Bachmann's double stuffle completeness conjecture for bi-brackets

Let bi-brackets be the $q$-multiple zeta values defined in the paper, equipped with their stuffle and dual stuffle products and the duality relation. Bachmann's double stuffle conjecture. The resulting double stuffle (that is, stuffle and dual stuffle) relations exhaust all the relations between the bi-brackets. Equivalently, the stuffle relations and the duality exhaust all the relations between the bi-brackets. This conjecture asserts that these explicitly constructed algebraic relations give a complete description of the relations among bi-brackets; the source provides no resolution of the claim.