Sойбельman's conjecture on the full COHA of the quiver $A_1$

Let $A_1$ be the one-vertex quiver, and let $\operatorname{COHA}(A_1)$ denote its full cohomological Hall algebra. Let $Cl_c$ be the infinite Clifford algebra generated by $\phi_n^+$ and $\phi_n^-$ for $n\in\mathbb{Z}$, together with a central element $c$, with the standard anticommuting relations among the $\phi_n^+$ and among the $\phi_n^-$.

Sойбельman's conjecture. The full COHA for the quiver $A_1$ is isomorphic to $Cl_c$, with mixed generators satisfying

$$\phi_n^+\phi_m^-+\phi_m^-\phi_n^+=\delta_{n,m}c.$$

This identifies the full COHA with an infinite Clifford algebra and extends the finite Clifford-algebra representation constructed in the paper. The source attributes the conjecture to Soibelman; its resolution is not specified here.