}$$

provided by the main theorem. Write $\zeta_A(\mathfrak{s})$ and $\zeta_A^{\dagger}(\mathfrak{s})$ for the ordinary and dagger multiple zeta values, respectively.

Involution compatibility conjecture. For every $\mathfrak{s}\in\mathcal{I}$,

$$\iota\bigl(\zeta_A(\mathfrak{s})\bmod \zeta_A(q-1)\mathcal{Z}_R\bigr)=\zeta_A^{\dagger}(\mathfrak{s})\bmod \zeta_A(q-1)\mathcal{Z}_R.$$

The main theorem establishes the analogous identity for multiple polylogarithms, while this zeta-value statement is explicitly described as still open.