Garvan–Jennings-Shaffer nonnegativity conjecture for M_C1 and M_C5

Let $M_{C1}(m,n)$ and $M_{C5}(m,n)$ be the coefficients defined by the corresponding two-variable generating functions in the source, with $m\in\mathbb{Z}$ and $n\in\mathbb{N}$, where $\mathbb{N}$ denotes the positive integers. Garvan–Jennings-Shaffer nonnegativity conjecture. For every $m\in\mathbb{Z}$ and $n\in\mathbb{N}$, both $M_{C1}(m,n)$ and $M_{C5}(m,n)$ are nonnegative. The paper's title states that this conjecture is proved, so its status is solved; the claim concerns the nonnegativity of coefficients associated with the rank-like functions $M_{C1}$ and $M_{C5}$.