The characteristic-two spanning conjecture for v-adic multiple zeta relations

Let $K=\mathbb{F}_q(t)$, and let $W(K)$ be the product over monic primes $v$ of the vector spaces $W_v(K)$ spanned over the relevant coefficient field by the $v$-adic multiple zeta values $\zeta_v(\mathbf{s})$ at integer tuples. Characteristic-two spanning conjecture. If $\operatorname{char}(\mathbb{F}_q)=2$, the linear relations over $\mathbb{F}_q$ in $W(K)$ are spanned by the relations in Theorem 2 and by trivial zeros. The conjecture proposes a complete description of the linear relations in characteristic two, based on the relations proved earlier and computational evidence.