The equivalence conjecture for the classical BCOV interactions $I$ and $\widehat I$

On $\mathbb{C}^3$, let $I$ be the previously defined classical BCOV interaction on the fields $\PV^{*,*}(\mathbb{C}^3)[[t]][2]$, and let $\widehat I$ be the classical interaction obtained by restricting the unique quantum open-closed BCOV theory to its closed-string sector. Both satisfy the classical master equation. Interaction-equivalence conjecture. The functionals $I$ and $\widehat I$ are equivalent solutions to the classical master equation. If true, this would identify the interaction recalled from earlier work with the interaction produced by the quantized open-closed theory; the paper states the equivalence as a conjecture.