then implies that $F_g^{0+}|_{{\bf t}(\psi)=0}$ is [*equal*]{} to the $B$-model genus $g$ pre-potential, expanded near a “large complex structure" point for the mirror of $X$.

The proof of Theorem \[Main Thm\] is given in sections 4 and 5 of the paper. In fact, we formulate and prove a stronger cycle-level comparison for the virtual classes under change of stability parameter from $\infty$ to some $\ke\geq 0+$. The first statement of this kind was established by Marian, Oprea, and Pandharipande in [@MOP] when the target ${W/\!\!/{{\bf G}}}$ is a Grassmannian. Our proof for toric targets is inspired by theirs, and in particular uses crucially a genus-reduction lemma from [@MOP], but requires also several completely new ideas.

As we remark at the end of §5, the proof we give works for other interesting non-compact Calabi-Yau GIT targets. In particular we obtain the following result.

\[local Grass\] Let $X$ be the total space of the canonical bundle over a Grassmannian, viewed as a GIT quotient in the canonical way. Then Conjectures \[main conj intro\] and \[equivalent\] hold for $X$. More generally, the same is true for the total space of the canonical bundle over any type $A$ partial flag manifold.

Aknowledgments
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The 