Boundary generating-function non-D-finiteness conjecture for selected quarter-plane models

For a small-step quarter-plane model with stepset $S$, let $Q(x,y;t)$ be its generating function, and let $Q(0,1;t)$ and $Q(1,0;t)$ denote its two boundary specializations. The models referred to in Tables~ and ~ are the models for which the numerical boundary-exponent computations described in the surrounding text suggest the stated behavior. Boundary non-D-finiteness conjecture. The models in Tables~ and ~ have the property that at least one of $Q(0,1;t)$ and $Q(1,0;t)$ is not D-finite. The claim is motivated by numerical estimates of coefficient exponents, but the supplied source does not provide a resolution.