Gessel's non-D-finiteness conjecture for the full generating function

Let $G(x,y,t)$ be the full generating function for Gessel walks with step set $\\{\nearrow,\swarrow,\leftarrow,\rightarrow\\}$. Gessel's conjecture. The generating function $G(x,y,t)$ is not D-finite. This is the second conjecture equivalent to the hypergeometric excursion statement in the surrounding discussion. The supplied text gives no resolution status, so it is recorded as open.