Capparelli–Meurman–Primc–Primc odd-modulus conjecture

Let $k_0,\ldots,k_n$ be non-negative integers, let $E_1$ be the set of parts, and let $\mathcal{Q}^{k_0,\ldots,k_n}_{\mathds{1}}$ be the partitions into parts in $E_1$ whose frequencies, augmented by fictitious occurrences with $f_{(-1)_{2n-1-2i}}=k_i$ for $i\in\{0,\ldots,n-1\}$ and $f_{(0)_0}=k_n$, satisfy

$$f_{e_0}+\cdots+f_{e_{2n-1}}\leq k_0+\cdots+k_n$$

for every path $(e_0,\ldots,e_{2n-1})$ of $E_{-1}$. Write $k=k_0+\cdots+k_n$. CMPP odd conjecture. One has

$$\sum_{\pi\in\mathcal{Q}^{k_0,\ldots,k_n}_{\mathds{1}}}q^{|\pi|}=\frac{\prod_{a\in \{2n+2k+1\}^n;b\in \Delta(k_1+1,\ldots,k_n+1);\ j=a,b,2n+2k+1-b}(q^j;q^{2n+2k+1})_\infty}{(q;q)_\infty^n}.$$

This is the odd-modulus analogue attributed in the paper to Capparelli, Meurman, Primc and Primc; the case $n=1$ recovers the Andrews–Gordon identities. The supplied text gives no resolution status.