The modular identity predicted by mirror symmetry for Schoen's Calabi–Yau threefold

Let $U=\exp(2\pi i t)$ and let $\gamma=(1,1,1,1,1,1,1,-1)$. Let $A^{res}(t)$ be the restricted A-model factor, let $B(t)=\sum_{n\geq0}b_nU^n$ be the B-model factor, and let $\Theta_{E_8}(3t,t\gamma)$ be the corresponding $E_8$ theta function.

Modular mirror-symmetry identity.

$$A^{res}(t)\equiv B(t),$$

equivalently,

$$\sum_{n\geq0}b_nU^n=\Theta_{E_8}(3t,t\gamma)\prod_{n\geq1}(1-U^{3n})^{-12}.$$

This identity is extracted from the first-order asymptotic expansions of the two prepotentials and is presented as a consequence predicted by the mirror conjecture. The paper does not independently prove the mirror conjecture or this identity.