Minets' critical CoHA conjecture for zero-dimensional sheaves

Let $X$ be a quasiprojective $3$-Calabi–Yau variety. Let $\operatorname{W}^+(X)$ be the algebra generated by symbols $T_m^+(\lambda)$, with $m\in\mathbb{N}$ and $\lambda\in\operatorname{H}(X,\mathbb{Q})$, subject to the stated multilinearity and commutator relations involving $c_2(X)$, the diagonal class $\Delta_X$, and the symmetric-group relation. Minets' critical CoHA conjecture. There is an isomorphism of algebras

$$\mathcal{H}_X^{\operatorname{crit}}\cong\operatorname{W}^+(X).$$

The conjecture proposes an explicit presentation of the critical CoHA of zero-dimensional sheaves on a quasiprojective $3$-Calabi–Yau variety.