The logarithmic double ramification cycle tautologicality conjecture

Let $\overline{\mathcal{M}}_{g,n}$ be the moduli space of stable pointed curves, let $\partial\overline{\mathcal{M}}_{g,n}$ be its boundary, and write

$$\log R^*(\overline{\mathcal{M}}_{g,n},\partial\overline{\mathcal{M}}_{g,n}) :=\left\langle R^*(\overline{\mathcal{M}}_{g,n}),\varinjlim\mathsf{PP}(\Sigma'_{\overline{\mathcal{M}}_{g,n}})\right\rangle \subset\log\mathsf{CH}(\overline{\mathcal{M}}_{g,n},\partial\overline{\mathcal{M}}_{g,n}).$$

Logarithmic double ramification tautologicality conjecture. The logarithmic double ramification cycle belongs to

$$\log R^*(\overline{\mathcal{M}}_{g,n},\partial\overline{\mathcal{M}}_{g,n}).$$

This is a logarithmic refinement of the double ramification cycle with improved functorial properties. The source attributes the statement to a conjecture of Möller, Pandharipande and Schmitt, while the cited work of Ranganathan, Holmes–Schmitt, and Holmes–Molcho–Pandharipande–Pixton–Schmitt is presented as proving it.