Acyclicity conjecture for the involutive quotient bialgebra

Let $X$ be a set with an involutive solution $csigma$ of the Yang–Baxter equation, satisfying $csigma(x,y)^2=(x,y)$. Let $B$ be the differential bialgebra associated to this solution, and let

$$Invo=\langle e_xe_y+e_ze_t:(x,y)\in X,\ \sigma(x,y)=(z,t)\rangle$$

be the two-sided differential Hopf ideal generated by these elements. The quotient $B/Invo$ is a differential graded bialgebra. Acyclicity conjecture. $B/Invo$ is acyclic in positive degrees. This predicts that the involutive quotient has no positive-degree homology, strengthening the established differential Hopf ideal and bialgebra properties; the supplied text gives no resolution status.