Faber–Pandharipande Gorenstein conjecture for the compactified tautological ring

Let $\overline{M}_{g,n}$ be the moduli space of stable curves and let $R^*(\overline{M}_{g,n})$ denote its tautological ring.

Faber–Pandharipande's compactified Gorenstein conjecture. The ring $R^*(\overline{M}_{g,n})$ is Gorenstein with socle in degree

$$3g-3+n.$$

This is part of the proposed Gorenstein picture for tautological rings; the source states it as a conjecture without supplying evidence of resolution.