Bozec–Schiffmann positivity conjecture for absolutely cuspidal polynomials

Let $Q$ be a quiver and let $\mathbf{d}\in\mathbf{N}^{Q_0}$ be a dimension vector. The polynomial $C^{\mathrm{abs}}_{Q,\mathbf{d}}(q)$ is the absolutely cuspidal polynomial associated with $Q$ and $\mathbf{d}$. Bozec–Schiffmann positivity conjecture. For $\mathbf{d}\in\mathbf{N}^{Q_0}$, the polynomial $C^{\mathrm{abs}}_{Q,\mathbf{d}}(q)$ has nonnegative coefficients. This conjecture concerns positivity of the polynomials encoding absolutely cuspidal elements of the constructible Hall algebra. The paper proves it, so the conjecture is no longer open.