Main genus-1 mirror-map conjecture for Fano hypersurfaces

Let $M_N^k$ be a degree-$k$ hypersurface in ${\mathbb P}^{N-1}$. Let $F_1^{N,k,A}(t^0,t^1,\ldots,t^{N-2})$ be the generating function of genus-$1$ Gromov–Witten invariants, let $F_{1,\mathrm{vir.}}^{N,k,B}(x^0,x^1,\ldots,x^{N-2})$ be the generating function of genus-$1$ multi-point virtual structure constants, and let $x^p(t^*)$ be the inverse of the mirror map. Main conjecture.

$$F_1^{N,k,A}(t^0,t^1,\ldots,t^{N-2})=F_{1,\mathrm{vir.}}^{N,k,B}(x^0(t^*),x^1(t^*),\ldots,x^{N-2}(t^*)).$$

This proposes the genus-$1$ analogue of the genus-$0$ mirror-map correspondence, relating the A-model elliptic Gromov–Witten theory to the B-model elliptic virtual structure constants. The source presents it as the main conjecture; its general validity is not established there.