Almost-complex-structure invariance conjecture for stringy category elements

Let $J_1$ and $J_2$ be choices of almost complex structure, and let ${\Bbb R}_1$ and ${\Bbb R}_2$ be the corresponding elements of the completed exterior-algebra construction. Let $G(\Lambda^*({\cal A}))$ act as described in the source. Almost-complex-structure invariance conjecture. The elements $\exp({\Bbb R}_1)$ and $\exp({\Bbb R}_2)$ are $G(\Lambda^*({\cal A}))$-equivalent with respect to this action. The conjecture asserts independence, up to the indicated equivalence, of the almost complex structure used to construct the stringy-category data. The supplied text says that proving it requires a detailed understanding of moduli spaces of open holomorphic curves, but gives no resolution.