The half-integrality conjecture for resolved-conifold coefficients

Let $\Psi^{(a)}_{0,1}(t;x)$ be the resolved-conifold open-string one-point function, and set $Q=-e^{-t}$. Half-integrality conjecture. There are half-integers $e^{(a)}_{k,m}$ such that

$$x\frac{\partial}{\partial x}\Psi^{(a)}_{0,1}(t;x)=\sum_{m,n\geq 1}m e^{(a)}_{k,m}\log(1-Q^k x^m).$$

The claimed arithmetic property concerns the coefficients in the logarithmic expansion of the open-string amplitude. The source gives no resolution of this claim or explanation of the apparent index mismatch between the summation variables and $e^{(a)}_{k,m}$.