Integrality and symmetry conjecture for higher-genus BPS invariants

For a symplectic log Calabi–Yau fourfold $(X,D)$, let $A\in H_2(X,\mathbb Z)$ and $g\geq 1$. Define

$$F_A(q)=\frac{\sin(h/2)}{h/2}\sum_{\substack{B\in H_2(X,\mathbb Z)\\ dB=A,\ d>0}}(-1)^{s_B-1}\mu(d)d^{2g-2}\sum_{g\geq 0}N_{g,B}h^{2g},$$

where $\mu$ is the Möbius function, $q=\operatorname{e}^{\mathrm{i}h/2}$, $s_B$ is the maximal tangency order associated with $B$, and $N_{0,A}=N_A$. Integrality and symmetry conjecture. The function $F_A$ is a well-defined rational function of $q$ invariant under $q\to q^{-1}$; furthermore, it is a Laurent polynomial in $q$ with integer coefficients. This is a higher-genus BPS integrality prediction for symplectic log Calabi–Yau fourfolds; the supplied source identifies it as a conjecture and attributes it to B2, but provides no resolution evidence.