Pi-formality conjecture for bordered Floer algebras

Let $\mathcal{Z}$ be an arc diagram and let $i$ be an integer. Pi-formality conjecture. The algebra $\mathcal{A}(\mathcal{Z},i)$ is $\pi$-formal, in the sense of Definition~. This assertion would provide the technical formality condition needed for the localization and Hochschild-homology constructions in the paper. The source gives no evidence of resolution.