  We regard the work of Maulik and Toda, proposing a sheaf-theoretic approach
to Gopakumar-Vafa invariants, as defining a BPS structure, that is, a
collection of BPS invariants together with a central charge. Assuming their
conjectures, we show that a canonical flat section of the flat connection
corresponding to this BPS structure, at the level of formal power series,
reproduces the Gromov-Witten partition function for all genera, up to some
error terms in genus 0 and 1. This generalises a result of Bridgeland and Iwaki
for the contribution from genus 0 Gopakumar-Vafa invariants.
