Strong tau-sequence conjecture for antimorphic-digraph R-systems

Let $G=(V,E)$ be an antimorphic digraph with antimorphism $\eta$, and let $Y(t)$ be a sequence indexed by the vertices and time. A strong $\tau$-sequence is one that realizes the $R$-system through the stated substitution.

Antimorphic-digraph tau-sequence conjecture. The $R$-systems associated with antimorphic digraphs possess strong $\tau$-sequences $Y(t)$ with the substitution

$$R_v(t+1)=\frac{Y_{\eta^t(v)}(t-1)}{Y_{\eta^t(v)}(t)}.$$

The claim extends the explicitly exhibited examples of antimorphic digraphs in the surrounding discussion. No proof or resolution is supplied in the given text.