  We study the equivariantly perturbed mirror Landau-Ginzburg model of the
projective line. We show that the Eynard-Orantin recursion on this model
encodes all genus all descendants equivariant Gromov-Witten invariants of the
projective line. The non-equivariant limit of this result is the Norbury-Scott
conjecture, while by taking large radius limit we recover the Bouchard-Marino
conjecture on simple Hurwitz numbers.
