  The open Gromov--Witten (OGW) potential is a function from the set of weak
bounding cochains on a closed Lagrangian in a closed symplectic manifold to the
Novikov ring. Existing definitions of the OGW potential assume that the ground
field of the Novikov ring is either $\mathbb{R}$ or $\mathbb{C}$. In this
paper, we give an alternate definition of the OGW potential in the pearly model
for Lagrangian Floer theory which yields an invariant valued in the Novikov
ring over any field of characteristic zero. We work under simplifying
regularity hypotheses which are satisfied, for instance, by any monotone
Lagrangian. Our OGW potential is defined in terms of an appropriate weakening
of a strictly cyclic pairing on a curved $A_{\infty}$-algebra, which can be
thought of as a version of a proper Calabi--Yau structure. Such a structure is
obtained by constructing a version of the cyclic open-closed map on the pearly
Lagrangian Floer cochain complex. We also explain an analogue of our
construction in de Rham cohomology, and show that it recovers the OGW potential
constructed by Solomon and Tukachinsky.
