A-model conifold value is an eigenvalue of quantum multiplication by c1

Prove that for any Fano manifold X, the A-model conifold value TA,con—defined as the inverse of the convergence radius of the regularized quantum period GX(t)—is an eigenvalue of the linear operator c1(X)⋆|q=1 acting on the even cohomology H^(X).

Background

The authors define the A-model conifold value TA,con via the regularized quantum period and show that, for many classes (e.g., toric Fano manifolds and Fano threefolds admitting convenient weak Landau–Ginzburg mirrors with nonnegative coefficients), TA,con coincides with the mirror conifold value and is an eigenvalue of quantum multiplication by c1(X).

They conjecture that this phenomenon holds for any Fano manifold, elevating TA,con to a canonical spectral feature of c1(X)⋆|q=1.