Galkin–Golyshev–Iritani's Gamma conjecture I

Let $X$ be a Fano manifold satisfying Conjecture O. Let $A_X\in H(X)$ be the principal asymptotic class arising from the asymptotic expansion at infinity of the restriction of Givental's big $J$-function to the anti-canonical line. Let $x_1,\dots,x_n$ be the Chern roots of $TX$, and define the Gamma class by

$$\hat{\Gamma}_X=\prod_{i=1}^n\Gamma(1+x_i).$$

Gamma conjecture I. There exists a constant $C\in\mathbb{C}$ such that

$$\hat{\Gamma}_X=CA_X.$$

The conjecture relates Gromov–Witten invariants to the topology of $X$ through the principal asymptotic class and the Gamma class. The source gives no resolution status.