  Using the interpretation of certain generalised Donaldson-Thomas invariants,
including stable pairs curve counts, as the monodromy of a flat connection on a
formal principal bundle, we show that the conjectural Gopakumar-Vafa
contributions of all genera to the Gromov-Witten partition function appear in
the asymptotics of the corresponding flat sections. The Fourier-Laplace
integrals used to produce flat sections lead naturally to the GW/DT change of
variable -q = e^{i u}.
