Yoo's conjecture on the rational cuspidal divisor class group

Let $N$ be a positive integer. Let $\mathscr{C}_N(\mathbf{Q})$ be the rational cuspidal subgroup of $J_0(N)$, and let $\mathscr{C}(N)$ be the rational cuspidal divisor class group of $X_0(N)$. Yoo's conjecture. For every positive integer $N$,

$$\mathscr{C}_N(\mathbf{Q})=\mathscr{C}(N).$$

The conjecture is presented as a problem motivated by the explicit but incompletely understood nature of the cuspidal subgroup and its rational part; no general resolution is given here.