Qin's punctual-partition generating-function conjecture

Let $r\ge2$, and let $P_r(n)$ and $\widetilde P_r(n)$ denote the two partition-counting functions defined earlier in the paper. Qin's punctual-partition generating-function conjecture. One has

$$\frac{\sum_{n=0}^{+\infty}\widetilde P_r(n)q^n}{\sum_{n=0}^{+\infty}P_r(n)q^n}=\frac{1}{(1-q)^{r-2}}.$$

The preceding theorem gives the Euler-number generating series for the relevant moduli spaces in terms of this quotient, so the conjecture would provide an explicit simplification; its status is not resolved in the supplied text.