  Let $X$ be a Calabi-Yau 4-fold and $D$ a smooth divisor on it. We consider
tautological complex associated with $L=\mathcal{O}_X(D)$ on the moduli space
of Le Potier stable pairs and define its counting invariant by integrating the
Euler class against the virtual class. We conjecture a formula for their
generating series expressed using genus zero Gopakumar-Vafa invariants of $D$
and genus one Gopakumar-Vafa type invariants of $X$, which we verify in several
examples. When $X$ is the local resolved conifold, our conjecture reproduces a
conjectural formula of Cao-Kool-Monavari in the PT chamber. In the JS chamber,
we completely determine the invariants and confirm one of our previous
conjectures.
