Jin–Szenes conjecture for perturbed genus-zero Gromov–Witten invariants

Let $M_N^k$ be the degree-$k$ projective Fano hypersurface considered in the paper, and let $\langle {\cal O}_{h^a}{\cal O}_{h^b}\rangle_0(t^0,t^1,\ldots,t^{N-2})$ denote the perturbed two-point genus-zero Gromov–Witten invariant. Let $w({\cal O}_{h^a}{\cal O}_{h^b})_0$ be the corresponding virtual structure constant, and let $x^p(t^*)=x^p(t^0,t^1,\ldots,t^{N-2})$ be the coordinate transformation specified by the inverse relation referred to in the source. Jin–Szenes conjecture.

$$\langle {\cal O}_{h^a}{\cal O}_{h^b}\rangle_0(t^0,t^1,\ldots,t^{N-2})=w({\cal O}_{h^a}{\cal O}_{h^b})_0\bigl(x^0(t^*),x^1(t^*),\ldots,x^{N-2}(t^*)\bigr).$$

This is the genus-zero Gromov–Witten/virtual-structure-constant correspondence proposed in the cited work. The supplied source does not indicate whether the conjecture has been proved or disproved.