The topological recursion implication for universal equations

Let

denote the universal equation relating higher-genus Gromov–Witten invariants to Hodge integrals, and let the degree-$g$ topological recursion relations proposed by Clader and Janda be the corresponding relations on the moduli space of stable curves. **Topological recursion implication.** The universal equation

is a consequence of the degree-$g$ topological recursion relations proposed in the cited work. This proposed connection relates universal equations for higher-genus Gromov–Witten invariants to topological recursion relations; the source does not establish whether the implication holds.