The conjectural string partition function product formula

Let $\mathcal{Z}$ be the string partition function, let $x$ be the string coupling parameter, and let $F_0^{(0)}$ and $F_1^{(0)}$ be the classical genus-zero and genus-one potentials above. Let $p,q,\zeta,y$ be the multiplicative variables, let $D(\ell n,\gamma,j)$ be the integral coefficients defined from the Jacobi-form data, and let $(\ell,n,\gamma,j)>0$ denote the positivity condition used in the source. Let $q_1$ be the base expansion parameter. The string partition function conjecture. The string partition function behaves as

$$\mathcal{Z}=\exp\left(x^{-2}F_0^{(0)}+F_1^{(0)}\right)\left[\prod_{(\ell,n,\gamma,j)>0}(1-p^\ell q^n\zeta^\gamma y^j)^{D(\ell n,\gamma,j)}+O(q_1)\right].$$

This conjecture packages the preceding conjectural Gromov–Witten formulas into an infinite-product expression, up to the omitted $\zeta(1)$ factor mentioned in the source and terms of order $q_1$. The source presents it as the main conjecture and supplies examples corroborating related genus-zero and genus-one formulas, but no general resolution is stated.