  The Fano classification program proposed by
Coates-Corti-Galkin-Golyshev-Kasprzyk is based on the mirror symmetry
prediction that the regularized quantum period of a Fano should be equivalent
to the classical period of its mirror Landau-Ginzburg potential. We prove that
this mirror equivalence follows from versions of the Frobenius structure
conjecture of Gross-Hacking-Keel. We also find that the regularized quantum
period, which is defined in terms of descendant Gromov-Witten numbers, is in
fact given by certain naive curve counts.
