The Clifford–Heisenberg structure conjecture for full COHA of one-vertex quivers

Let $Q$ be a quiver with one vertex and $m$ arrows. For even $m$, let $Cl_c$ denote the infinite Clifford algebra with generators $\xi_n^{+}$ and $\xi_n^{-}$ for $n\in 2\mathbb{Z}+1$, together with a central element $c$, subject to anticommutation relations among the $\xi_n^{+}$, respectively among the $\xi_n^{-}$, and

$$\xi_n^{+}\xi_m^{-}+\xi_m^{-}\xi_n^{+}=\delta_{nm}c.$$

For odd $m$, replace the anticommutation relations in the corresponding formulas by commutation relations to obtain the infinite graded Heisenberg algebra. Full COHA structure conjecture. For even $m$, the full cohomological Hall algebra of $Q$ is isomorphic to $Cl_c$; for odd $m$, it is isomorphic to the infinite graded Heisenberg algebra.

This proposes a uniform Clifford-algebra description in even arrow parity and a Heisenberg-algebra description in odd arrow parity for the full cohomological Hall algebra of the one-vertex quiver. The supplied text gives no evidence that the claim has been proved or disproved.