Gross–Hacking–Keel Frobenius structure conjecture

Let $S$ be the dual intersection complex of $D$, let $B$ be the cone over $S$, and let $B_0=B\setminus\{0\}$. The integer points $q\in B(\mathbb Z)$ index prime fundamental classes $\vartheta_q\in QH^0_{\log}(X,D)$. For $s\geq2$, define the symmetric multilinear function by logarithmic Gromov–Witten invariants, and set $\langle\vartheta_0\rangle=1$, $\langle\vartheta_q\rangle=0$ for $q\in B_0(\mathbb Z)$. Frobenius structure conjecture. There is a unique associative product $*$ on $QH^0_{\log}(X,D)$ such that

$$\langle\vartheta_{q_1},\ldots,\vartheta_{q_s}\rangle=\langle\vartheta_{q_1}*\cdots*\vartheta_{q_s}\rangle.$$

This conjecture concerns the existence and uniqueness of the algebra structure encoded by punctured logarithmic Gromov–Witten invariants. It was proved by Gross and Siebert by explicitly defining all structure constants in terms of punctured Gromov–Witten invariants.