The induced involution conjecture for v-adic multiple zeta values

Let $v\in A$ be an irreducible monic polynomial, let $\mathcal{Z}_{v,R}$ be the $R$-module spanned by all $v$-adic multiple zeta values, and let $\iota$ be the involution on $\mathcal{Z}_{R}/\zeta_A(q-1)\mathcal{Z}_{R}$. Via the conjectural identification of this quotient with $\mathcal{Z}_{v,R}$, the map $\iota$ is induced on the $v$-adic algebra.

Induced involution conjecture. The map $\iota$ induces an $R$-algebra involution on $\mathcal{Z}_{v,R}$.

This is presented as a consequence of the conjectured isomorphism between the quotient of ordinary multiple zeta values and the algebra of $v$-adic multiple zeta values. No resolution is supplied.