Conrad–Edixhoven–Stein conjecture for rational torsion on $J_1(p)$

Let $p\geq 5$ be a prime, and let $X_1(p)$ be the modular curve with Jacobian $J_1(p)$. The rational cuspidal subgroup is the subgroup generated by divisor classes given by differences of $\mathbb{Q}$-rational cusps. Conrad–Edixhoven–Stein conjecture. The $\mathbb{Q}$-rational torsion subgroup of $J_1(p)$ is generated by differences of $\mathbb{Q}$-rational cusps on $X_1(p)$.

This is the prime-level $\Gamma_1(p)$ case of the question relating rational torsion on modular Jacobians to rational cuspidal classes. The source attributes the conjecture to Conrad, Edixhoven, and Stein and does not state whether it has been resolved.