Bijection conjecture for models of two-point configuration spaces

Let $A$ be a $1$-connected Poincaré duality CDGA of formal dimension $n$ odd. For each $\xi\in (A\otimes A)^{2n-2}$, let $C(\xi)$ be the associated CDGA, and let

$$\psi\colon H^{2n-2}(A\otimes A)/([\Delta])\longrightarrow \{C(\xi)\colon \xi\in (A\otimes A)^{2n-2}\}/\simeq_{A\otimes A}$$

be the natural surjection from the preceding corollary, where the codomain consists of equivalence classes under $A\otimes A$ of the CDGAs $C(\xi)$. Bijection conjecture. The map $\psi$ is a bijection. This conjecture asserts that the cohomology class of $\xi$ modulo the diagonal class $[\Delta]$ completely determines the relative equivalence class of the corresponding CDGA model. Its resolution would classify these models and clarify the rational homotopy types of configuration spaces of two points in simply connected closed manifolds.