Generating-series correspondence conjecture for lambda-class invariants with point insertions

Let $C$ be a curve class, let $g_0$ be fixed, and define the generating series

$$\mathcal{R}_{g_0,C}=\sum_{g\geqslant g_0}\langle \lambda_{g-g_0};\mathrm{pt}^{g_0}\rangle_{g,C}u^{2g-2}.$$

Let $R_{g_0,C}(q)$ denote the corresponding refined tropical generating series, and set $q=e^{iu}$. Generating-series correspondence conjecture. Through the change of variable $q=e^{iu}$, one has

$$\mathcal{R}_{g_0,C}=(-1)^{g_0-1}R_{g_0,C}(q).$$

This is proposed as a generalization to abelian surfaces of a correspondence result relating refined tropical invariants to Gromov–Witten invariants with lambda-class insertions. The source notes that the identity is known for primitive curve classes and for arbitrary curve classes when $g_0=2$.