Algebraic formality conjecture for Poincaré duality algebras

Let $V$ be a differential Poincaré duality algebra with \H^0(V)=\operatorname{Span}\{1\} and \H^1(V)=0, and suppose that $V$ is formal as a differential graded algebra. A Poincaré duality model of $V$ is a model $\Model(V)$ equipped with the induced canonical construction $\dIBL^\MC(\CycC(\Model(V)))$. Algebraic formality conjecture. Any Poincaré duality model $\Model(V)$ of $V$ is $\IBLInfty$-formal, namely $\dIBL^\MC(\CycC(\Model(V)))$ and $\dIBL^\MC(\CycC(\H(V)))$ are weakly $\IBLInfty$-homotopy equivalent. This extends the known special case supplied by the preceding uniqueness proposition; the general implication from DGA-formality remains open.