Automaticity of number walls

Let $k$ and $q$ be positive integers, and let a sequence over $\mathcal{F}_q$ be $k$-automatic. Its number wall is the associated two-dimensional array of Hankel determinants. Automaticity of number walls. The number wall of a $k$-automatic sequence over $\mathcal{F}_q$ is itself a two-dimensional $k$-automatic sequence.

The paper reports significant empirical evidence from several examples, but the morphisms used to generate the number walls have not been validated because the corresponding windows have unbounded size. The conjecture therefore remains open.