Representation-theoretic positivity conjecture for absolutely cuspidal curve polynomials

Let $g$ and $r$ be integers, let $C_{g,r}^{\mathrm{abs}}$ be the absolutely cuspidal polynomial for curves of genus $g$ and rank $r$, let $GSp(2g,\overline{\mathbb{Q}_l})$ be the group of symplectic similitudes, and let $ch$ denote the character map. Let $\tau$ be the involution on the relevant representation ring sending each $\eta_i$ to $-\eta_i$. Absolutely cuspidal representation conjecture. For any $g,r$ there exists a non-virtual $GSp(2g,\overline{\mathbb{Q}_l})$-representation $\mathbb{C}_{g,r}^{\mathrm{abs}}$ such that

$$C_{g,r}^{\mathrm{abs}}=\tau\bigl(ch(\mathbb{C}_{g,r}^{\mathrm{abs}})\bigr).$$

This is a representation-theoretic positivity conjecture for the absolutely cuspidal curve polynomials; the supplied text does not state whether it has been resolved.