Norton's replicability conjecture for rational formal q-series

Let $f=q^{-1}+\sum_{n=1}^\infty a_nq^n$ be a formal $q$-series with rational coefficients that is replicable. Norton's conjecture. The series $f$ is either a Hauptmodul for a genus-zero group of moonshine type, or one of $q^{-1}$ and $q^{-1}\pm q$. This conjecture proposes a converse to the result of Conway and Norton that Hauptmoduln with rational $q$-coefficients for moonshine-type groups are replicable; the source gives no resolution.