Andrews–Merca–Guo–Zeng coefficient non-negativity conjecture for averaged Jacobi truncations

Let $(a;q)_\infty=\prod_{j\ge 0}(1-aq^j)$ and $(a,b,c;q)_\infty=(a;q)_\infty(b;q)_\infty(c;q)_\infty$. For positive integers $m,k,R,S$ with $1\le S<R/2$, consider the coefficient of $q^m$ in

$$\frac{(-1)^{k-1}}{(q^S,q^{R-S},q^{R};q^{R})_{\infty}} \sum_{0\le n<k}(-1)^nq^{\binom{n+1}{2}R-nS}(1-q^{(2n+1)S}).$$

Andrews–Merca–Guo–Zeng conjecture. This coefficient is non-negative. This conjecture generalizes non-negativity results for averaged truncations of Euler's pentagonal number theorem and Jacobi's triple product identity. Its resolution is not specified in the source.