  In analogy with the Gopakumar-Vafa (GV) conjecture on Calabi-Yau (CY)
3-folds, Klemm and Pandharipande defined GV type invariants on Calabi-Yau
4-folds using Gromov-Witten theory and conjectured their integrality. In a
joint work with Maulik and Toda, the author conjectured their genus zero
invariants are $\mathrm{DT_4}$ invariants of one dimensional stable sheaves. In
this paper, we study this conjecture on the total space of canonical bundle of
a Fano 3-fold $Y$, which reduces to a relation between twisted GW and
$\mathrm{DT_3}$ invariants on $Y$. Examples are computed for both compact and
non-compact Fano 3-folds to support our conjecture.
