The edge-map conjecture for integral modular forms on $\mathcal{M}_0(n)$

For every positive integer $n$, let $\operatorname{TMF}_0(n)$ denote the associated spectrum of topological modular forms and let $\operatorname{MF}_0(n)_0$ denote the degree-zero modular forms for the moduli problem with level-$\Gamma_0(n)$ structure. The natural edge map

$$\pi_0\operatorname{TMF}_0(n)\to \operatorname{MF}_0(n)_0$$

is defined by the descent spectral sequence. Edge-map conjecture. For every positive integer $n$, this natural edge map is an isomorphism. Such an isomorphism would allow the relevant argument to proceed without inverting $\gcd(6,\phi(n))$; the source introduces it as a conjectural way to remove that localisation hypothesis, and gives no resolution.