The Kontsevich–Seidel folklore conjecture on quantum eigenvalues and mirror critical values

Let $X$ be the A-side space, let $X^\vee$ be its mirror B-side space, let the mirror Landau–Ginzburg superpotential on $X^\vee$ have critical values, and let quantum multiplication by the first Chern class on $X$ be the corresponding quantum operator.

Kontsevich–Seidel folklore conjecture. The critical values of the mirror Landau–Ginzburg superpotential on $X^\vee$ are the eigenvalues of quantum multiplication by the first Chern class on $X$.

This folklore conjecture is presented as additional numerical evidence for the proposed SYZ statement and is attributed in the source to Kontsevich and Seidel. No resolution is supplied, so its status remains open.