The cohomological Hall algebra conditional surjectivity conjecture

Let $X$ be a smooth surface, let $Z_1$ and $Z_2$ be curves with $Z=Z_1\cup Z_2$, and let $\mathbf{HA}^T_{X,Z}$ denote the corresponding $T$-equivariant cohomological Hall algebra. Assume that both $Z_1$ and $Z_2\setminus(Z_1\cap Z_2)$ are cohomologically pure. The cohomological Hall algebra conditional surjectivity conjecture. The amalgamation map

$$\mathbf{HA}^T_{X,Z_2}\widehat{\otimes}_{\mathbf{HA}^T_{X,Z_1\cap Z_2}}\mathbf{HA}^T_{X,Z_1}\longrightarrow\mathbf{HA}^T_{X,Z}$$

and the induced map from the kernel of the tensor-product map to the kernel of the Hall multiplication map are topologically surjective. The conjecture addresses the failure of ordinary topological surjectivity in general and predicts density under cohomological-purity assumptions. The supplied text gives no resolution evidence, so the claim is recorded as open.