Norbury–Scott conjecture on stationary Gromov–Witten invariants of the projective line

Let $W_{g,n}^{\mathbb{P}^1}(t_1,\dots,t_n)$ denote the Eynard–Orantin differential forms associated with the stationary Gromov–Witten theory of $\mathbb{P}^1$, and let $F_{g,n}^{\mathbb{P}^1}(t_1,\dots,t_n)$ be the corresponding generating functions. For stable $(g,n)$, write $d_i$ for differentiation with respect to $t_i$. Norbury–Scott conjecture. The stationary Gromov–Witten invariants of $\mathbb{P}^1$ satisfy the Eynard–Orantin recursion; equivalently, for $(g,n)$ in the stable range,

$$W_{g,n}^{\mathbb{P}^1}(t_1,\dots,t_n)=d_1\cdots d_nF_{g,n}^{\mathbb{P}^1}(t_1,\dots,t_n).$$

The conjecture asserts that the generating functions of stationary Gromov–Witten invariants are governed by the spectral-curve recursion, extending the explicitly verified initial cases to all stable $(g,n)$.