The Chow tautological-generation conjecture for moduli spaces of stable curves

Let $A^k(\overline{\mathcal{M}}_{g,n})_{\mathbb{Q}}$ be the codimension-$k$ Chow group with rational coefficients, and let the tautological cycles be the cycles generated by the tautological ring.

Chow tautological-generation conjecture. The Chow group

$$A^k(\overline{\mathcal{M}}_{g,n})_{\mathbb{Q}}$$

is generated by tautological cycles for $k\leq10$.

This is motivated by the absence of known non-tautological cycles below codimension 11 and by results on holomorphic forms and Chow groups. The conjecture is explicitly described as optimistic and remains open.