Biran–Cornea identification of the discrete s-dot operads

Let $M$ be the ambient symplectic manifold, and let $\operatorname{Lag}(M)$ and $\operatorname{Fukaya}(M)$ denote the relevant categories of Lagrangian branes and Fukaya-theoretic objects. Let $T^s$ denote the categories introduced by Biran and Cornea. The discrete colored planar operads associated to the $s$-dot constructions of these categories encode their corresponding planar operadic structures.

Biran–Cornea identification conjecture. The categories $T^s$ of Biran and Cornea are the discrete colored planar operads associated to the $s$-dot constructions of $\operatorname{Lag}(M)$ and $\operatorname{Fukaya}(M)$, and the map in the compatibility conjecture recovers the map in their work.

This conjecture relates the geometric and categorical constructions in the paper to the discrete colored planar operads of Biran and Cornea. It is conditional on verifying the analytical details needed to construct the cited results in the monotone setting, and the source gives no resolution.