Independence-of-chi conjecture for DT4 invariants of irreducible curve classes

Let $X$ be a smooth projective Calabi–Yau $4$-fold, let $\beta\in H_2(X,\mathbb{Z})$ be an irreducible curve class, and let $\gamma_1,\ldots,\gamma_l$ be integral cohomology classes used as insertions. Denote by $\mathop{\rm DT}\nolimits_4(n,\beta\,|\,\gamma_1,\ldots,\gamma_l)$ the DT4 invariant obtained from the moduli space of one-dimensional stable sheaves with Chern character $(0,0,0,\beta,n)$. Independence-of-chi conjecture. For certain choices of orientation in defining them, the invariants

$$\mathop{\rm DT}\nolimits_4(n,\beta\,|\,\gamma_1,\ldots,\gamma_l)$$

are independent of the choice of $n$. This predicts that, for irreducible curve classes, changing the Euler-characteristic parameter does not change the DT4 invariant after compatible orientation choices; the statement is proposed in the appendix and remains open.